The DOI matches its Crossref record; 43 of the 52 references it cites were found in a registry or an index, and 9 are not checked yet; none of the 18 sources its claims cite is checked for support yet.
Elementary gates for quantum computation
Open accessAbstract
We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,x\ensuremath{\bigoplus}y)] is universal in the sense that all unitary operations on arbitrarily many bits n [U(${2}^{\mathit{n}}$)] can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical and of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.
Checked 2026-10-06 · 9 references not checked yet
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper proves that all one-bit quantum gates together with the two-bit exclusive-or gate are universal for quantum computation, and derives explicit gate constructions and bounds for generalized Toffoli and arbitrary unitary operations. It gives polynomial-size constructions for many important gates, including Θ(n²) basic operations for general ∧_{n−1}(U) gates and Θ(n³4ⁿ) two-bit gates for arbitrary n-bit unitaries.
Key findings
- The set consisting of all one-bit gates U(2) and the two-bit XOR gate is universal: every unitary operation on n bits, U(2ⁿ), can be expressed as a composition of these gates.
- A ∧₁(U) gate can be simulated by at most six basic gates: four one-bit gates and two XOR gates (Corollary 5.3). A ∧₂(U) gate can be simulated by at most sixteen basic gates: eight one-bit gates and eight XOR gates (Corollary 6.2).
- For n ≥ 7, a ∧_{n−2}(σ_x) gate can be simulated by 8(n−5) three-bit Toffoli gates, or by 48n−204 basic operations (Corollary 7.4).
- General ∧_{n−1}(U) gates can be simulated in Θ(n²) basic operations, specifically 48n² + O(n) (Corollary 7.6), with an Ω(n) lower bound for nonscalar ∧_{n−1}(U) (Lemma 7.7). Approximation within ε is possible in Θ(n log(1/ε)) basic operations (Lemma 7.8).
- Special cases are more efficient: for W ∈ SU(2), ∧_{n−2}(W) can be simulated in Θ(n) basic operations (Corollary 7.10), and with one fixed workspace bit, general ∧_{n−2}(U) also takes Θ(n) basic operations (Corollary 7.12).
- Any unitary operator on n bits can be simulated exactly using Θ(n³4ⁿ) two-bit gates and no work bits, via a Reck-type decomposition (Section 8).
Methods
- Theoretical quantum gate-array formalism: defines ∧_m(U) gates, Toffoli gates, and the two-bit XOR gate, then constructs networks from basic operations consisting of one-bit gates ∧₀(U) and the XOR gate ∧₁(σ_x).
- Proofs use matrix factorizations of 2×2 unitaries, SU(2) identities, recursive gate constructions, grey-code sequences, gate merging, phase-congruence arguments, and asymptotic recurrence/lower-bound analysis.
- No physical experiments are reported; the paper mentions numerical study as evidence that some constructions are minimal for small cases (Section 8).
Limitations
- The paper explicitly does not address physical realization difficulties, stating that error correction and quantum coherence are “very serious” problems and referring the reader elsewhere.
- It states that for most examples there is no proof the constructions are the most economical, though numerical study gives compelling evidence of minimality.
- The exact simulation of arbitrary n-bit unitaries uses Θ(n³4ⁿ) two-bit gates, which is exponential; the paper notes this is unlikely to provide a polynomial-time simulation for the special unitaries of most interest in quantum computation, and that a truly efficient design methodology remains to be found.
