The DOI matches its Crossref record; 243 of the 243 references it cites were found in a registry or an index; 22 of the 151 sources its claims cite were checked for support.
Linear optical quantum computing with photonic qubits
Open accessAbstract
Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.
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TL;DR
This review explains how linear optics, single-photon sources, and photon counting can in principle enable scalable quantum computing via the Knill-Laflamme-Milburn protocol and its successors. It surveys probabilistic optical gates, cluster-state and circuit-based improvements, realistic component errors, and error-correction thresholds for linear optical quantum computing.
Key findings
- The KLM protocol showed that scalable quantum computing is possible with single photons, linear optical elements, and projective measurements, but its original resource overhead is prohibitively large.
- Probabilistic optical gates have been demonstrated and improved: the KLM nonlinear sign gate succeeds with probability \(p_{\rm NS}=1/4\), Ralph et al.’s version with \(p'_{\rm NS}=(3-\sqrt{2})/7\), Knill’s CZ gate with \(2/27\), and several CNOT experiments with success probabilities \(1/4\), \(1/9\), and \(1/4\), with reported errors or fidelities such as approximately 21% error, approximately 84% fidelity, and 81% fidelity for generated entanglement.
- Cluster-state and fusion-based protocols reduce resource requirements: type-I and type-II fusion gates succeed with probability \(p=1/2\), and circuit-based parity encoding can implement universal gates with >99% success probability using about \(10^2\) operations.
- Fault-tolerance studies give thresholds such as detector loss up to 50% correctable in cluster states, combined detector/source/memory efficiencies \(\eta>55\%\) in a circuit-based model, and scalable cluster-state computing for loss probability \(\gamma<3\times10^{-3}\) and depolarising probability \(\epsilon<10^{-4}\) with a 23-qubit code.
Methods
- Review article synthesizing theoretical and experimental work on linear optical quantum computing, with emphasis on the KLM protocol, its improvements, and error correction.
- No new primary data are reported; the paper reviews and compares protocols and cites experimental demonstrations of two-qubit gates, single-photon sources, detectors, and memories.
- Main analysis covers linear optical elements, N-port interferometers, qubit encodings, probabilistic gates, teleportation-based scaling, cluster-state and circuit-based architectures, realistic component errors, and fault-tolerant thresholds.
Limitations
- Stated: the review restricts discussion to single-photon implementations of quantum information processors and excludes continuous-variable optical quantum information processing; squeezing is excluded as a resource except for generating single photons.
- Stated: practical LOQC faces probabilistic gates, photon loss, detector inefficiency, imperfect single-photon sources, mode mismatching, lossy optical switches, and the need for quantum memories.
- Evident: as a review, it does not present new experimental results, and several fault-tolerance thresholds rely on simplified noise models whose parameters are not all directly measurable quantities.
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Claims the paper makes
22 of 151 cited sources checked · 8 supported · 1 flagged · accuracy not yet measured
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“However, in this representation the single-qubit operations cannot be implemented deterministically with linear optical elements, since these transformations do not preserve the photon number (Paris 2000).”
§ Linear optical quantum computing > C. Qubits in linear optics
What the sources say
- Partly supportedcites Paris 2000 sourceExperimental — accuracy not yet measured
The Introduction identifies vacuum and one-photon states as an optical qubit, and the Conclusions describe preparing their superpositions with linear optical elements only conditionally (no page numbers provided). The paper does not state that deterministic single-qubit operations are impossible with linear optics or give photon-number nonconservation as the reason; preparation of a state is also not the same as an operation on an arbitrary qubit. (LLM, conf=0.78)
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Every source the paper cites for this claim was checked and supports it.
In the paper
“The CNOT truth table for this experiment, based on four-fold coincidences, is shown in Fig. 17.This shows the operation of the CNOT gate.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Supportedcites Gasparoni et al. (2004) source
Figure 3’s caption (p. 4) says it shows four-fold coincidences for all 16 input–output combinations and that the results demonstrate the CNOT operation: the target is unchanged for control 0 and flipped for control 1. The experimental discussion (p. 3) likewise says those count rates verify that the gate works in this basis. (LLM, conf=0.94)
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The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“The last experiment we consider in some detail is the realization of an optical CNOT by Gasparoni, Pan, Walther, Rudolph, and Zeilinger (2004).The experiment is based on the four-photon logic gate by Pittman et al. (2001) depicted in Fig. 11.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Partly supportedcites Gasparoni, Pan, Walther, Rudolph, and Zeilinger (2004) sourceExperimental — accuracy not yet measured
The paper says its four-photon CNOT scheme was first proposed in reference [15] (p. 1), which the reference list identifies as a Pittman, Jacobs and Franson paper from 2002 (p. 4). This supports the connection to a Pittman-associated scheme, but not the claim that it was based on a Pittman et al. (2001) gate. (LLM, conf=0.88)
- Supportedcites Pittman et al. (2001) source
Section II describes Pittman et al.’s probabilistic CNOT gate using a four-photon entangled state. The citation identifies that gate as the one referenced in the citing sentence. (LLM, conf=0.90)
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The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Indeed, numerical evidence strongly suggests an upper bound of one third for infinite feed-forward without entangled ancillæ (Scheel et al. 2005).”
§ Linear optical quantum computing > B. Parity gates and entangled ancillæ
What the sources say
- Could not verifycites Scheel et al. 2005 sourceExperimental — accuracy not yet measured
The Conclusions and Discussion state that the paper is limited to single-shot gates without conditional feed-forward. The Introduction reports a 1/4 bound without feed-forward, but neither passage addresses numerical evidence for a one-third bound with infinite feed-forward. Searches for that bound and for repeated feed-forward attempts found no supporting passage. (LLM, conf=0.76)
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The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“can be implemented with probability 1/N 2 [see also Scheel and Audenaert (2005)].”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Partly supportedcites Scheel and Lütkenhaus (2004) sourceExperimental — accuracy not yet measured
The Introduction and Special cases section report that the ordinary nonlinear sign-shift gate can be implemented with success probability 1/4, matching 1/N² for the two-photon case. The Conclusion and discussion section says that scaling for generalized nonlinear sign-shift gates was left for future investigation; this paper does not establish the claimed 1/N² probability for general N. (LLM, conf=0.86)
- Partly supportedcites Eisert (2005) sourceExperimental — accuracy not yet measured
The paper’s non-linear sign-shift discussion (section labeled Abstract; page unavailable) establishes an achievable optimal probability of 1/4 for N=2. For the three-photon gate, it gives only an upper bound of 1/9. These cases do not establish that the NS_N gate can be implemented with probability 1/N² for arbitrary N. (LLM, conf=0.88)
- Supportedcites Scheel and Audenaert (2005) source
Section III, Eq. (15), gives a success probability of 1/N² for the generalized nonlinear sign-shift gate. Section III.B, Eq. (56), states that a beam-splitter network can implement it with that probability, using an N-dimensional ancilla with photon numbers 0 through N−1. (LLM, conf=0.92)
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The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“The second experiment we consider is the CNOT gate by O'Brien, Pryde, White, Ralph, and Branning, depicted in Fig. 14 (O 'Brien et al. 2003), which is an implementation of the gate proposed by Ralph et al. (2002a).”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not checked — no full text of the sourcecites O'Brien et al. 2003 source
- Partly supportedcites Ralph et al. (2002a) sourceExperimental — accuracy not yet measured
Section IV (p. 4) proposes a conditional linear-optics CNOT gate, supporting the attribution of a gate proposal to Ralph et al. Our copy does not identify O’Brien et al.’s 2003 experiment or establish that it implemented this particular gate. (LLM, conf=0.82)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesEvery source the paper cites for this claim was checked and supports it.
