Photonic quantum information processing: a review

In the paper

“Among probabilistic sources we mention (a) parametric down-conversion (PDC) in bulk crystals [204], semiconductors [166,215], microresonators [183, 185] and optical waveguides [32, 172-175, 177-182, 209, 210, 212-214] and (b) four-wave mixing (FWM) in optical waveguides [184,189,211], few-mode fibers [186] and microdisks [187].”

What the sources say

• ?Not checked — no full text of the sourcecites [204] Portalupi, 2015, Nano Lett. source
• Partly supported

  The Introduction (page unavailable) identifies cavity parametric down-conversion as a way to obtain single-photon states, supporting the PDC portion of the claim. The paper does not substantiate the listed range of source platforms or the four-wave-mixing examples; it focuses on temporal encoding of PDC-generated photons. (LLM, conf=0.84)

  cites [166] Hayat, 2012, Opt. Express sourceExperimental — accuracy not yet measured
• Disputed

  The citation is attached to parametric down-conversion in semiconductors. The paper’s Abstract instead describes its semiconductor quantum-dot molecule as producing photon triplets by triple cascade recombination, and contrasts that approach with SPDC-based schemes. It does not present the quantum-dot molecule as a parametric down-conversion source. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  cites [215] Khoshnegar, 2017, Nat. Commun. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [183] Huntington, 2004, Phys. Rev. A source
• Supported

  The Introduction describes spontaneous parametric down-conversion in nonlinear crystals, and the paper reports generating photon pairs with a crystal placed inside a cavity. It therefore supports the crystal-based PDC example for which it is cited; the other platforms in the sentence have separate citations. (LLM, conf=0.88)

  cites [185] Tian, 2016, J. Phys. Soc. Japan source

In the paper

“Next to the discrete-variable schemes of the first demonstrations, teleportation was also reported on squeezed entangled states [352][353][354][355][356][357][358], for which a review is available [359].”

What the sources say

• ?Not checked — no full text of the sourcecites [352] Raussendorf, 2001, Phys. Rev. Lett. source
• Disputed

  The Next Steps (p. 6) identifies this experiment as transferring a photon's polarization state using polarization-entangled photon pairs, not squeezed entangled states. The Results (p. 5) likewise report teleportation of photon polarization states. The cited paper therefore describes a different kind of demonstration from the one attributed to it here. (LLM, conf=0.90)

  Checked by a reasoning model — may be wrong.

  cites [353] Bouwmeester, 1997, Nature sourceExperimental — accuracy not yet measured
• Disputed

  The experimental description (page unavailable) says the EPR pair for teleportation is provided by photon path (k-vector) entanglement. The paper reports teleporting linearly and elliptically polarised states, not teleportation on squeezed entangled states. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  cites [354] Boschi, 1998, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [355] Furusawa, 1998, Science source
• Disputed

  The paper describes teleportation by entanglement swapping, but specifies that its experiment uses polarization-entangled photon pairs in Bell states (p. 2). That is a discrete-variable scheme, not teleportation on squeezed entangled states. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  cites [356] Jennewein, 2001, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Partly supported

  The paper reports high-fidelity teleportation through entanglement swapping (p. 1), so it supports the general point that teleportation was reported. But its experiment uses polarization-entangled photon pairs and Bell-state measurements (pp. 1, 3), not squeezed entangled states; that defining part of the attributed claim is unsupported. (LLM, conf=0.85)

  cites [357] Pan, 2002, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Disputed

  The experiment described in the paper (section labeled Abstract; page unavailable) teleports entangled states in a vacuum–one-photon qubit, not squeezed entangled states. It explicitly describes the states used as simple single-photon states prepared with a beam splitter. (LLM, conf=0.83)

  Checked by a reasoning model — may be wrong.

  cites [358] Lombardi, 2002, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Single-photon qubits have been teleported on atomic ensembles [363,364] such as Caesium atoms [365] or 87 Rb atoms [366][367][368], on a pair of trapped calcium ions [369] or diamond [370].”

What the sources say

• Partly supported

  The Experiment section describes teleporting a single-photon state across a 143 km free-space optical link. It does not report teleportation onto caesium or rubidium atoms, trapped calcium ions, or diamond; the receiving system uses another photon. No page numbers are available in our copy. (LLM, conf=0.85)

  cites [363] Ma, 2012, Nature sourceExperimental — accuracy not yet measured
• Disputed

  The 'Teleportation through one-link channel' section describes teleporting a photon's polarization state to another photon across a free-space optical link, not onto an atomic ensemble. The separate citations for caesium, rubidium, trapped ions and diamond are not attributed to this source. (LLM, conf=0.85)

  Checked by a reasoning model — may be wrong.

  cites [364] Yin, 2012, Nature sourceExperimental — accuracy not yet measured
• Partly supported

  The figure caption reports teleportation of single-photon qubits from a ground observatory to a satellite. The paper does not report teleportation onto caesium or rubidium ensembles, trapped calcium ions, or diamond, so it supports the general teleportation point but not the listed destinations. (LLM, conf=0.88)

  cites [365] Ren, 2017, Nature sourceExperimental — accuracy not yet measured
• Disputed

  The Introduction and Conclusion describe this paper’s experiment as continuous-variable teleportation of optical fields, using squeezed beams and coherent-state inputs. That is contrary to attributing to it teleportation of single-photon qubits on atomic ensembles, trapped calcium ions, or diamond. The passages provide section labels but no page numbers. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  cites [366] Zhang, 2003, Phys. Rev. A sourceExperimental — accuracy not yet measured
• ?Could not verify