- The Ω(n) lower bound leaves open the possibility of a linear-size simulation of ∧_{n−1}(U) gates, which the paper says it cannot presently show.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 18 cited sources checked · 0 supported · 0 flagged
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
“Lemma 5.1: For a unitary 2 × 2 matrix W , a ∧ 1 ( W ) gate can be simulated by a network of the form”
- Also stated in: § 5.1 Simulation of General ∧ 1 ( U ) Gates · p. 10 · plain
“where A , B , and C ∈ SU (2) , if and only if W ∈ SU (2) .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § 5.1 Simulation of General ∧ 1 ( U ) Gates · p. 10 · plain
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
“Corollary 5.6: For any unitary 2 × 2 matrix U , a ∧ 1 ( U ) gate can be simulated by at most six basic gates: four 1-bit gates ( ∧ 0 ), and two gates ( ∧ 1 ( V ) ), where V is of the form V = R z ( α ) · R y ( θ ) · R z ( α ) · σ x .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“Still, the presence of a workspace plays an important role in the quantum gate constructions - we find that to implement a family of ∧ m gates exactly, the time required for our implementation can be reduced from Θ( m 2 ) to Θ( m ) merely by the introduction of one bit for workspace.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe 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
“Lemma 6.1: For any unitary 2 × 2 matrix U , a ∧ 2 ( U ) gate can be simulated by a network of the form”
- Also stated in: § 6.1 Simulation of General ∧ 2 ( U ) Gates · p. 14 · plain
“where V is unitary.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § 6.1 Simulation of General ∧ 2 ( U ) Gates · p. 14 · plain
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
“Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form”
- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 12 · plain
“where A and B ∈ SU (2) if and only if W is of the form”
- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 12 · plain
“where α and θ are real-valued.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 12 · plain
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
“Corollary 6.2: For any unitary 2 × 2 matrix U , a ∧ 2 ( U ) gate can be simulated by at most sixteen basic gates: eight 1-bit gates ( ∧ 0 ) and eight XOR gates ( ∧ 1 ( σ x ) ).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“We will also exhibit a number of explicit constructions of ∧ m ( U ) using ∧ 1 ( U ), which can all be made polynomial in m .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe 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
“Lemma 4.3: For any special unitary matrix W ( W ∈ SU (2) ), there exist matrices A , B , and C ∈ SU (2) such that A · B · C = I and A · σ x · B · σ x · C = W .”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearThe 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
“Corollary 5.3: For any unitary 2 × 2 matrix U , a ∧ 1 ( U ) gate can be simulated by at most six basic gates: four 1-bit gates ( ∧ 0 ), and two XOR gates ( ∧ 1 ( σ x ) ).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe 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
“Examples of matrices of the form of Lemma 5.5 are the Pauli matrices”
- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 13 · plain
“(as well as σ x itself).”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 13 · plain
- The quote only partly states this claim. 3
- Probably not a substantial claim. 11
- It may state two separate claims as one. 8
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
“Lemma 5.5: A ∧ 1 ( V ) gate can be simulated by a construction of the form”
- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 13 · plain
“where A and B are unitary if and only if V is of the form”
- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 12 · plain
“where α and θ are real-valued.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
- Also stated in: § Lemma 5.4: A ∧ 1 ( W ) gate can be simulated by a network of the form · p. 13 · plain
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 particular feature of the ∧ 1 ( σ z ) gates is that they are symmetric with respect to their input bits.”
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
“Examples of matrices of the form of Lemma 5.4 are R y ( θ ) itself, as well as R z ( α ) = R z ( α 2 ) · R y (0) · R z ( α 2 ). However, R x ( θ ) is not of this form.”
Strength:plain· 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
“Lemma 5.2: For any δ and S = Ph ( δ ) , a ∧ 1 ( S ) gate can be simulated by a network of the form”
- Also stated in: § 5.1 Simulation of General ∧ 1 ( U ) Gates · p. 11 · plain
“where E is unitary.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
- Also stated in: § 5.1 Simulation of General ∧ 1 ( U ) Gates · p. 11 · plain
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 example, the ' x -axis rotation matrix' (to use the language suggested by the mapping between SU(2) and SO(3), the group of rigid-body rotations[43])”
- Also stated in: § 5.2 Special Cases · p. 12 · plain
“is special unitary.”
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.
- Also stated in: § 5.2 Special Cases · p. 12 · plain
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
“Lemma 4.1: Every unitary 2 × 2 matrix can be expressed as”
- Also stated in: § 4 Matrix Properties · p. 8 · plain
“where δ , α , θ , and β are real-valued. Moreover, any special unitary 2 × 2 matrix (i.e., with unity determinant) can be expressed as”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one. The quote only partly states this claim.