In the paper
“no amount of linear optics and bucket detection can lead to perfect, albeit inefficient, singlephoton resolution (Kok 2003).”
§ Linear optical quantum computing > A. Photon detectors
What the sources say
- Supportedcites Kok 2003 source
The paper states that a single-photon-resolution device cannot be built from linear optics and ordinary non-photon-number-discriminating detectors, even when failures are unambiguously signalled. Its proof specifies a finite number of optical modes, which is consistent with the claim’s reference to an inefficient but otherwise perfect device. Our copy provides no page number for these passages. (LLM, conf=0.91)
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The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Using the seven qubit CSS quantum code, the photon loss ǫ in the KLM scheme is allowed to be as large as 1.78% ≤ ǫ ≤ 11.5%, depending on the construction of the entangling gates (Silva et al. 2005).”
§ Linear optical quantum computing > A. Correcting for photon loss
What the sources say
- Partly supportedcites Silva et al. 2005 sourceExperimental — accuracy not yet measured
The Abstract gives a 1.78%–11.5% range for the gate-error threshold using the seven-qubit CSS code, depending on entangling-gate construction. But the Conclusions (page not specified) define ǫ as the probability of an erasure caused by photon loss or teleportation failure—not photon loss alone. The claim assigns the reported range to the wrong quantity. (LLM, conf=0.88)
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The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Scheel (2005) showed that there is a lower bound on the absorption amplitude in physical beam splitters.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
What the sources say
- Could not verifycites Scheel 2005 sourceExperimental — accuracy not yet measured
Section II discusses a beam splitter’s transmission coefficient, while Section IV reports a bound on the success probability of a linear-optical gate. Neither passage addresses a lower bound on absorption amplitude in physical beam splitters. Searches for absorption amplitude and beam-splitter loss found no supporting passage; page numbers were unavailable in our copy. (LLM, conf=0.76)
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Every source the paper cites for this claim was checked and supports it.
In the paper
“For example, Ralph (2003) proposed a simple demonstration circuit that detects and corrects bit flip errors on a single qubit using the encoded qubit state α|0 |0 + β|1 |1 and an ancilla qubit |0 .”
§ Linear optical quantum computing > B. General error correction in LOQC
What the sources say
- Supportedcites Ralph (2003) source
In THE CIRCUIT, Ralph proposes a simplified bit-flip correction circuit, gives the encoded state α|0⟩|0⟩ + β|1⟩|1⟩, and prepares an ancilla in |0⟩. The same section explains that measuring the ancilla detects a bit flip on the second physical qubit, which can then be corrected by flipping that qubit. (LLM, conf=0.93)
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- It may state two separate claims as one. 91
- Probably not a substantial claim. 81
- The quote only partly states this claim. 5
At least one cited source doesn’t support this claim or points to a different paper, and none confirmed it — see the verdicts below.
In the paper
“In a subsequent experiment by Pittman et al., the parity encoding was prepared in a somewhat different manner and, in order to correct the bit-flip errors, a feed-forward mechanism was implemented (Pittman et al. 2005).”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
What the sources say
- Disputedcites Pittman et al. 2005 sourceExperimental — accuracy not yet measured
The Introduction and Results describe parity encoding and a feed-forward bit flip used to recover a qubit after a Z-measurement error. But the Discussion explicitly says this procedure cannot correct physical bit-flip errors. The claim confuses the corrective operation with the type of error corrected; page numbers are unavailable in our copy. (LLM, conf=0.90)
Checked by a reasoning model — may be wrong.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Disputed
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Finally, in Fig. 10, the circuit of the CZ gate by Knill (2002) is shown.The success probability is 2/27.This is the most efficient CZ gate known to date.”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Partly supportedcites Knill (2002) sourceExperimental — accuracy not yet measured
Section III, “Conditional Phase Shifts” (page unavailable), reports a conditional sign-flip gate with success probability 2/27, improving on the 1/16 solution it compares against. It does not establish that this is the most efficient CZ gate known to date; the section says whether the reported solutions are optimal remains an open problem. (LLM, conf=0.86)
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- Partly supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“A CNOT gate that needs post-selection to make sure there is one polarised photon in each output mode was proposed by Ralph et al. (2002a).It makes use only of beam splitters with reflection coefficient of 1/3, and polarising beam splitters.The success probability is 1/9.”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Partly supportedcites Ralph et al. (2002a) sourceExperimental — accuracy not yet measured
Section IV (p. 4) describes a conditional CNOT gate and says polarizing beam splitters can convert polarization qubits to the gate’s spatial encoding. Section V (p. 6) describes selecting successful operation by photon detection. But the claimed beam-splitter reflectivity and success probability do not match: Section IV (pp. 4, 6) specifies 50:50 beam splitters and a 1/16 success factor, while the simplified gate in Section V (p. 7) succeeds with probability approximately 0.05, not 1/9. (LLM, conf=0.90)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Partly supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Unfortunately, even the largest natural cross-Kerr nonlinearities are extremely weak (χ (3) ≈ 10 -22 m 2 V -2 ).Operating in the optical single-photon regime with a mode volume of approximately 0.1 cm 3 , the Kerr phase shift is only τ ≈ 10 -18 (Kok et al. 2002).”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
What the sources say
- Partly supportedcites Kok et al. 2002 sourceExperimental — accuracy not yet measured
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“An improvement of this system was proposed by Hofmann et al. (2003).These authors showed how a phase shift of π can be achieved with a single two-level atom in a onesided cavity.”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
What the sources say
- Supportedcites Hofmann et al. (2003) source
The Abstract states that a nonlinear phase shift of π can be obtained using a single two-level atom in a one-sided cavity with negligible losses. The paper proposes this configuration rather than reporting an experimental demonstration, which is consistent with the citing sentence. (LLM, conf=0.95)
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Rests on an assumption: The losses in the Hofmann et al. one-sided cavity system are negligible.
- Supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Notice that, for this construction, an overall improvement in gate success is not achieved unless f < 1/2.Using these results one finds that first level concatenation and t 3 ( f = 1/4) teleporters are required to achieve a CZ gate with better than 95% probability of success.It can be estimated that of order 10 4 operations would be required in order to implement such a gate (Hayes et al. 2004).”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
What the sources say
- Partly supportedcites Hayes et al. 2004 sourceExperimental — accuracy not yet measured
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“The first proposal for linear optical quantum computing along these lines by Yoran and Reznik (2003) is not strictly based on the cluster-state model, but it has many attributes in common.Most notably, it uses”
§ Linear optical quantum computing > B. The Yoran-Reznik protocol
What the sources say
- Supportedcites Yoran and Reznik (2003) source
The paper describes entangled photon chains that carry input states through a circuit by teleportation (Abstract, passages 5 and 7). It also says that although preparing the linked state uses nondeterministic gates, computation then proceeds through deterministic teleportation (Abstract, passages 5 and 8), supporting the claim about circumventing probabilistic teleportation during computation. (LLM, conf=0.93)
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Supported
In the paper
“Using weak coherent pulses, Turchette et al. found φ s = 17.5 • ± 1, φ p = 12.5 • ± 1, and δ = 16 • ± 3.”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
What the sources say
- Not matchedcites Turchette et al.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The success probability of the gate is given by d.”