  Our copy describes teleportation of optical-field quadratures and modulation sidebands of a bright beam (Abstract; page unavailable). Searches for atomic ensembles, caesium, rubidium, calcium ions, diamond, and single-photon qubits found no passage reporting the claimed teleportations. The paper’s different experimental system does not establish that those teleportations did not occur. (LLM, conf=0.75)

  cites [367] Bowen, 2003, Phys. Rev. A sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s Abstract reports teleportation of a coherent optical state and mentions earlier experiments with photonic qubits and atomic qubits separately. Neither that passage nor the additional passages searched for Caesium, 87Rb, trapped calcium ions, diamond, and atomic ensembles addresses teleporting single-photon qubits onto any of the listed systems. (LLM, conf=0.74)

  cites [368] Takei, 2005, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Since 2015, a number of alternative schemes have been proposed: driven BosonSampling, where the input photons are generated within the interferometer [585], BosonSampling with microwave photons [586] or squeezed states [587,588], one using Gaussian measurements and the symmetry of the evolution under time reversal [589,590], and one time-bin loop-based [150]”

What the sources say

• Disputed

  The citation [150] is attached to the time-bin loop-based scheme. The experimental-scheme description (p. 2) instead identifies this paper’s circuit as using spatial and polarization modes with integrated optical-fibre beam splitters, not a time-bin loop. The cited paper also predates the sentence’s “Since 2015” timeframe. (LLM, conf=0.84)

  Checked by a reasoning model — may be wrong.

  cites [585] Broome, 2013, Science sourceExperimental — accuracy not yet measured
• ?Could not verify

  Citation [150] is attached specifically to the time-bin loop-based scheme. The paper’s experimental description (p. 2) reports a three-photon experiment in a five-mode integrated photonic chip; searches for time bins and optical loops found no passage addressing a time-bin loop-based scheme. (LLM, conf=0.76)

  cites [586] Crespi, 2013, Nat. Photon. sourceExperimental — accuracy not yet measured
• Disputed

  The citation to this paper is attached specifically to the time-bin loop-based scheme. Instead, the paper’s Experiment section (p. 2) describes three photons entering a five-mode integrated waveguide circuit, and its optical-network description (p. 3) specifies spatial input and output modes, not a time-bin loop. The paper is also dated 2013, not since 2015. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  cites [587] Tillmann, 2013, Nat. Photon. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction discusses BosonSampling experiments and robustness to losses, while the Summary and Open Problems addresses photon loss in the network. Searches for the named alternative schemes found no passage in our copy discussing driven, microwave-photon, squeezed-state, Gaussian-measurement, or time-bin loop-based BosonSampling. (LLM, conf=0.74)

  cites [588] Aaronson, 2015, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“While, in fact, polarization encoding requires to resolve only two components, which can be done easily by means of waveplates and polarizing beam splitters, the number of OAM modes is potentially unbounded and as such challenging to characterize [68].”

What the sources say

• Partly supported

  The Results section says OAM offers an infinitely large Hilbert space, supporting the claim that the number of modes is potentially unbounded. The paper does not say that this makes OAM modes challenging to characterize; its detection scheme addresses a selected two-mode subspace. (LLM, conf=0.86)

  cites [68] Nape, 2017, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“Besides quantum communication, timebin encoding has been proposed as a suitable scheme also for quantum walks [146-148] and for photonic BosonSampling [149, 150] (see Section 3.2).”

What the sources say

• ?Could not verify

  The paper describes time-bin encoding for quantum communication and reports transmission of entangled photons over optical fiber (pp. 1, 4). Searches for quantum walks and photonic BosonSampling found no passage proposing time-bin encoding for either application. (LLM, conf=0.76)

  cites [146] Marcikic, 2004, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s main text describes a time-bin phase-encoding scheme for measurement-device-independent quantum key distribution. Searches for quantum walks and photonic BosonSampling found no passage addressing either proposed application, so our copy does not verify the claim. (LLM, conf=0.76)

  cites [147] Tang, 2016, Chin. Phys. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper discusses storing time-bin qubits and describes them as a resource for quantum communication and processing (Abstract section; page unavailable). Searches for quantum walks and photonic BosonSampling found no passage proposing time-bin encoding for either application, so our copy does not verify the attributed claim. (LLM, conf=0.74)

  cites [148] Gündoǧan, 2015, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The BosonSampling part of the citing sentence is the relevant attribution; quantum walks have separate citations. Our copy’s Introduction discusses time-bin encoding for communication and fundamental experiments, and its supplementary section discusses higher-dimensional time-bin states, but neither addresses BosonSampling. Searches for “BosonSampling” and “boson sampling” found no supporting passage. (LLM, conf=0.73)

  cites [149] Donohue, 2013, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  Section II describes time-bin qubits, and the Introduction discusses their use in long-distance quantum communication. Searches for quantum walks and photonic BosonSampling found no passage proposing time-bin encoding for either application; page numbers are unavailable in our copy. (LLM, conf=0.76)

  cites [150] Marcikic, 2002, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“At a fundamental level, OAM has enabled researches on optimal quantum cloning of OAM-encoded qubits [66,81] and photonic quantum walks in the orbital angular momentum states, with theoretical analyses [82,83] and experimental demonstrations [51,54,60].”

What the sources say

• Supported

  The Introduction and Experimental Scheme describe a proposed photonic quantum walk using OAM states as positions, and the Abstract calls it a proposed scheme. In the citing sentence, this paper supports the theoretical-analysis portion of the quantum-walk claim; the cloning and experimental-demonstration portions have separate citations. (LLM, conf=0.93)

  cites [66] Zhang, 2010, Phys. Rev. A source
• ?Not checked — no full text of the sourcecites [81] Forbes, 2016, Adv. Opt. Photonics source
• ?Not checked — no full text of the sourcecites [82] Zhao, 2017, Opt. Lett. source
• ?Could not verify

  The Results (Experimental demonstration; page unavailable) describe measurements of the moments of OAM superpositions, not cloning or photonic quantum walks. The Discussion (page unavailable) identifies the demonstration as a classical-optics experiment. Searches for quantum walks and cloning found no passage addressing the research attributed to this source. (LLM, conf=0.76)

  cites [83] Piccirillo, 2015, Nat. Commun. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [51] Kwiat, 1997, J. Mod. Opt. source
• ?Could not verify

  The Introduction describes OAM applications, and the Experimental implementation and Conclusions describe a time-mapping OAM spectrometer. None addresses optimal cloning of OAM-encoded qubits or photonic quantum walks; searches for those topics found no relevant passage in our copy. (LLM, conf=0.76)

  cites [54] Bierdz, 2013, New J. Phys. sourceExperimental — accuracy not yet measured
• Supported

  The citation is offered for an experimental demonstration of a photonic quantum walk in OAM states, not for quantum cloning. The Results sections on the quantum-walk protocol and experimental results describe an OAM-encoded walker and measurements after a six-step walk, alongside theoretical predictions. (LLM, conf=0.93)

  cites [60] Cardano, 2016, Nat. Commun. source

In the paper

“Several approaches for single-photon sources have been developed in the last decades (see Table 2) [172][173][174][175].”