- Also stated in: § 4 Matrix Properties · p. 8 · plain
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
“Note that the 'extra' bit above may be reused in the course of several simulations of ∧ m ( U ) gates.”
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 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
“The following is a more efficient simulation of a gate congruent to ∧ 2 ( σ x ) modulo phase shifts:”
- Also stated in: § 6.2 Three-bit gates congruent to ∧ 2 ( U ) · p. 16 · plain
“where A = R y ( π 4 ). In the above, the ' ∼ =' indicates that the networks are not identical, but differ at most in the phases of their amplitudes, which are all ± 1 (the phase of the | 101 〉 state is reversed in this case).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Also stated in: § 6.2 Three-bit gates congruent to ∧ 2 ( U ) · p. 16 · plain
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
“When the arbitrary two-bit gate is taken as the basic operation, then as we have seen, 5 operations suffice to produce the Toffoli gate (recall Lemma 6.1), 3 produce the Toffoli gate modulo phases (we permit a merging of the operations in the construction of Sec. 6.2), and 13 can be used to produce the 4-bit Toffoli gate (see Lemma 7.1).”
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
“Corollary 7.4: On an n -bit network (where n ≥ 7 ), a ∧ n -2 ( σ x ) gate can be simulated by 8( n -5) ∧ 2 ( σ x ) gates (3-bit Toffoli gates), as well as by 48 n -204 basic operations.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Note that in this construction and in the ones following, although many of the bits not involved in the gate are operated upon, the gate operation is performed correctly independent of the initial state of the bits (i.e., they do not have to be 'cleared' to 0 first), and they are reset to their initial values after the operations of the gate (as in the computations which occur in [41] and [40]).”
What the sources say
- Not checked yetcites [41] [41] Michael Ben-Or and Richard Cleve, 'Computing algebraic formulas using a constant number of registers', SIAM J. Comput. 21 , 54 (1992). -
- Not checked yetcites [40] [40] Richard Cleve, 'Reversible Programs and Simple Product Ciphers' in Methodologies for Designing Block Ciphers and Cryptographic Protocols , PhD Thesis, University of Toronto, pp. 2-56 (1989). -
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
“Later we will use the fact that because ∧ 2 ( σ x ) is its own inverse, either the simulation of Lemma 6.1 or the time-reversed simulation (in which the order of the gates is reversed, and each unitary operator is replaced by its Hermitian conjugate) may be used.”
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
“The formalism we use for quantum computation, which we call a quantum 'gate array' was introduced by Deutsch [24], who showed that a simple generalization of the Toffoli gate (the three-bit gate ∧ 2 ( R x ), in the language introduced later in this paper) suffices as a universal gate for quantum computing.”
What the sources say
- Not matchedcites [24] [24] D. Deutsch, 'Quantum computational networks', Proc. Roy. Soc. Lond. A 425 , 73 (1989). -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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.
- Not matched
In the paper
“It is possible to perform any computation in a way that is reversible both logically -i.e., the computation is a sequence of bijective transformations-and thermodynamically -the computation could in principle be performed by a physical apparatus dissipating arbitrarily little energy [2].”
What the sources say
- Not checked yetcites [2] [2] R. Landauer, 'Irreversibility and heat generation in the computing process', IBM J. Res. Dev. 5 , 183 (1961); C. H. Bennett, 'Logical reversibility of computation', IBM Journal of Research and Development, 17 , 525 (1973); Yves Lecerf, 'Machines de Turing reversibles. Recursive insolubilite en nεN de l'equation u = θ n ou θ est un 'isomorphism de codes'. Comptes Rendus 257 , 2597-2600 (1963); C. H. Bennett, 'Time/space trade-offs for reversible computation', SIAM J. Comput. 18 , 766 (1989). For a review, see C. H. Bennett and R. Landauer, 'Physical limits of computation', Scientific Americ source
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“Fortunately, Yao has shown [27] that acyclic quantum gate arrays can simulate quantum Turing machines.”