§ Linear optical quantum computing > E. General probabilistic nonlinear gates
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Making a projective measurement in mode c onto the complementary basis (|H ± |V )/ √ 2 then yields a parity check: If we detect a single photon in mode c, we know that the input qubits had the same logical value.This value is transmitted into the output qubit in mode d (up to a σ z transformation depending on the measure- ment result).On the other hand, if we detect zero or two photons in mode c,”
§ Linear optical quantum computing > B. Parity gates and entangled ancillæ
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“When we choose σ ≃ 150.5 • and θ ≃ 61.5 • , this yields the NS gate with the same probability cos 2 θ = (3 -√ 2)/7.”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Not matchedcites Rudolph and Pan (2001)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:hedged· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe quote only partly states this claim.
- The authors state this as an assumption: The input mode for the Rudolph-Pan gate is horizontally polarised.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For instance, the operation of a CNOT gate on the initial state (|H c -|V c )|V t creates the maximally entangled singlet state |H c |V t -|V c |H t .This is sufficient to show the coherence properties of the gate.”
§ Linear optical quantum computing > D. Characterisation of linear optics gates
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Depending on the polarisation of the measured ancillary photon in mode a (and one photon in the control and target modes) a CNOT gate up to a local transformation is applied to the control and target qubits.For a horizontally measured |H a photon the CNOT gate is exactly implemented, while for a vertically measured |V a photon the control and target qubits undergo a CNOT gate up to a bit flip on”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For the twoqubit CNOT gate (d = 16), we require 256 different settings of input states and measurement projectors.”
§ Linear optical quantum computing > D. Characterisation of linear optics gates
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The VLPC is thus effectively a large detector cascade (N ≈ 10 4 ) with high detection efficiency (≈ 88% at 694 nm).”
§ Linear optical quantum computing > A. Photon detectors
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“The efficiency of emission was found to be about 8%, that is to say, 92% of the pump pulses did not lead to a single-photon detection event.”
§ Linear optical quantum computing > B. Photon sources
What the sources say
- Not checked — no full text of the sourcecites Keller et al. (2004) source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Hence, the type-II fusion gate with bucket detectors is a (2,2)-strategy, and the growth requirement is m > 2/p.”
§ Linear optical quantum computing > A. Correcting for photon loss
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: In the circuit-based model analysis, bucket detectors have a certain detection efficiency η and a negligible dark count rate.
- The authors state this as an assumption: In the type-II fusion gate analysis, photon sources are perfect.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“These gates cannot be implemented deterministically on parityencoded qubits.”
§ Linear optical quantum computing > E. Circuit-based optical quantum computing revisited
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Dark counts can be made as low as 6 • 10 3 Hz at room temperature and around 25 Hz at cryogenic temperatures.”
§ Linear optical quantum computing > A. Photon detectors
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A typical (unfiltered) detector efficiency for such a detector is 85% at a wavelength of 660 nm.”
§ Linear optical quantum computing > A. Photon detectors
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“On the other hand, typical photon detectors in LOQC experiments are bucket detectors.”
§ Linear optical quantum computing > A. Photon detectors
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“The experiment revealed a clear suppression of the peak at T = 0 in the normalised correlation function g (2) (T), thus passing the first test of a good single photon source.”
§ Linear optical quantum computing > B. Photon sources
What the sources say
- Not checked — no full text of the sourcecites Keller et al. (2004) source
Strength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Currently, the most common detectors in experiments on LOQC are Avalanche Photo-Diodes (APDs).”
§ Linear optical quantum computing > A. Photon detectors
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This shows the highly entangled singlet state of the form |H c |V t -|V c |H t”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, it subsequently spurred on new experiments in quantum optics, demonstrating the operation of high-fidelity probabilistic two-photon gates.”
§ Linear optical quantum computing > Abstract
Strength:boosted· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Initially, the KLM protocol was designed as a proof that linear optics and projective measurements allow for scalable quantum computing in principle.”
§ Linear optical quantum computing > Abstract
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“On the theoretical front, several improvements of the protocol were proposed, leading to ever smaller overhead cost on the computation.”
§ Linear optical quantum computing > Abstract
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In the paper
“A number of these improvements are based on cluster-state quantum computing, or the one-way quantum computer.”
§ Linear optical quantum computing > Abstract
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In the paper
“Recently, a circuit-based model was shown to have similar scaling properties as the bestknown cluster state model.”
§ Linear optical quantum computing > Abstract
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In the paper
“The difficulty with this technique is that such optical quantum gates are probabilistic: More often than not, the gate fails and destroys the information in the quantum computation.”
§ Linear optical quantum computing > Abstract
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In the paper
“Although the set of gates in the Pauli and Clifford groups does not satisfy the universality requirements, the addition of a singlequbit π /8 gate will render the set universal.”
§ Linear optical quantum computing > C. Qubits in linear optics
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In the paper
“This can be circumvented by using an exponential number of optical modes, but this is by definition not scalable”
§ Linear optical quantum computing > Abstract
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In the paper
“The Gottesman-Knill theorem (1999) states that any quantum algorithm that initiates in the computational basis and employs only transformations (gates) from the the Clifford group, along with projective measurements in the computational basis, can be efficiently simulated on a classical computer.”
§ Linear optical quantum computing > C. Qubits in linear optics
What the sources say
- Not matchedcites Gottesman-Knill theorem (1999)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
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In the paper
“polarisation qubits on a polarising beam splitter (Pittman et al. 2002b), and a two-photon conditional phase switch (Resch et al. 2002).”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not matchedcites Pittman et al. 2002b
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked yetcites Resch et al. 2002 source
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In the paper
“A number of experimental groups have already demonstrated all-optical probabilistic quantum gates.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
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In the paper
“For example, operations that cause a change in the Fock layers (for instance the Hadamard operator) are generally difficult but not impossible.”
§ Linear optical quantum computing > E. General probabilistic nonlinear gates
What the sources say
- Not checked yetcites Scheel et al. (2003) source
Checked before — its earlier verdict is held back until a new check runs.
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In the paper
“In the Pittman et al. experiment the control qubit and the ancillary qubit are created us-ing pulsed parametric down conversion.The target qubit is generated by an attenuated laser pulse where the pulse is branched off the pump laser.The pulse is converted by a frequency doubler to generate entangled photon pairs at the same frequency as the photon constituting the target qubit.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not checked yetcites Pittman et al. (2003) source
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In the paper
“In singlephoton quantum information processing we have easy access to such single-qubit operations.”
§ Linear optical quantum computing > C. Qubits in linear optics
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In the paper
“The fidelity of the gate is approximately 84% with conditional fringe visibilities exceeding 90% in non-orthogonal bases.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not checked — no full text of the sourcecites O'Brien et al. (2003) source
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In the paper
“However, showing such coherences does not fully characterise the gate.To this end, we can perform state tomography.”