What the sources say

• ?Could not verify

  The passages labeled Abstract discuss approaches to producing continuous-variable cluster states, not single-photon sources. Searches for single-photon sources and generation found no passage addressing the cited claim; the paper’s mention of photon counting concerns detection, not source development. No page numbers are supplied in our copy. (LLM, conf=0.76)

  cites [172] Menicucci, 2010, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction discusses several methods for constructing continuous-variable cluster states, not approaches for single-photon sources. The Discussion likewise concerns cluster-state generation; searches for “single-photon sources” and “single photon source generation” found no passage addressing the attributed claim. (LLM, conf=0.78)

  cites [173] Menicucci, 2011, Phys. Rev. A sourceExperimental — accuracy not yet measured
• ?Could not verify

  The main text discusses approaches to generating continuous-variable cluster states and notes probabilistic photon-pair generation, but it does not discuss the development of several approaches to single-photon sources. A search for single-photon sources and single-photon generation found no passage addressing that claim; no page number is available in our copy. (LLM, conf=0.76)

  cites [174] Yokoyama, 2013, Nat. Photon. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s Abstract describes generating multipartite entanglement in optical frequency-comb modes, not approaches for single-photon sources. Searches for “single-photon sources” and “single photon source generation heralded photons” found no passage in our copy addressing the cited claim. (LLM, conf=0.76)

  cites [175] Chen, 2014, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Polarization encoding has always played an important role in a significant number of investigations in quantum information, ranging from quantum simulation [16,17] to quantum computation [18][19][20][21][22] and communication [23,24].”

What the sources say

• Supported

  This citation appears in the quantum-computation group of references. The section on polarization and spin representations (p. 10) describes encoding quantum information in optical polarization variables, and the experimental dense-coding section (p. 59) reports a conditional quantum gate that used polarization-mode encoding. Together, these support the cited example of polarization encoding in quantum information processing. (LLM, conf=0.84)

  cites [16] Braunstein, 2014, Rev. Mod. Phys. source
• ?Could not verify

  The Introduction and Conclusions discuss polarization as a component of light-beam angular momentum, not polarization encoding in quantum information. Searches for quantum computation and for quantum simulation, computation, and communication found no passage addressing those applications. (LLM, conf=0.76)

  cites [17] Martínez-Herrero, 2010, Opt. Express sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [18] Kok, 2010 source
• Partly supported

  Section 3.3 (p. 33) identifies quantum information as a potential application of polarization-related spin-direction locking. It does not establish that polarization encoding has played an important role across quantum simulation, computation, and communication; the passage describes a potential application, not that broader history. (LLM, conf=0.82)

  cites [19] Bliokh, 2015, Phys. Rep. sourceExperimental — accuracy not yet measured
• Partly supported

  The introduction (p. 1) identifies polarization as a photon degree of freedom, and the Concluding remarks (p. 17) say spin degrees of freedom promise applications in optical communications and quantum information processing. The paper does not establish that polarization encoding has already played an important role across quantum simulation, computation, and communication; it frames the applications chiefly as prospective and does not address simulation. (LLM, conf=0.78)

  cites [20] Bliokh, 2015, Nat. Photon. sourceExperimental — accuracy not yet measured
• Partly supported

  The Introduction describes applications of mutually unbiased bases in quantum key distribution and quantum state estimation, and §2.1 describes measurements on polarization qubits in optical experiments. This supports the broad point that polarization is important in quantum-information work, but the paper does not establish the claimed range extending to quantum simulation and computation. (LLM, conf=0.82)

  cites [21] Hou, 2015, Opt. Express sourceExperimental — accuracy not yet measured
• Supported

  The paper describes a quantum-walk simulation using two-photon polarization-entangled states (main text, pp. 3–4). This supports its citation as an example of polarization-based quantum simulation; the sentence cites other works for computation and communication. (LLM, conf=0.91)

  cites [22] Sansoni, 2012, Phys. Rev. Lett. source
• Supported

  This paper is cited among the quantum-simulation examples, not for the separately cited computation and communication examples. Its Abstract describes using polarisation entanglement in a photonic chip to simulate particle statistics, so it supports the part of the sentence attributed to it. (LLM, conf=0.91)

  cites [23] Matthews, 2013, Sci. Rep. source
• Supported

  The citation is attached to quantum computation, not to the separate examples of simulation or communication. In “Experimental One-Way Quantum Computing” (pp. 3, 7), the paper identifies photon polarization as its physical qubits and reports implementing quantum circuits and a search algorithm with a four-photon cluster state. (LLM, conf=0.92)

  cites [24] Walther, 2005, Nature source

In the paper

“In this direction, a spectrum analyzer is a device capable to measure the instantaneous power and phase distributions of OAM components [48,52,[69][70][71][72][73][74].”