What the sources say
- Not checked yetcites [27] [27] A. C.-C. Yao, 'Quantum Circuit Complexity', Proceedings of the 34th Annual Symposium on the Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, CA, 1993), p. 352. -
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.
In the paper
“( R x is of special interest because ∧ 2 ( iR x ) is the 'Deutsch gate'[24], which was shown to be universal for quantum logic.)”
What the sources say
- Not matchedcites [24] [24] D. Deutsch, 'Quantum computational networks', Proc. Roy. Soc. Lond. A 425 , 73 (1989). -
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
In the paper
“Sleator and Weinfurter[9], who exhibited a scheme for obtaining the Toffoli gate with a sequence of exactly five two-bit gates.”
What the sources say
- Not matchedcites [9] [9] Tycho Sleator and Harald Weinfurter, 'Realizable universal quantum logic gates', preprint (1994). -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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.
- Not matched
In the paper
“In fact, it is well known that only a tiny fraction of Boolean functions (those which are linear with respect to modulo 2 arithmetic) can be generated with these gates[39].”
What the sources say
- Not checked yetcites [39] [39] D. Coppersmith and E. Grossman, 'Generators for Certain Alternating Groups with Applications to Cryptography', SIAM J. Applied Math. 29 , No. 4, pp. 624-627 (1975). -
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
In the paper
“Fredkin and Toffoli[3] showed that there exists a 3-bit 'universal gate' for reversible computation, that is, a gate which, when applied in succession to different triplets of bits in a gate array, could be used to simulate any arbitrary reversible computation.”
What the sources say
- Not matchedcites [3] [3] E. Fredkin and T. Toffoli, 'Conservative Logic', Internat. J. Theoret. Phys. 21 , 219 (1982). -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- Not matched
In the paper
“This unitary evolution on a normalized state vector is known to be the correct physical description of an isolated system evolving in time according to the laws of quantum mechanics[1].”
What the sources say
- Not checked yetcites [1] [1] P. A. M. Dirac, The Principles of Quantum Mechanics , (Oxford, 1958), Chap. 5; for a modern treatment, see A. Peres, Quantum Theory: Concepts and Methods , (Kluwer, 1993), Chap. 8.6. - source
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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 source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In fact for general k, time-efficient design as in Fig. 5a requires k-2 zeroed work qubits within depth 2k-3, whereas space-efficient design as in Fig. 5b uses only one arbitrary qubit within depth 8k-24 (for k ≥ 5) [32].”
From Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2 (2018) · cites this paper as [32]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Any two-qubit gate can be obtained from this minimal set by using circuit decompositions (Barenco et al. , 1995; Blaauboer and De Visser, 2008; de Guise et al. , 2018; Peterson et al. , 2020; Watts et al. , 2013).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Barenco et al., 1995
In the citing paper
“We should point out here that the results presented here give faster gates than any results for the maximum speed of Toffoli gates in the literature [2,3].”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [3]
In the citing paper
“In particular, one can compare the factor 1.9 in Table II with the corresponding factor of 2.2 in Ref. [3]: an improvement of about 15%.”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [3]
In the citing paper
“An optimal-control-theory-related calculation based on certain forms of pulses has found a gate time of about 2.2 times the CNOT gate time for qubits coupled in a triangle geometry [3].”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [3]
In the citing paper
“Although computational universality might at first seem to be a stringent demand on a physical system, a wide variety of physical systems - ranging from nearest neighbor Ising models 52 to quantum electrodynamics 84 and conformal field theories 86 - are known to be computationally universal 51 -53 , 55 -65 .”
From Ultimate physical limits to computation (2000) · cites this paper as [59]
In the citing paper
“In other words, given an arbitrary quantum gate, there is a circuit built from one-and two-qubit gates that can enact it to arbitrary precision.”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [47]
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.
Corollary 7.4 miscounts the remaining Toffoli gates
MinorThe stated total is 8(n−5) Toffoli gates. If 4 are simulated exactly, the number of other gates is 8n−44, not 8n−36.