§ Linear optical quantum computing > D. Characterisation of linear optics gates
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In the paper
“To fully understand the operation of a gate we need to create a complete map Ê of all the input states to the output states.”
§ Linear optical quantum computing > D. Characterisation of linear optics gates
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In the paper
“The success probability for teleporting a two-qubit gate is then the square of this probability, n 2 /(n + 1) 2 , because we need to teleport two qubits successfully.”
§ Linear optical quantum computing > G. The Knill-Laflamme-Milburn protocol
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In the paper
“Experimentally, the map is obtained by performing quantum process tomography (Chuang and Nielsen 1997;Poyatos et al. 2001).”
§ Linear optical quantum computing > D. Characterisation of linear optics gates
What the sources say
- Not checked yetcites Chuang and Nielsen 1997 source
- Not matchedcites Poyatos et al. 2001
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“A variation on this is the cross-Kerr medium, in which the phase shift of a signal beam is proportional to the intensity of a second probe beam.”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
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In the paper
“The vacuum state is replaced with a single horizontally polarised photon, |0 → |H , and the one-photon state is replaced with a vertically polarised photon, |1 → |V .There are now 2n rather than n photons in the state |t n .”
§ Linear optical quantum computing > G. The Knill-Laflamme-Milburn protocol
What the sources say
- Not matchedcites Spedalieri et al. (2005)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
In the paper
“In the KLM scheme, the qubits are chosen from the dual-rail representation.However, in the KLM protocol the teleportation trick applies to the single-rail state α|0 + β|1 , where |0 and |1 denote the vacuum and the single-photon Fock state respectively, and α and β are complex coefficients (this is because the CZ gate involves only one optical mode of each qubit).”
§ Linear optical quantum computing > G. The Knill-Laflamme-Milburn protocol
What the sources say
- Not checked — no full text of the sourcecites Knill, Laflamme, and Milburn (2001) source
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In the paper
“Since this protocol requires an exponential number of optical modes, this is a simulation rather than a fully scalable quantum computer.”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
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In the paper
“An identical gate was proposed independently by Hofmann and Takeuchi (2002).”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Not checked yetcites Hofmann and Takeuchi (2002) source
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It erases all path information of the incoming modes, and can be interpreted as the n-mode generalisation of the 50:50 beam splitter.”
§ Linear optical quantum computing > G. The Knill-Laflamme-Milburn protocol
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In the paper
“However, the construction of the truth table is in itself not sufficient to show that a CNOT operation has been performed.It is essential to show the quantum coherence of the gate.”
§ Linear optical quantum computing > D. Characterisation of linear optics gates
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In the paper
“From fundamental gates, three CNOTs are required to build such an operation.However, from fundamental optical resources only two beam splitters and a phase shifter are necessary.”
§ Linear optical quantum computing > E. General probabilistic nonlinear gates
What the sources say
- Not checked yetcites Scheel et al. (2003) source
Checked before — its earlier verdict is held back until a new check runs.
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- Not checked yet
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is immediately clear that we cannot make the NS gate with a regular phase shifter, because only the state |2 picks up a phase.A linear optical phase shifter would also induce a factor i (or -i) in the state |1 .”
§ Linear optical quantum computing > A. Elementary gates
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In the paper
“The teleportation procedure remains the same, except that we now count the total number of vertically polarised photons.”
§ Linear optical quantum computing > G. The Knill-Laflamme-Milburn protocol
What the sources say
- Not matchedcites Spedalieri et al. (2005)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
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In the paper
“A special optical gate that will become important in section III is the so-called parity check.It consists of a single polarizing beam splitter, followed by photon detection in the complementary basis of one output mode.”
§ Linear optical quantum computing > B. Parity gates and entangled ancillæ
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In the paper
“Since quantum computing can be cast into the shape of single-qubit operations and two-qubit projections (Nielsen 2003;Leung 2004), we can approach the problem of making nonlinear gates via complete discrimination of multi-qubit bases.”
§ Linear optical quantum computing > E. General probabilistic nonlinear gates
What the sources say
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In the paper
“As mentioned before, Knill (2003) demonstrated that this is not the case, and that instead the highest possible success probability for the NS gate (using feed-forward) is one half.”
§ Linear optical quantum computing > B. Parity gates and entangled ancillæ
What the sources say
- Not checked yetcites Knill (2003) source
Checked before — its earlier verdict is held back until a new check runs.
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- Not checked yet
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In the paper
“For teleportation to work, we also need the entangled resource |Φ + , which can be prepared offline.”
§ Linear optical quantum computing > F. Scalable optical circuits and quantum teleportation
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In the paper
“In such an encoding, both single-and two-qubit gates are easily implemented using (polarisation) beam splitters and phase shifters.”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
What the sources say
- Not matchedcites Cerf, Adami, and Kwiat (1998, 1999)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
In the paper
“Before the work of Knill, Laflamme, and Milburn (KLM), quantum information processing with linear optics was studied (among other things) in non-scalable architectures by Cerf, Adami, andKwiat (1998, 1999).”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
What the sources say
- Not matchedcites Cerf, Adami, and Kwiat (1998, 1999)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
In the paper
“The success probability of such an event is 1/9.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not checked — no full text of the sourcecites O'Brien et al. (2003) source
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe quote only partly states this claim.
In the paper
“First, we consider the three-photon CNOT gate performed by Pittman, Fitch, Jacobs, and Franson (2003).The gate is shown in Fig. 12 and consists of three polarisation-encoded single photon qubits and two polarising beam splitters.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not checked yetcites Pittman, Fitch, Jacobs, and Franson (2003) source
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For large N and small p, this probability is minuscule.As a consequence, we have to repeat the calculation on the order of p -N times, or run p -N such systems in parallel.Either way, the resources (time or circuits) scale exponentially with the number of gates.”
§ Linear optical quantum computing > F. Scalable optical circuits and quantum teleportation
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, as we have argued in section I.C, this is not enough to make deterministic linear optical quantum computing possible, and we have to turn our attention instead to probabilistic gates.”
§ Linear optical quantum computing > A. Elementary gates
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In the paper
“The absence of the |1, 1 cd term is called the Hong-Ou-Mandel effect (Hong et al. 1987), and it lies at the heart of linear optical quantum computing.”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Not checked — no full text of the sourcecites Hong et al. 1987 source
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In the paper
“Finally, a scheme equivalent to the one by Ralph et al. was proposed by Rudolph and Pan (2001), in which the variable beam splitters are replaced with polarisation rotations .”
§ Linear optical quantum computing > A. Elementary gates
What the sources say
- Not matchedcites Rudolph and Pan (2001)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This indicates that entanglement has been generated in the experiment: The gate can create entangled output states from separable input states.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
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In the paper
“Prior to KLM, it was widely believed that scalable alloptical quantum computing needed a nonlinear component, such as a Kerr medium.”
§ Linear optical quantum computing > D. Early optical quantum computers and nonlinearities
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In the paper
“These are particularly useful when we need to distinguish between nonorthogonal states, and they can be implemented with N ports as well (Myers and Brandt 1997).”