What the sources say

• ?Could not verify

  The indexed passages (labeled Abstract; page not provided) describe polarization-based quantum key distribution and measurements of photon states. Searches for an OAM spectrum analyzer and for measurements of OAM-mode power and phase found no passage addressing the claimed capability. (LLM, conf=0.76)

  cites [48] Chen, 2006, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Experiment section (page unavailable) describes CCD-based polarization tomography and reconstruction of a beam’s polarization pattern, not an OAM spectrum analyzer. Searches for instantaneous power and phase measurements of OAM components found no passage in our copy addressing that capability. (LLM, conf=0.77)

  cites [52] Cardano, 2012, Appl. Opt. sourceExperimental — accuracy not yet measured
• Partly supported

  The Results and Discussion section (page unavailable) explains how interference images yield the complex coefficients of OAM components, supporting measurement of their power and phase. It says full decomposition requires four images and interferometric stability; it does not establish that the distributions are measured instantaneously. (LLM, conf=0.86)

  cites [69] D’Errico, 2017, Optica sourceExperimental — accuracy not yet measured

In the paper

“Path-encoded qubits, as well as qudits [119], are perfectly fit for photonic integrated circuits, since waveguide arrays inherently implement a spatial separation and coupling between modes is easily accomplished with directional couplers.”

What the sources say

• ?Could not verify

  Section IV (Information Encoding; page unavailable) distinguishes path from the polarization degree of freedom used to encode the paper’s qubits. Searches for qudits, photonic integrated circuits, waveguide arrays, and directional couplers found no passage addressing the cited claim. Section VIII discusses limitations of OAM-based networks, not the suitability of path-encoded states for integrated circuits. (LLM, conf=0.75)

  cites [119] Garcia-Escartin, 2012, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“Two methods can be adopted to circumvent the issue of noisy channels: to increase the resilience of a protocol to losses and noise [380][381][382] (two-way classical communications), or to decrease their influence by encoding information in immune states (decoherence-free subspaces, DFS), for both quantum computation [383] and quantum communication tasks [384].”

What the sources say

• Partly supported

  The main text says the teleportation fidelity is insensitive to photon losses, supporting the loss-resilience part of the clause to which this paper is cited. The Figure 1 description says Bell-state measurement results are sent from Alice to Bob over a classical channel; it does not describe two-way classical communication as the source of resilience, or establish resilience to channel noise generally. The decoherence-free-subspace method is cited separately in the citing sentence. (LLM, conf=0.86)

  cites [380] Chen, 2008, Nat. Phys. sourceExperimental — accuracy not yet measured
• Partly supported

  The Abstract describes teleportation as an alternative to direct transfer over lossy channels, and the Efficiency of the protocol section says successful transfers are heralded. This supports the loss-resilience part of the cited clause, but our copy does not establish the claimed use of two-way classical communication or general resilience to channel noise. The DFS clause is cited to other sources, not this paper. (LLM, conf=0.82)

  cites [381] Nölleke, 2013, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Partly supported

  The Experimental details (page unavailable) describe heralded state preparation, a trigger for successful teleportation, and classical measurement results sent to node B. These support the use of classical signaling in a heralded protocol, but the paper does not establish the cited claim that two-way classical communication increases resilience to channel losses and noise. The decoherence-free-subspace alternative is attributed to other citations, not this paper. (LLM, conf=0.79)

  cites [382] Bao, 2012, Proc. Natl Acad. Sci. USA sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [383] Riebe, 2004, Nature source
• ?Could not verify

  The citation appears to support using decoherence-free subspaces for quantum communication. The Results (Photon-to-phonon teleportation scheme; Experimental realization of teleportation) describe teleportation and measured noise, but do not describe encoding information in decoherence-free subspaces to protect it from noisy channels. Searches for decoherence-free subspaces and protected encoding found no passage addressing that method. (LLM, conf=0.74)

  cites [384] Hou, 2016, Nat. Commun. sourceExperimental — accuracy not yet measured

In the paper

“Importantly, their scheme was also alignmentfree, i.e. with no need for a shared reference frame, and dense coding quantum teleportation entanglement swapping entanglement purification decoherence-free subspaces insensitive to phase fluctuations in the interferometer.”

What the sources say

• ?Could not verify

  The Introduction and Experimental Results discuss polarization-dependent propagation in waveguide arrays; the Conclusion describes a compact polarizing beam splitter. Searches for an alignment-free scheme, a shared reference frame, and interferometer phase fluctuations found no passage addressing the attributed claim about Chen et al. (LLM, conf=0.74)

  cites [42] Rojas-Rojas, 2014, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“Other significant features reported in their work were the capability to extend the scheme to multipartite states, thanks precisely to the state-independence, and its applicability also with single-mode fibers.”

What the sources say

• ?Could not verify

  The Introduction and Conclusions describe Khalique and Sanders’s entanglement-swapping model, not features of Yamamoto et al.’s work. Searches for Yamamoto, multipartite states, state-independence, and single-mode fibers found no passage in our copy addressing the attributed capabilities. (LLM, conf=0.76)

  cites [388] Khalique, 2014, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“On the above platforms, photonic circuits can be implemented [243,244] according to linear-optical interferometric schemes capable to perform arbitrary unitary evolutions [245,246], or designs optimized for Fourier and Hadamard transformations [241, 244].”

What the sources say

• Partly supported

  The Experimental results section (page unavailable) describes a silicon photonic circuit using cascaded Mach–Zehnder interferometers and phase shifters to prepare and measure quantum states. This supports the citation as an example of an implemented interferometric circuit, but our copy does not identify its design as optimized for Fourier or Hadamard transformations. The arbitrary-unitary claim is attached to different citations. (LLM, conf=0.80)

  cites [243] Ding, 2017, npj Quantum Inf. sourceExperimental — accuracy not yet measured
• Partly supported

  The processor description (p. 3) supports citing this paper as an example of an implemented photonic interferometric circuit: it reports 88 Mach–Zehnder interferometers and programmable phase shifters. The Discussion (p. 6) discusses arbitrary unitary operators as a possibility using embedded circuits, but our copy does not report a design optimized for Fourier or Hadamard transformations, the other part of the sentence citing this source. (LLM, conf=0.85)

  cites [244] Harris, 2017, Nat. Photon. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [245] Taballione, 2018, 8×8 programmable quantum photonic processor based on silicon nitride waveguides source
• Partly supported