“a ∧ n -2 ( σ x ) gate can be simulated by 8( n -5) ∧ 2 ( σ x ) gates”
“only 4 of the Toffoli gates, the ones which involve the last bit in the diagram above, need to be simulated exactly according to the construction of Corollary 6.2. Thus these 4 gates are simulated by 16 basic operations, while the other 8 n -36 Toffoli gates are simulated in just 6 basic operations.”
Citations
Cites
The Principles of Quantum Mechanics
Dirac, P. A. M., & Polkinghorne, J. C. (1958) · Physics Today · doi:10.1063/1.3062610 · Cited by 5,409
Irreversibility and heat generation in the computing process
Landauer, R. (1961) · IBM Journal of Research and Development · doi:10.1147/rd.53.0183 · Cited by 4,980
Quantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597
Quantum Computations with Cold Trapped Ions
Cirac, J. I., & Zoller, P. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4091 · Cited by 3,733
Logical Reversibility of Computation
Bennett, C. H. (1973) · IBM Journal of Research and Development · doi:10.1147/rd.176.0525 · Cited by 3,679
Self-citationRapid solution of problems by quantum computation
Deutsch, D., & Jozsa, R. (1992) · Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences · doi:10.1098/rspa.1992.0167 · Cited by 2,700
Irreversibility and heat generation in the computing process
Landauer, R. W. (2000) · IBM Journal of Research and Development · doi:10.1147/rd.441.0261 · Cited by 2,665
Experimental realization of any discrete unitary operator
Reck, M., Zeilinger, A., Bernstein, H. J., & Bertani, P. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.58 · Cited by 2,155
Fredkin, E., & Toffoli, T. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf01857727 · Cited by 1,896
Feynman, R. P. (1986) · Foundations of Physics · doi:10.1007/bf01886518 · Cited by 1,770
Flagged first, then by citations
Research works printed but not linked: 2
- A. C. C. Yao, Proceedings of the 34th Annual Symposium on the Foundations of Computer Science
- D. P. DiVincenzo, Proceedings of the Workshop on Physics and Computation, PhysComp '94
Cited by
Sorted by citations
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472
Self-citationQuantum computation with quantum dots
Loss, D., & DiVincenzo, D. P. (1998) · Physical Review A · doi:10.1103/physreva.57.120 · Cited by 6,840
Self-citationMixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272
Self-citationRaussendorf, R., & Briegel, H. J. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5188 · Cited by 4,477
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1999) · SIAM Review · doi:10.1137/s0036144598347011 · Cited by 3,904
Self-citationQuantum information and computation
Bennett, C. H., & DiVincenzo, D. P. (2000) · Nature · doi:10.1038/35005001 · Cited by 3,263
Self-citationBlais, A., Huang, R.-S., Wallraff, A., Girvin, S. M., & Schoelkopf, R. J. (2004) · Physical Review A · doi:10.1103/physreva.69.062320 · Cited by 2,989
Quantum-state engineering with Josephson-junction devices
Makhlin, Y., Schön, G., & Shnirman, A. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.357 · Cited by 2,510
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
Engineering atomic and molecular nanostructures at surfaces
Barth, J. V., Costantini, G., & Kern, K. (2005) · Nature · doi:10.1038/nature04166 · Cited by 2,134
A quantum engineer's guide to superconducting qubits
Krantz, P., Kjærgaard, M., Yan, F., Orlando, T. P., Gustavsson, S., & Oliver, W. D. (2019) · Applied Physics Reviews · doi:10.1063/1.5089550 · Cited by 2,321
Decoherence-Free Subspaces for Quantum Computation
Lidar, D. A., Chuang, I. L., & Whaley, K. B. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.2594 · Cited by 1,818
Gottesman, D., & Chuang, I. L. (1999) · Nature · doi:10.1038/46503 · Cited by 1,860
Measurement-based quantum computation on cluster states
Raussendorf, R., Browne, D. E., & Briegel, H. J. (2003) · Physical Review A · doi:10.1103/physreva.68.022312 · Cited by 1,655
Demonstration of a Fundamental Quantum Logic Gate
Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M., & Wineland, D. J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4714 · Cited by 1,586
Bulk Spin-Resonance Quantum Computation
Gershenfeld, N. A., & Chuang, I. L. (1997) · Science · doi:10.1126/science.275.5298.350 · Cited by 1,528
Bernstein, E., & Vazirani, U. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796300921 · Cited by 1,503
Coupled quantum dots as quantum gates
Burkard, G., Loss, D., & Divincenzo, D. P. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.59.2070 · Cited by 1,483
Self-citationQuantum computations: algorithms and error correction
Kitaev, A. Y. (1997) · Russian Mathematical Surveys · doi:10.1070/rm1997v052n06abeh002155 · Cited by 1,424
Quantum computation and Shor's factoring algorithm
Ekert, A., & Jozsa, R. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.733 · Cited by 1,354
Trapped-ion quantum computing: Progress and challenges
Bruzewicz, C. D., Chiaverini, J., McConnell, R., & Sage, J. M. (2019) · Applied Physics Reviews · doi:10.1063/1.5088164 · Cited by 1,483
Microwave photonics with superconducting quantum circuits
Gu, X. Q., Kockum, A. F., Miranowicz, A., Liu, Y.-X., & Nori, F. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.10.002 · Cited by 1,337
Cleve, R., EKERT, A. K., Macchiavello, C., & Mosca, M. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0164 · Cited by 1,399
Self-citationBernstein, E., & Vazirani, U. (1993) · Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93 · doi:10.1145/167088.167097 · Cited by 1,284
Stabilizer Codes and Quantum Error Correction
Gottesman, D. (1997) · arXiv · doi:10.48550/arxiv.quant-ph/9705052 · Cited by 753
Steane, A. (1998) · Reports on Progress in Physics · doi:10.1088/0034-4885/61/2/002 · Cited by 1,391
Quantum computation and decision trees
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.58.915 · Cited by 1,215
Quantum computing with trapped ions
HAFFNER, H., ROOS, C., & BLATT, R. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.003 · Cited by 1,154
Ultimate physical limits to computation
Lloyd, S. (2000) · Nature · doi:10.1038/35023282 · Cited by 1,120
Quantum Computation with Ions in Thermal Motion
Sørensen, A. S., & Mølmer, K. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1971 · Cited by 1,088
Measurement-based quantum computation
Briegel, H. J., Browne, D. E., Dür, W., Raussendorf, R., & Van den Nest, M. (2009) · Nature Physics · doi:10.1038/nphys1157 · Cited by 1,090
Circuit-centric quantum classifiers
Schuld, M., Bocharov, A., Svore, K. M., & Wiebe, N. (2020) · Physical Review A · doi:10.1103/physreva.101.032308 · Cited by 1,057
Quantum information processing with superconducting circuits: a review
Wendin, G. P. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa7e1a · Cited by 1,022
Universal quantum computation with the exchange interaction
DiVincenzo, D. P., Bacon, D., Kempe, J., Burkard, G., & Whaley, K. B. (2000) · Nature · doi:10.1038/35042541 · Cited by 924
Self-citationFault-tolerant quantum computation
Shor, P. W. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1996.548464 · Cited by 1,195
Self-citationMolecular spins for quantum computation
Gaita‐Ariño, A., Luis, F., Hill, S., & Coronado, E. (2019) · Nature Chemistry · doi:10.1038/s41557-019-0232-y · Cited by 914
Power of One Bit of Quantum Information
Knill, E. H., & Laflamme, R. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.5672 · Cited by 918
Prescription for experimental determination of the dynamics of a quantum black box
Chuang, I. L., & Nielsen, M. A. (1997) · Journal of Modern Optics · doi:10.1080/09500349708231894 · Cited by 949
Quantum Algorithms for Quantum Chemistry and Quantum Materials Science
Bauer, B., Bravyi, S., Motta, M., & Chan, G. K.-L. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00829 · Cited by 848
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
Abrams, D. S., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.5162 · Cited by 817