§ Linear optical quantum computing > E. General probabilistic nonlinear gates
What the sources say
- Not checked — no full text of the sourcecites Myers and Brandt 1997 source
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In the paper
“The success probability for this gate is p = 1/4 with an error of approximately 21%.”
§ Linear optical quantum computing > C. Experimental demonstrations of gates
What the sources say
- Not checked yetcites Pittman et al. (2003) source
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For quantum computing applications, however, we usually want the resulting nonlinear transformation M to be unitary.This is because non-unitary operations will reveal information about the qubits in the projective measurement, and hence corrupts the computation.”
§ Linear optical quantum computing > E. General probabilistic nonlinear gates
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similarly if the measurement result is V we have: α|0 L + β|1 L → α|V + β|H (40 ) Again the superposition is preserved, but this time a bitflip occurs.However, the bit-flip is heralded by the measurement result and can therefore be corrected.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, when the fusion gates are applied to two qubits inside a cluster (i.e., the qubits have two or more links to other qubits in the cluster), then the failure modes of the two fusion gates differ dramatically: In particular when we apply the fusion gate to a qubit in a chain, a failed type-I gate will break the chain, while a failed type-II gate will only shorten the chain and create one”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When the type-I gate fails, it performs a Z measurement on the input qubits.When the type-II gate fails, it performs an X measurement on the input qubits.Recall that there is a fundamental difference between a Z and an X measurement on qubits in cluster states: A Z measurement will break all bonds with the qubits neighbours and removes it from the cluster.An X measurement will also remove the qu”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A more efficient procedure is to encode against gate failure.This is possible because of the welldefined failure mode of the teleporters.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“So if the photon detectors are lossy, the rate of coincidence counts is reduced.Since the fusion operation is already probabilistic, a reduced success rate translates into a larger overhead in the cluster-state generation.”
§ Linear optical quantum computing > V. GENERAL ERROR CORRECTION
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In the paper
“In other words, the encoding has become smaller but the quantum information has not been erased.”
§ Linear optical quantum computing > A. Correcting for photon loss
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Inaccurate Hamiltonian parameters generally reduce the level of mode matching, leading, for example, to a reduced Hong-Ou-Mandel effect and hence inaccurate CZ gates.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“First, the single-qubit gate Z is still implemented deterministically: Z = Z (p) = nσ z .Therefore, in order to ap- ply a Z gate, a σ z operation must be applied to all n photons in one and only one parity qubit.”
§ Linear optical quantum computing > A. Correcting for photon loss
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This is the second essential diagnostic for a single-photon source.”
§ Linear optical quantum computing > B. Photon sources
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In the paper
“Finally, Nielsen introduces so-called micro-clusters consisting of multiple qubits connected to the end point of a cluster chain.Such a micro-cluster is depicted in Fig. 26d, where the central qubit is an endpoint of a cluster chain.Having such a fan of qubits at the end of a chain, we can retry the entangling gate as many times as there are”
§ Linear optical quantum computing > C. The Nielsen protocol
What the sources say
- Not matchedcites Nielsen and Dawson 2004
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
In the paper
“This operation has been demonstrated experimentally (O'Brien et al. 2005).In this experiment the projections given by Eqs.(39) and (40) were confirmed up to fidelities of 96%.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
What the sources say
- Not checked yetcites O'Brien et al. 2005 source
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The LOQC protocols described in this review all make critical use of perfect single-photon sources.”
§ Linear optical quantum computing > B. Photon sources
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Nevertheless, such states are very desirable, since they would dramatically reduce the cost of linear-optical quantum computing.”
§ Linear optical quantum computing > B. Photon sources
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“One can obtain the probability of success after concatenation iteratively.For example the probability of success after one concatenation is P Z1 = 1 -F Z1 where F Z1 = F 2 Z (2 -F Z )/(1 -F Z (1 -F Z )).The probability of success for a CZ gate between two logical qubits is P CZ = (1 -F Z ) 2 .”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Whereas perfect number-resolving detectors can be modelled using the projection operators onto the Fock states |n n|, realistic detectors give rise to Positive Operator Valued Measures, or POVMs.”
§ Linear optical quantum computing > A. Photon detectors
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, we can give a general meaning to the concepts of photon loss and dark counts for arbitrary input states when we define the loss or dark counts as a property of the detector (i.e., independent of the input state).”
§ Linear optical quantum computing > A. Photon detectors
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that we do not have to couple a photonic qubit into a quantum memory: We can use two photon memories to store one qubit, provided the memory does not retain information about whether a photon was stored or not.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The orig-inal KLM proposal relies critically on the availability of number-resolving detectors.”
§ Linear optical quantum computing > A. Photon detectors
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A change in the polarization of the photon will then induce an error in the computational circuit.”
§ Linear optical quantum computing > A. Photon detectors
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In the paper
“The main observation is that the resources required to construct the entangled state of Eq. ( 41) are much less than those required to construct |t 3 .As a result, error encoding turns out to be a more efficient way to scale up teleportation and hence gate success.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We noted in the previous section that the teleporters fail if zero or n + 1 photons are detected because we can then infer the logical state of the input qubit.In other words the failure mode of the teleporters is to measure the logical value of the input qubit.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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In the paper
“This means that, instead of using very large n to make the CZ gate near-deterministic, links can be added on average with a modest CZ 9/16 -gate, or n = 3.This leads to similarly reduced resource requirements as the Yoran-Reznik protocol, while still keeping (in principle) errorfree quantum computing.”
§ Linear optical quantum computing > C. The Nielsen protocol
What the sources say
- Not checked yetcites Nielsen 2004 source
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Using the failure behaviour of the type-II fusion gate, we can construct an efficient way of creating the vertical links between linear cluster chains.We attempt a type-II fusion between two qubits that are part of different chains.If the gate succeeds, we have created a vertical link on the neighbouring qubits.If the gate fails, one neighbouring qubit to each detected qubit becomes redundantly”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
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In the paper
“Indeed, Browne and Rudolph introduced a protocol for generating cluster states using the probabilistic parity gates of section II.B (Browne and Rudolph 2005;Cerf et al. 1998;Pittmann et al. 2001).The notable advantage of this gate is that it is relatively easy to implement in practice (Pittman et al. 2002b), and that it can be made robust against common experimental errors.”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
What the sources say
- Not checked yetcites Browne and Rudolph 2005 source
- Not matchedcites Pittman et al. 2002b
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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None of the sources cited for this claim have been checked yet.
In the paper
“Feed-forward control for LOQC was demonstrated by Pittman et al. (2002a) and Giacomini et al. (2002).”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
What the sources say
- Not matchedcites Pittman et al. 2002a
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked yetcites Giacomini et al. 2002 source
Checked before — its earlier verdict is held back until a new check runs.
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- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The same error models for single-photon sources apply to entangled-photon sources.”
§ Linear optical quantum computing > B. Photon sources
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In the paper
“This circuit-based protocol for linear optical quantum computation has many features in common with the Browne-Rudolph protocol.”
§ Linear optical quantum computing > E. Circuit-based optical quantum computing revisited
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None of the sources cited for this claim have been checked yet.