  Section VI (page not provided) describes integrated photonic circuits and says a spatial Hadamard gate can be realized with a 50/50 directional coupler. The cited paper does not substantiate the Fourier-transform design attributed to it. The arbitrary-unitary claim is attached to different citations in the citing sentence. (LLM, conf=0.85)

  cites [246] Tanzilli, 2012, Laser Photonics Rev. sourceExperimental — accuracy not yet measured
• Partly supported

  The Introduction and Section 8 describe integrated SiN photonic circuits and characterize a linear-optical CNOT circuit, supporting the citation for implementing photonic circuits. The paper does not describe designs optimized for Fourier or Hadamard transformations, which the citing sentence also attributes to this source. Its Section 4 statement that beam splitters and phase shifters can generate any unitary operation is relevant background, but the citing sentence assigns that point to different references. (LLM, conf=0.85)

  cites [241] Poot, 2016, Opt. Express sourceExperimental — accuracy not yet measured

In the paper

“A solution to this issue consists in exploiting hyperentangled photons [44], leading to complete BM demonstrations in orbital angular momentum/polarization [324], momentum/polarization [325] and time/polarization [326,327].”

What the sources say

• ?Could not verify

  The OAM/polarization demonstration is the part of the citing sentence associated with this source; the momentum/polarization and time/polarization demonstrations have separate citations. The paper reports transferring polarization entanglement to OAM and verifying it with an entanglement witness (Abstract; Additional information), but the passages searched for complete Bell-state measurement do not describe such a demonstration. (LLM, conf=0.78)

  cites [44] Fickler, 2012, Science sourceExperimental — accuracy not yet measured
• ?Could not verify

  The citation to this paper is attached to the time/polarization Bell-measurement demonstration. Section 2.4 describes a plug-and-play quantum key distribution system, not hyperentangled photons or a complete Bell measurement. Searches for those terms and for time/polarization found no passage addressing the attributed demonstration. (LLM, conf=0.75)

  cites [324] Stucki, 2011, New J. Phys. sourceExperimental — accuracy not yet measured
• ?Could not verify

  Citation [44] is attached to exploiting hyperentangled photons as a solution; the separate demonstration claims have other citations. Our copy’s Technical introduction (§1.1; page unavailable) describes a Faraday–Michelson interferometer for phase-coded quantum key distribution, not hyperentangled photons or complete Bell measurements. Searches for those terms found no passage addressing the attributed solution. (LLM, conf=0.77)

  cites [325] Xu, 2009, Chin. Sci. Bull. sourceExperimental — accuracy not yet measured

In the paper

“To this aim, in 2014 Bell et al. reported the experimental demonstration of a graph-state quantum secret sharing protocol [605], whose implementation was subsequently verified using the scheme in Ref. [604]”

What the sources say

• ?Could not verify

  The citation to this paper, [604], is attached to the claim that a scheme verified the secret-sharing implementation, not to Bell et al.’s demonstration [605]. The Abstract and Conclusions describe Gaussian Boson Sampling, and searches for graph-state secret sharing and verification found no passage in our copy addressing that claim. Page numbers were not available. (LLM, conf=0.76)

  cites [605] Hamilton, 2017, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [604] Peropadre, 2016, Phys. Rev. Lett. source

In the paper

“Furthermore, the scalability of parametric down-conversion sources and the relevance of non-ideal detectors' efficiencies have been addressed in Ref. [579] and investigated experimentally in 2015 with the Scattershot implementation [580,581]”

What the sources say

• Partly supported

  The Boson sampling section says parametric-downconversion sources scale poorly and describes scattershot sampling as an alternative using many sources. It also notes a scattershot implementation, but does not address non-ideal detector efficiencies specifically (searched: detector efficiency). The citing sentence assigns the 2015 experimental investigation to separate references, not to this source. (LLM, conf=0.87)

  cites [579] Harrow, 2017, Nature sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Abstract and Introduction (page numbers unavailable) address the computational complexity of the permanent, not optical sources or detectors. Searches for parametric down-conversion, detector efficiency, and Scattershot found no relevant passage in our copy. In the citing sentence, the experimental Scattershot claim is attached to [580,581], rather than [579]. (LLM, conf=0.78)

  cites [580] Valiant, 1979, Theor. Comput. Sci. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [581] Scheel, 2008, Acta Phys. Slovaca source

In the paper

“In 2016, further improvements led McCutcheon et al. to a verification of multipartite entanglement for photonic quantum networks, adopting two single-photon sources similar to Ref. [605] to produce three-and four-photon polarization encoded states [606]”

What the sources say

• ?Not checked — no full text of the sourcecites [606] Kruse, 2018, A detailed study of gaussian boson sampling source
• ?Could not verify

  The Introduction and Conclusions discuss Gaussian boson sampling and photonic inputs, not McCutcheon et al.’s entanglement experiment. Searches for McCutcheon, multipartite entanglement, and three- and four-photon polarization-encoded states found no passage addressing the attributed claim. (LLM, conf=0.76)

  cites [605] Hamilton, 2017, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Notwithstanding, two approaches exist to circumvent these issues: reducing the transmission loss using free-space communication [43,96,105,348,350,351,393-399] and decoherencefree subspaces [42,116,385,386,[388][389][390][391], or employing quantum repeaters.”

What the sources say

• ?Could not verify

  The discussion of telecom networks (p. 2) and the conclusion on reducing losses in integrated circuits (p. 5) do not address free-space communication, decoherence-free subspaces, or quantum repeaters as ways to overcome transmission loss. Searches for those approaches and for transmission loss found no supporting passage in our copy. (LLM, conf=0.76)

  cites [43] Bonneau, 2012, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Partly supported

  The Abstract says quantum repeaters are needed for long-range quantum communication and discusses transmission through the atmosphere. It does not say that free-space communication reduces transmission loss or identify decoherence-free subspaces as an approach to that problem. (LLM, conf=0.85)

  cites [96] Goyal, 2014, Sci. Rep. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction (page unavailable) discusses photon loss during orbital-angular-momentum imprinting and a method for generating hybrid entangled states, not transmission loss during communication. Searches for free-space communication, decoherence-free subspaces, and quantum repeaters found no passage in our copy supporting the approaches attributed to this paper. (LLM, conf=0.75)

  cites [105] Jabir, 2017, Sci. Rep. sourceExperimental — accuracy not yet measured
• Partly supported

  The Conclusion and outlook (page unavailable) identifies encoding qubits into decoherence-protected subspaces as a possible improvement and describes entanglement distillation as a way to counteract decoherence in extended networks. It does not say that such subspaces reduce transmission loss, or present free-space communication and quantum repeaters as the two approaches claimed. (LLM, conf=0.84)

  cites [348] Kalb, 2017, Science sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s discussion of teleportation and fault-tolerant quantum gates (p. 1) does not address the proposed ways to reduce transmission loss. Searches for free-space communication, decoherence-free subspaces, and quantum repeaters found no passage in our copy that evaluates those approaches. (LLM, conf=0.76)

  cites [350] Gottesman, 1999, Nature sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Abstract describes a multi-port quantum teleportation protocol, and the concluding passage discusses its asymptotic fidelity and use as a programmable processor (page numbers unavailable). Searches for transmission loss, free-space communication, decoherence-free subspaces, and quantum repeaters found no passage addressing the claimed approaches. (LLM, conf=0.75)

  cites [351] Ishizaka, 2008, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Partly supported

  The introductory passage (labelled Abstract; page unavailable) identifies entanglement swapping as a key element of long-distance quantum communication using quantum repeaters. The conclusion (also labelled Abstract) discusses transmission loss, but our copy does not describe free-space communication or decoherence-free subspaces as ways to reduce it. (LLM, conf=0.82)

  cites [393] Takeda, 2015, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Abstract discusses extending secure QKD distance by tolerating higher bit-error rates, and Section III discusses entanglement purification over a noisy channel. Neither passage addresses reducing transmission loss through free-space communication or decoherence-free subspaces, or using quantum repeaters; searches for those terms found no supporting passage in our copy. (LLM, conf=0.76)

  cites [394] Gottesman, 2003, IEEE Trans. Inf. Theory sourceExperimental — accuracy not yet measured
• ?Could not verify

  The main text discusses extending the range of quantum communication through entanglement distillation, but it does not describe the claimed approaches of free-space communication, decoherence-free subspaces, or quantum repeaters. Searches for those approaches and for transmission loss found no passage in our copy that establishes the attributed claim. (LLM, conf=0.73)

  cites [395] Xiang, 2010, Nat. Photon. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s Abstract discusses transmission loss and heralded noiseless amplification as a way to mitigate it. Searches for free-space communication, decoherence-free subspaces, and quantum repeaters found no passage in our copy describing the two approaches attributed to this source. (LLM, conf=0.76)

  cites [396] Kocsis, 2013, Nat. Phys. sourceExperimental — accuracy not yet measured

In the paper

“Soon after its introduction, in 2013 four experimental demonstrations with n = 3 photons were re-ported [240, 567-569]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [240] Flamini, 2015, Light Sci. Appl. source
• ?Could not verify

  The Abstract and section 4 discuss environment-assisted quantum transport, not BosonSampling experiments. Searches for BosonSampling and three-photon demonstrations found no passage addressing the reported 2013 experiments. (LLM, conf=0.78)

  cites [567] Rebentrost, 2009, New J. Phys. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s ‘B. Entanglement dynamics’ section discusses excitations in a light-harvesting complex, while ‘A. Destructive interference suppression’ uses a single-photon interferometer as an illustration. Searches for BosonSampling and four three-photon demonstrations in 2013 found no passage addressing the claim; no page numbers were available in our copy. (LLM, conf=0.78)

  cites [568] Caruso, 2009, J. Chem. Phys. sourceExperimental — accuracy not yet measured
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [569] Caruso, 2011, Phys. Rev. A source

In the paper

“The computational complexity for exact classical BosonSampling was given in the same year in Ref.[565] by Clifford and Clifford (CC): state-ofthe-art sampling time is equal, within a factor of 2, to computing the permanent of one single scattering matrix[566]”

What the sources say

• ?Not checked — no full text of the sourcecites [565] Abouraddy, 2012, Phys. Rev. A source
• ?Could not verify

  The cited paper’s experimental setup (p. 1) concerns light propagation in disordered optical waveguide lattices. Searches for BosonSampling, classical sampling time, matrix permanents, and Clifford and Clifford found no passage addressing the factor-of-two comparison attributed to citation [566]. (LLM, conf=0.78)

  cites [566] Lahini, 2008, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“The second generation of QRs (II) employs (i) HEG to reduce the deterioration induced by losses and (ii) quantum error correction (QEC) to correct gate errors [414,415].”

What the sources say

• ?Not checked — no full text of the sourcecites [414] Briegel, 1998, Phys. Rev. Lett. source
• Supported

  The Results section, under “Three generations of quantum repeaters,” states directly that second-generation QRs use HEG to suppress loss errors and QEC to correct operation errors. “Gate errors” is a reasonable paraphrase of operation errors here. (LLM, conf=0.95)

  cites [415] Muralidharan, 2016, Sci. Rep. source

In the paper

“Further results were reported also with continuous-time QWs, with the observation of two-photon quantum correlations [17,532,535,538], quantum Rabi model [35], floquet topological insulators [536], growth of entanglement in spin chains [529], Majorana dynamics [539], Fano interference [540] and Bloch oscillations [541].”