In the paper
“A Z measurement removes a qubit from a cluster and severs all the bonds that it had with the cluster (Raussendorf et al. 2003;Hein et al. 2004).An X measurement on a qubit in a cluster removes that qubit from the cluster, and it will transfer all the bonds of the original qubit to a neighbour.All the other neighbours become single connected qubits to the neighbour that inherited the bonds (Rauss”
§ Linear optical quantum computing > A. Cluster states in optical quantum computing
What the sources say
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The errors that we discussed so far originate from the probabilistic nature of linear optical photon manipulation”
§ Linear optical quantum computing > E. Circuit-based optical quantum computing revisited
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In the paper
“To achieve quantum computing despite inevitable physical errors in the quantum computer, we have to employ Error Correction (EC).”
§ Linear optical quantum computing > V. GENERAL ERROR CORRECTION
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such states, while a useful heuristic, are not physical.”
§ Linear optical quantum computing > B. Photon sources
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In the paper
“We can group them according to the optical components: detection errors, source errors, and circuit errors (Takeuchi 2000a).”
§ Linear optical quantum computing > IV. REALISTIC OPTICAL COMPONENTS AND THEIR ERRORS
What the sources say
- Not matchedcites Takeuchi 2000a
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
In the paper
“Instead of teleporting the two qubits simultaneously, we first teleport the disconnected qubit, and secondly teleport the qubit at the end of the cluster.We know that a teleportation failure will remove the qubit from the cluster, so we attempt the second teleportation protocol only after the first has succeeded.The first teleportation protocol then becomes part of the off-line resource”
§ Linear optical quantum computing > C. The Nielsen protocol
What the sources say
- Not checked yetcites Nielsen 2004 source
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is easily verified that the probability of success for this gate is p = 1/2.When the type-I fusion gate is applied to two photons belonging to two different cluster states containing n 1 and n 2 photons, respectively, a successful operation will generate a cluster chain of n 1 + n 2 -1 photons.However, when the gate fails, it effectively performs a σ z measurement on both photonic qubits, and”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this model, every incoming photon has the same probability of being lost, leading to Poissonian statistics.”
§ Linear optical quantum computing > A. Photon detectors
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In the paper
“This also indicates a significant difference between this protocol and the previous ones: Using only single-photon sources, the fusion gates alone cannot create cluster states.We can, however, use any method to create the necessary Bell pairs (such as the CZ gate in section II.A), as they constitute an off-line resource.”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
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In the paper
“If we can encode against accidental measurements of this type then our qubit will be able to survive gate failures and the probability of eventually succeeding in applying the gate will be increased.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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In the paper
“The success probability of this gate is p = 1/2, and it is a (2, 1)-strategy (i.e., d s = 2 and d f = 1).The ideal growth requirement is thus m > (1 + p)/p = 3.The type-II fusion gate is essentially a version of the incomplete optical Bell measurement (Braunstein and Mann 1996;Weinfurter 1994).”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
What the sources say
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We have already seen that the teleportation trick in the KLM scheme employs error correction to turn the non-deterministic gates into near-deterministic gates.”
§ Linear optical quantum computing > IV. REALISTIC OPTICAL COMPONENTS AND THEIR ERRORS
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In the paper
“This is known as antibunching and is the first essential diagnostic for a sequence of single photon pulses with one and only one photon per pulse.”
§ Linear optical quantum computing > B. Photon sources
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In the paper
“Fixing the gauge of the field in the detection plane then causes a mixing of left-and right-handed polarization.This introduces a detection error that is fundamental, since the uncertainty principle prevents the transverse momentum in a beam from being exactly zero (Peres and Terno 2002).”
§ Linear optical quantum computing > A. Photon detectors
What the sources say
- Not matchedcites Peres and Terno 2002
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Not matched
None of the sources cited for this claim have been checked yet.
In the paper
“However, if we can add small chains of qubits to the cluster, this requirement may be relaxed.Suppose that the success probability of creating a link between two cluster chains is p, and that in each successful linking of two chains we lose d s qubits from the chain.This might happen when the entangling operation joining the two clusters involves the detection of qubits in the cluster.Similarly,”
§ Linear optical quantum computing > D. The Browne-Rudolph protocol
What the sources say
- Not matchedcites Barrett and Kok 2005
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked yetcites Browne and Rudolph 2005 source
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- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Secondly, the gate Z π /2 is diagonal in the computational basis, and can therefore be implemented using one Z (p) π /2 .”
§ Linear optical quantum computing > A. Correcting for photon loss
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Real photon detectors of any kind give rise to two different types of errors:”
§ Linear optical quantum computing > A. Photon detectors
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This is an important resource in both the Browne-Rudolph and the Gilchrist-Hayes-Ralph protocol.”
§ Linear optical quantum computing > B. Photon sources
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In the paper
“The three main errors that need to be coded against are inefficient detectors, noisy photon sources, and unfaithful quantum memories.”
§ Linear optical quantum computing > V. GENERAL ERROR CORRECTION
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The CZ gate is of course non-deterministic and so the Z π /2 gate becomes nondeterministic for the logical qubit.Thus both the Z π /2 and the logical CZ gate must be implemented with the teleportation gates in order to form a universal gate set for the logical qubits.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Apart from linear cluster states, we also need the ability to make the two-dimensional clusters depicted in Fig. 25.This is equivalent to linking a qubit to two cluster chains, and hence needs two successful CZ gates.Arguing along the same lines as before, it is easily shown that the success probability is 4/9 for this procedure using two ancillæ per teleportation gate.Since this is smaller than”
§ Linear optical quantum computing > C. The Nielsen protocol
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In the paper
“The absence of a photon in the output state is an obvious failure mechanism, but other ways the memory can fail include qubit decoherence and mode mismatching of the input/output modes.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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In the paper
“It is the entangling operation that is problematic in optics, since a linear optical CZ gate in our qubit representation is inherently probabilistic.”
§ Linear optical quantum computing > A. Cluster states in optical quantum computing
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- Rests on an assumption: A linear optical CZ gate in the dual-rail/polarisation qubit representation is inherently probabilistic.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The type-II fusion operation described in section III.D must give a coincidence count in the two detectors.Any other detector signature heralds an error.”
§ Linear optical quantum computing > V. GENERAL ERROR CORRECTION
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this sense, the design specifications of a solid-state based quantum memory are more stringent than those for solid-state single-photon sources: Not only does it need to produce a single photon with very high fidelity, it also needs the ability to couple a photon into the device with very high probability.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the real world, this is far from true.”
§ Linear optical quantum computing > IV. REALISTIC OPTICAL COMPONENTS AND THEIR ERRORS
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- The authors state this as an assumption: The KLM scheme assumes that photon sources, mode matching of optical circuits, and photon counting are all perfect.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The detection errors have been discussed in section IV.A and classical computing is virtually error-free due to robust classical error correction.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The probability for creating n photon pairs is p(n) = (1 -|λ| 2 )|λ| 2n , which exhibits pair bunching.”
§ Linear optical quantum computing > B. Photon sources
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At first sight this effect might seem negligible, but later we will see that concatenation of error correcting codes will amplify small errors.”