What the sources say

• ?Could not verify

  The Introduction and Conclusions discuss the angular momentum of nonparaxial light beams, not continuous-time quantum walks. Searches for the listed quantum-walk results, including Bloch oscillations, found no passage addressing them in our copy. (LLM, conf=0.76)

  cites [17] Martínez-Herrero, 2010, Opt. Express sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [532] Buluta, 2009, Science source
• ?Not checked — no full text of the sourcecites [535] Gräfe, 2016, J. Opt. source
• Partly supported

  The passage labeled Abstract (page not provided) reports that an earlier study [14] observed quantum correlations during a simultaneous two-particle walk. It does not identify that result as a continuous-time, two-photon walk; this paper’s own experiment is a single-photon, discrete quantum walk. (LLM, conf=0.84)

  cites [538] Schreiber, 2011, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• Partly supported

  The paper’s quantum-state-tomography passage reports measured polarization correlations between two photons as a signature of entanglement. It does not report continuous-time quantum walks, so it supports the two-photon-correlation portion of the cited claim but not the setting attributed to it. (LLM, conf=0.85)

  cites [35] Müller, 2014, Nat. Photon. sourceExperimental — accuracy not yet measured
• Partly supported

  The citation is attached to the two-photon correlations item, not to the later results in the sentence. The Conclusions report observed quantum correlations in photon walks and, separately, a two-photon continuous-time walk. Our copy does not explicitly say that the observed photon correlations were in a two-photon continuous-time walk. (LLM, conf=0.78)

  cites [536] Venegas-Andraca, 2012, Chapter: Quantum walks: a comprehensive review sourceExperimental — accuracy not yet measured

In the paper

“Topological transitions have been also the focus of a recent study carried out with orbital angular momentum encoding [54].”

What the sources say

• ?Could not verify

  The Introduction describes an OAM-to-time mapping study, while §4.3.2 discusses topological charge error. Neither passage addresses a study focused on topological transitions; searches for “topological transitions” and “orbital angular momentum encoding topological phase transitions” found no such passage in our copy. (LLM, conf=0.76)

  cites [54] Bierdz, 2013, New J. Phys. sourceExperimental — accuracy not yet measured

In the paper

“Current sources can fullfil only a limited number of the above requirements, while keeping very high performances for specific applications.”

In the paper

“Photons naturally fit this quantum revolution [5] as an effective system to process information: they propagate fast, do not interact with the environment and can be easily manipulated.”

What the sources say

• Not checked yetcites [5] Ladd, 2010, Nature source

In the paper

“In the so-called tuning condition, a qplate implements the transformations QP L / R |l = L / R |l ± 2q , i.e. it flips the qubit polarization in the circular basis and shifts the OAM of a quantity ∆l = ±2q.”

In the paper

“Indeed, in the limit of paraxial waves of Eq.( 1), the SAM component interacts with anisotropic transparent systems such as birefringent crystals, which are consequently widely employed for polarization manipulation.”

In the paper

“The ease and versatility of SLMs can be exploited in many applications ranging from optical communication [55,56] to holography-based optical tweezers [57,58].”

What the sources say

• Not checked yetcites [55] D’Ambrosio, 2016, Photonic high dimensional systems and their applications in fundamental quantum mechanics, quantum information and quantum communication
• ?Not checked — no full text of the sourcecites [56] Willner, 2015, Adv. Opt. Photon. source
• Not checked yetcites [57] Cardano, 2015, Sci. Adv. source
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [58] Gruneisen, 2011, New J. Phys. source

In the paper

“Photons are by far the most suitable physical system to implement flying qubits to deliver information: they experience negligible decoherence through free space or optical fibers, they allow a high spatial control, and the technology for linear-optical devices to manipulate qubits is accessible and at an advanced stage [316,317].”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [316] Schuck, 2016, Nat. Commun. source
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [317] Beyer, 2015, Waveguide-coupled superconducting nanowire single-photon detectors source

In the paper

“More recently, in 2005 Jiang et al. reported a test of DFS against collective noise on polarization and phase with four two-qubit states again from PDC [386]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [386] Gao, 2013, Nat. Commun. source

In the paper

“Similarly to teleportation, photons offer a convenient solution for an implementation of the scheme.”

In the paper

“In 2004, for instance, a single-mode discrete teleportation scheme using a quantum dot single-photon source has been demonstrated [345].”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [345] Sheng, 2015, Sci. Rep. source

In the paper

“Si-based devices present a very high refractive index that allows for reduced-size circuits and that is suitable for nonlinear processes.”

In the paper

“Entanglement swapping has also been tested with discrete [377,378] and continuous variables [354], or even with a hybrid approach [379].”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [377] Krauter, 2013, Nat. Phys. source
• ?Not checked — no full text of the sourcecites [378] Barrett, 2004, Nature source
• Not checked yetcites [354] Boschi, 1998, Phys. Rev. Lett. source
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [379] Sherson, 2006, Nature source

In the paper

“Due to the very low energy of a single photon (∼ 10 -19 J), a PNR detector requires high gain and low noise to be able to discriminate the correct number.”

In the paper

“Entanglement purification is a key ingredient also in quantum computation, such as for quantum errorcorrection protocols, in quantum cryptography and quantum teleportation.”

In the paper

“One further requirement for a reliable and practical quantum communication is the capability of storing information for subsequent uses.”

In the paper

“While the probability of success is 50% lower than the one with CNOT gates, the quality of these optical elements allow for a purification with much higher precision and control.”

In the paper

“Si-based platforms, including silicon (Si), silicon nitride (SiN) and silicon carbide (SiC), are advanced platforms whose development benefits from the know-how given by electronics technologies [235].”

What the sources say

• Not checked yetcites [235] Crespi, 2011, Nat. Commun. source

In the paper

“Si-based SPADs exhibit good performances with visible light but still suffer in the infrared window, due to the incompatibility between good IR absorption and low-noise.”

In the paper

“The original approach was based on CNOT operations [328]; few years later a simpler solution was introduced [329] and verified experimentally [330] based on only polarizing beam splitters.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [329] Hughes, Network-centric quantum communications with application to critical infrastructure protection
• ?Not checked — no full text of the sourcecites [330] Nielsen, 2010 source

In the paper

“To bridge the gap between discrete and continuous variables, a hybrid approach has been recently proposed and tested [360].”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [360] Xia, 2017, Quantum Sci. Technol. source

In the paper

“Future implementations of quantum repeaters in optical networks will require active synchronization of the single-photon sources involved in the exchange of information between the various nodes.”

In the paper

“The first experimental demonstration of DFS communication was reported in 2000 by Kwiat et al. [385], where the authors induced a controllable collective decoherence on an entangled photon pair generated by spontaneous parametric down-conversion (PDC) and observing that, as predicted, one specific entangled state was immune to decoherence.”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [385] Olmschenk, 2009, Science source

In the paper

“Limitations of the SoS technique are the need for a mask and the restriction to one polarization, due to the birefringence induced by the rectangular cross-sections.”

In the paper

“Limitations are the low mode-matching with optical fibers and the relatively high propagation losses.”

In the paper

“This technique does not require the adoption of masks, thus reducing the complexity of fabrication, and allows for arbitrary 3D geometries.”

In the paper

“Integrated optical circuits are built upon architectures of directional couplers, with additional geometries to account for deformationinduced phase shifts.”

In the paper

“First demonstrations of entanglement swapping go back to 1998 by Pan et al. [375], to 2001 by Jennewein et al. and to 2002 by Sciarrino et al., all based on parametric down-conversion sources.”

What the sources say

• Not checked yetcites [375] Kimble, 2008, Nature source

In the paper

“Future quantum networks, engineered to deliver quantum information between distant nodes on the globe, are the sought-after goal underlying most of the investigations described above (see Fig. 4).”

In the paper

“Entanglement is an essential physical resource to this aim [318] and, as such, it is necessary to protect it during the transfer.”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [318] Shainline, 2017, Opt. Express source

In the paper

“One widely adopted material for the integration remains fused silica thanks to its numerous benefits: low propagation losses, low birefringence, operation from visible to infrared, good coupling efficiency with single mode fibers and low temperature dependence.”

In the paper

“Detecting photons with high probability and reliability is a key requirement for most tasks, often representing a bottleneck for the overall efficiency of an apparatus.”

In the paper

“Additional features of their work were the use of backward propagation of coherent light in combination with single-photon states, and the violation of the Clauser-Horne-Shimony-Holt inequality [316] to prove nonlocality in the transmission.”

What the sources say

• ?Not checked — no full text of the sourcecites [389] Pan, 1998, Phys. Rev. Lett. source
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [316] Schuck, 2016, Nat. Commun. source

In the paper

“however, a good solution to this drawback could be multiplexing in one of the degrees of freedom (see Section 1.1) to increase the transmission rate.”

In the paper

“lattices subject to external gradient forces exhibit a characteristic periodic oscillation between spreading and localization of the wave packet, the so-called Bloch oscillations, which have been observed experimentally in photonic platforms [524,541,[554][555][556]”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [524,541,[554][555][556]

In the paper

“Recently the implementation of a lossy BosonSampling experiment has been reported [595]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [595] Rohde, 2012, Phys. Rev. A source

In the paper

“The idea here is to create entanglement between adjacent nodes and to use teleportation to exchange information.”

In the paper

“In addition, errors can occurr all along the transmission due to imperfect gates or measurements, without the possibility of duplicating quantum states deterministically [316] and with conditions much more sensitive than in the classical case.”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [316] Schuck, 2016, Nat. Commun. source

In the paper

“The key resource for its fulfillment is pro- blind quantum computing free-space QKD quantum repeater fiber-based QKD vided by quantum entanglement, at the core of quantum dense coding, teleportation, entanglement purification and entanglement swapping.”

In the paper

“recently BosonSampling was shown to be equivalent to short-time evolutions of n excitations in a XY model of 2n spins [586]”

What the sources say

• Not checked yetcites [586] Crespi, 2013, Nat. Photon. source

In the paper

“Indeed, analytical solutions for quantum many-body problems are available only for the simplest systems, thus making simulations necessary and heavily based on classical techniques such as the Born-Oppenheimer or Hartree-Fock approximations, the density-functional theory or even machine learning [622]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [622] Pappa, 2012, Phys. Rev. Lett. source

In the paper

“The approach adopted in the latter work consisted in encoding the state of the molecule on single-photon polarization qubits, simulating its evolution in the Born-Oppenheimer approximation and estimating the energy E of its eigenstates |ψ using the quantum phase estimation (QPE) algorithm [624], since e iEt/ |ψ = e i2πφ |ψ .”

What the sources say

• Not checked yetcites [624] McCutcheon, 2016, Nat. Commun. source
• Not checked yetcites [630] Agresti, 2017, Pattern recognition techniques for boson sampling validation

In the paper

“Currently there exist several protocols to validate BosonSampling, most of which have already been successfully demonstrated experimentally [122,149,241,474,516,581,582,595,[609][610][611][612][613]]”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [122,149,241,474,516,581,582,595,[609][610][611][612][613]

In the paper

“Very recently, a new quantum approach based on variational methods and phase estimation was introduced [634], and experimentally tested, to approximate eigenvalues for ground and excited states.”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [634] Dittel, 2018, Phys. Rev. Lett. source

In the paper

“The belief in this quantum approach was indeed supported in the 90's by the first efficient quantum algorithms [316], which were rapidly followed by breakthrough discoveries applicable to quantum chemistry [3,624]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [316] Schuck, 2016, Nat. Commun. source
• ?Not checked — no full text of the sourcecites [3] Lloyd, 1996, Science source
• Not checked yetcites [624] McCutcheon, 2016, Nat. Commun. source

In the paper

“First experimental demonstrations in bulk optics were reported in 2009 for the simulation of anyons, fractional-statistics particles responsible for the fractional quantum Hall effect [628,629] and for the calculation of the energy spectrum of a hydrogen molecule [630]”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [628] Viggianiello, 2017, Optimal photonic indistinguishability tests in multimode networks source
• ?Not checked — no full text of the sourcecites [629] Bentivegna, 2014, Int. J. Quantum Inf. source
• Not checked yetcites [630] Agresti, 2017, Pattern recognition techniques for boson sampling validation

In the paper

“An efficient certification protocol for photonic state preparation was also introduced theoretically [614], allowing to discriminate relevant classes of Fock states and Gaussian/non-Gaussian pure states.”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [614] Morimae, 2014, Phys. Rev. Lett. source