§ Linear optical quantum computing > A. Photon detectors
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The classical limit is 50%, showing that a true quantum memory was constructed.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The use of mere fibre loops then becomes problematic, as these induce photon losses (0.17 dB km -1 in a standard telecom fibre at 1550 nm).”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In addition, imperfect impedance matching of the boundaries will scatter photons back to the source.This amounts to photon loss in the optical circuit.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
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In the paper
“Two-dimensional cluster states, i.e., states with vertical as well as horizontal links, are essential for quantum computing, as linear cluster-state computing can be efficiently simulated on classical computers (Nielsen 2005).”
§ Linear optical quantum computing > A. Cluster states in optical quantum computing
What the sources say
- Not checked yetcites Nielsen 2005 source
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The typical physical mechanisms that reduce the indistinguishability of the single-photon sources are dephasing of the optical transition, spectral diffusion, and incoherent pumping.”
§ Linear optical quantum computing > B. Photon sources
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In the paper
“For an EC protocol to be useful, the error in the circuit after the EC protocol must be smaller than the error before the EC protocol.”
§ Linear optical quantum computing > V. GENERAL ERROR CORRECTION
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the probability of success of teleportation gates can be increased arbitrarily by preparing larger entangled states.However the asymptotic behaviour to unit probability is quite slow as a function of n.”
§ Linear optical quantum computing > H. Error correction of the probabilistic gates
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Although the clusterstate model is conceptually quite different from the circuit-based model, they have similar resource requirements.”
§ Linear optical quantum computing > E. Circuit-based optical quantum computing revisited
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In applications other than LOQC, such as cryptography, the requirement of indistinguishable sources may be relaxed.”
§ Linear optical quantum computing > B. Photon sources
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The dark count rate of 2 • 10 4 Hz is about an order of magnitude higher than the dark count rate for off-the-shelf APDs.”
§ Linear optical quantum computing > A. Photon detectors
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that there seem to be conflicting requirements in this code: In order to execute successful fusion gates, we want n to be reasonably large.On the other hand, we want n to be as small as possible such that the probability of measuring all n photons p = η n is not too small.”
§ Linear optical quantum computing > A. Correcting for photon loss
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“A storage time of 125 µs for entangled photons in a telecom fibre was reported by Li et al. (2005), with subsequent fringe visibilities of 82%.”
§ Linear optical quantum computing > C. Circuit errors and quantum memories
What the sources say
- Not matchedcites Li et al. 2005
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
None of the sources cited for this claim have been checked yet.
In the paper
“Thirdly, Franson, Jacobs, and Pittman proposed the implementation of a two-qubit √ SWAP gate using the quantum Zeno effect:”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The effect of this repeated two-photon measurement is to suppress the Hong-Ou-Mandel effect via the quantum Zeno effect.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If this problem is solved, considerable savings in resources could result from adopting such implementations.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Alternatively, relatively large nonlinearities can be obtained in photonic band-gap materials (Friedler et al. 2004).”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
What the sources say
- Not checked yetcites Friedler et al. 2004 source
Checked before — its earlier verdict is held back until a new check runs.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not checked yet
None of the sources cited for this claim have been checked yet.
In the paper
“Subsequently, it was realized by Nemoto and Munro (2004) that this technique can also be used to create a deterministic CNOT gate on photonic qubits.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
What the sources say
- Not checked yetcites Nemoto and Munro (2004) source
Checked before — its earlier verdict is held back until a new check runs.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not checked yet
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“single-mode phase shifts break the “special” symmetry (det U = 1), which is why an interferometer is described by U(N), rather than SU(N).”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This state can be obtained by an Xmeasurement of the central qubit in (a).”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“EC codes that correct specific errors such as photon loss or depolarisation may be smaller than generic EC codes, and therefore introduce less noise.”
§ Linear optical quantum computing > B. General error correction in LOQC
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“It was shown by Munro et al. (2005) how such nonlinearities can make a number-resolving QND detector, and Barrett et al. (2005) showed how a small cross-Kerr nonlinearity can be used to perform complete Bell measurements without destroying the photons.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
What the sources say
- Not matchedcites Munro et al. (2005)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When various parameters in a noise model differ significantly, it might be beneficial to diversify the error correction codes.”
§ Linear optical quantum computing > B. General error correction in LOQC
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Unfortunately, natural Kerr nonlinearities are extremely small, and this is not a practical method for creating optical gates.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Dawson, Haselgrove, and Nielsen (2006a,b) performed an extensive numerical study of fault-tolerant thresholds for linear optical cluster state quantum computing.”
§ Linear optical quantum computing > B. General error correction in LOQC
What the sources say
- Not matchedcites Dawson, Haselgrove, and Nielsen (2006a,b)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“Recent work in electromagnetically induced transparencies by Lukin andImamo ǧlu (2000, 2001) suggests that the small-but-not-tiny nonlinearities needed for this method are on the threshold of becoming practical.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
What the sources say
- Not matchedcites Lukin andImamo ǧlu (2000, 2001)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:hedged· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both gates also need a parity measurement, which is implemented by σ z measure- ments on the individual physical qubits.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Independently, Lim et al. (2005) showed how a similar setup can be used to implement deterministic two-qubit quantum gates.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
What the sources say
- Not checked yetcites Lim et al. (2005) source
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It is argued that the difference between correlated twoqubit noise and independent noise does not change the threshold much.”
§ Linear optical quantum computing > B. General error correction in LOQC
Strength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A simple 50:50 beam-splitter and polarisation rotation then furnishes a deterministic transformation from the computational basis to the Bell basis.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“It was shown by Munro et al. (2005) how such nonlinearities can make a number-resolving QND detector, and Barrett et al. (2005) showed how a small cross-Kerr nonlinearity can be used to perform complete Bell measurements without destroying the photons.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
What the sources say
- Not matchedcites Barrett et al. (2005)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In order to distribute quantum information over a network of quantum computers, the qubit of choice will most likely be optical.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✗ Based: failsProbably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A round of special error correction might be used to reduce large errors, and subsequent generic error correction will further reduce the errors below the faulttolerant threshold.”
§ Linear optical quantum computing > B. General error correction in LOQC
Strength:hedged· not yet calibratedCausal:conditional· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If it fails, then the two qubit states are lost.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this way, two single-photon qubits in the input modes are transformed into two single-photon qubits in the output modes and undergo a √ SWAP gate.”
§ Linear optical quantum computing > VI. OUTLOOK: BEYOND LINEAR OPTICS
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper relies on this without support.
Photons do not naturally interact with each other.
“The downside is that photons do not naturally interact with each other, and in order to apply two-qubit quantum gates such interactions are essential.”
“Physically, the reason why we cannot construct deterministic two-qubit gates in the polarisation and dual-rail representation, is that photons do not interact with each other.”
The paper relies on this without support.
The losses in the Hofmann et al. one-sided cavity system are negligible.
“The losses in this system are negligible.”
The paper relies on this without support.
Quantum information stored in a photon tends to stay there, so photons are potentially free from decoherence.
“Quantum computing with linear quantum optics, the subject of this review, has the advantage that the smallest unit of quantum information (the photon) is potentially free from decoherence: The quantum information stored in a photon tends to stay there.”
The paper relies on this without support.
Building a quantum computer requires both single-qubit operations and two-qubit operations.
“In order to build a quantum computer, we need both single-qubit operations as well as two-qubit operations.”
The authors state this as an assumption.
The detectors used in the KLM NS gate are perfect photon-number discriminating detectors.
“measured with perfect photon-number discriminating detectors”
The authors state this as an assumption.
The input mode for the Rudolph-Pan gate is horizontally polarised.
“Assume that the input mode is horizontally polarised.”
The paper relies on this without support.
The CZ gate is part of the Clifford group.
“Since the CZ gate is part of the Clifford group”
The paper relies on this without support.
Single-qubit rotations and CNOT gates are sufficient for universal computation.
“It is well known that such gates are sufficient for universal computation.”
The paper relies on this without support.
Quantum mechanics is linear.
“Linearity of quantum mechanics ensures”
The paper relies on this without support.
A fault-tolerant threshold exists such that making the error probability ε smaller than it enables scalable quantum computing.
“We can achieve scalable quantum computing by making ǫ smaller than the faulttolerant threshold.”
The paper relies on this without support.
A linear optical CZ gate in the dual-rail/polarisation qubit representation is inherently probabilistic.
“since a linear optical CZ gate in our qubit representation is inherently probabilistic.”
The authors state this as an assumption.
The KLM scheme assumes that photon sources, mode matching of optical circuits, and photon counting are all perfect.
“However, this assumes that the photon sources, the mode matching of the optical circuits, and the photon counting are all perfect.”
The authors state this as an assumption.
Quantum memories are needed for LOQC.
“In addition, we will address an assumption that has received little attention thus far: the need for quantum memories.”
The authors state this as an assumption.
In the model of a non-ideal single-photon source, the failure output results in a vacuum state.
“where we assumed that the failure output results in a vacuum state.”
The authors state this as an assumption.
In the cluster-state photon-loss correction, all stabiliser eigenvalues are +1.
“(we will assume that all eigenvalues are +1).”
The authors state this as an assumption.
In the circuit-based model analysis, bucket detectors have a certain detection efficiency η and a negligible dark count rate.
“We therefore assume that we have bucket detectors with a certain detection efficiency η and a negligible dark count rate.”
The authors state this as an assumption.
In the type-II fusion gate analysis, photon sources are perfect.
“(we assume perfect sources).”
The authors state this as an assumption.
Every parity qubit is encoded with the same number of photons n.
“We assumed that every parity qubit is encoded with the same number of photons n, but this is not necessary.”
The authors state this as an assumption.
In Dawson et al.'s model, any two single-photon qubits in the computation can serve as the inputs of the fusion gate.
“Furthermore, it is assumed that any two single-photon qubits in the computation can serve as the inputs of the fusion gate.”
The authors state this as an assumption.
In Dawson et al.'s model, the classical computation needed to control cluster state computing is sufficiently fast.
“Finally, the classical computation needed to control the cluster state computing is taken to be sufficiently fast.”
The authors state this as an assumption.
In the high-fidelity four-photon GHZ scheme, the Bell-pair source creates a state of the form p_s|0><0| + (1-p_s)|Ψ-><Ψ-|, where |Ψ-> is the two-photon polarization singlet state.
“Assume that the Bell-pair source creates a state of the form p s |0 0| + (1p s )|Ψ -Ψ -|, where |Ψ -is the twophoton polarization singlet state.”
The authors state this as an assumption.
In the deterministic polarisation-flip detection scheme, perfectly efficient detectors (not necessarily photon-number resolving) are available.
“If we assume the availability of perfectly efficient detectors (not necessarily photon-number resolving), deterministic polarisation-flip detection for distributing entanglement can be achieved (Kalamidas 2004).”
The authors state this as an assumption.
In the single-qubit error correction circuit, passive optical elements do not induce additional noise.
“Here, we assume that these passive optical elements do not induce additional noise.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Not long after its proposal, QOCT was experimentally demonstrated, achieving an improvement in resolution by a factor of 5 compared to OCT [25].”
From Two-photon interference: the Hong–Ou–Mandel effect (2021) · cites this paper as [25]
Experimental — accuracy not yet measuredIn the citing paper
“This epoch-making result opened the door to the linear optics quantum computation and has spurred a worldwide theoretical and experimental effort to realize such a device [16]”
From Realization of a Knill-Laflamme-Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities (2011) · cites this paper as [16]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Beam-splitter reflectivity conflicts with the stated convention
MinorThe paper defines reflectivity as R = sin2θ. For cos θ2 = 1/√3, reflectivity is 2/3, not 331⁄3%; 331⁄3% is the transmission coefficient.
“One of these output modes is mixed with a spatial mode of the control qubit on a beam splitter with cos θ 2 = 1/ √ 3 (that is, a beam splitter with a reflectivity of 33 1 3 %).”
“The reflection and transmission coefficients R and T of the beam splitter are R = sin 2 θ and T = 1 -R = cos 2 θ.”
The stated first-level CZ success probability does not exceed 95%
MinorUsing the stated f = 1/4 in Eq. (43) gives F_Z ≈ 0.1346. The quoted first-level concatenation formula then gives F_Z1 ≈ 0.0383 and a CZ success probability of (1 − F_Z1)2 ≈ 92.5%, not better than 95%.
“Using these results one finds that first level concatenation and t 3 ( f = 1/4) teleporters are required to achieve a CZ gate with better than 95% probability of success.”
“For example the probability of success after one concatenation is P Z1 = 1 -F Z1 where F Z1 = F 2 Z (2 -F Z )/(1 -F Z (1 -F Z )).The probability of success for a CZ gate between two logical qubits is P CZ = (1 -F Z ) 2 .”
The stated time unit does not make the frequencies integers
MinorFrom the paper's expressions, ωn = cnπ/L. Measuring time in units of πL/c would give a dimensionless frequency of nπ2, not n; the required time unit is L/(πc).
“If we measure time in units of π L/c, the allowed frequencies may simply be denoted by an integer ω n = n ∈ N.”
“The allowed wave vectors for plane wave modes form a denumerable set given by k n = nπ /L, with corresponding frequencies ω n = ck n .”
Citations
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Metadata
- Authors
- Kok, P., Munro, W. J., Nemoto, K., Ralph, T. C., Dowling, J. P., & Milburn, G. J.
- Affiliations
- University of Oxford (GB)
- National Institute of Informatics (JP)
- The University of Queensland (AU)
- Louisiana State University (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2007-01-24
- Volume
- 79
- Issue
- 1
- Pages
- 135-174
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1514675880
- Semantic Scholar
- dc30d510ec6b30e26082bf40b403b4c82f909e10
- Cited by
- 2,904
- References
- 231
- Citations by year
- 2026: 157 · 2025: 217 · 2024: 213 · 2023: 190 · 2022: 179 · 2021: 189 · 2020: 186 · 2019: 164 · 2018: 161 · 2017: 132 · 2016: 163 · 2015: 156 · 2014: 136 · 2013: 128 · 2012: 112
- FWCI
- 57.24
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OakTrust (Texas A&M University Libraries) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science
- Army Research Office
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Semiconductor Quantum Structures and Devices
- Keywords
- linear optical quantum computing, photonic qubits, photon counting, projective measurement, two-qubit gates, scalability, experimental implementation, error correction
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