A single-atom electron spin qubit in silicon
Pla, J. J., Tan, K. Y., Dehollain, J. P., Lim, W. H., Morton, J. J. L., Jamieson, D. N., Dzurak, A. S., & Morello, A. (2012) · Nature · doi:10.1038/nature11449 · Cited by 830
Quantum networks for elementary arithmetic operations
Vedral, V., Barenco, A., & EKERT, A. K. (1996) · Physical Review A · doi:10.1103/physreva.54.147 · Cited by 846
Self-citationOn the Power of Quantum Computation
Simon, D. R. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796298637 · Cited by 1,295
Le, P. Q., Dong, F., & Hirota, K. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0177-y · Cited by 797
Entanglement of Atoms via Cold Controlled Collisions
Jaksch, D., Briegel, H.-J., Cirac, J. I., Gardiner, C. W., & Zoller, P. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1975 · Cited by 795
Entanglement and quantum computation with ions in thermal motion
Sørensen, A. S., & Mølmer, K. (2000) · Physical Review A · doi:10.1103/physreva.62.022311 · Cited by 796
Superconducting persistent-current qubit
Orlando, T. P., Mooij, J. E., Tian, L., van der Wal, C. H., Levitov, L. S., Lloyd, S., & Mazo, J. J. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.60.15398 · Cited by 750
Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
Abrams, D. S., & Lloyd, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2586 · Cited by 745
Multiparticle generalization of entanglement swapping
Bose, S., Vedral, V., & Knight, P. L. (1998) · Physical Review A · doi:10.1103/physreva.57.822 · Cited by 749
Simulating Hamiltonian Dynamics with a Truncated Taylor Series
Berry, D. W., Childs, A. M., Cleve, R., Kothari, R., & Somma, R. D. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.090502 · Cited by 742
Self-citationQuantum-information processing with circuit quantum electrodynamics
Blais, A., Gambetta, J., Wallraff, A. J., Schuster, D., Girvin, S. M., Devoret, M., & Schoelkopf, R. J. (2007) · Physical Review A · doi:10.1103/physreva.75.032329 · Cited by 729
Quantum Walk Algorithm for Element Distinctness
Ambainis, A. (2007) · SIAM Journal on Computing · doi:10.1137/s0097539705447311 · Cited by 814
Experimental Implementation of Fast Quantum Searching
Chuang, I. L., Gershenfeld, N., & Kubinec, M. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.3408 · Cited by 707
Quantum computing with atomic qubits and Rydberg interactions: progress and challenges
Saffman, M. E. (2016) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/49/20/202001 · Cited by 740
Synthesis of quantum-logic circuits
Shende, V., Bullock, S. S., & Markov, I. L. (2006) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2005.855930 · Cited by 786
Josephson-junction qubits with controlled couplings
Makhlin, Y., Scöhn, G., & Shnirman, A. (1999) · Nature · doi:10.1038/18613 · Cited by 669
Knill, E., Laflamme, R., & Zurek, W. H. (1998) · Science · doi:10.1126/science.279.5349.342 · Cited by 663
The Complexity of the Local Hamiltonian Problem
Kempe, J., Kitaev, A., & Regev, O. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704445226 · Cited by 648
Fault-tolerant quantum computation with constant error
Aharonov, D., & Ben-Or, M. (1997) · Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97 · doi:10.1145/258533.258579 · Cited by 631
Building logical qubits in a superconducting quantum computing system
Gambetta, J., Chow, J. M., & Steffen, M. (2017) · npj Quantum Information · doi:10.1038/s41534-016-0004-0 · Cited by 680
Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms
Levine, H., Keesling, A., Semeghini, G., Omran, A., Wang, T. T., Ebadi, S., Bernien, H., Greiner, M., Vuletić, V., Pichler, H., et al. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.170503 · Cited by 604
Classification with Quantum Neural Networks on Near Term Processors
Farhi, E., & Neven, H. (2020) · doi:10.37686/qrl.v1i2.80 · Cited by 1,176
Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices
Li, G., Ding, Y., & Xie, Y. (2019) · Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems · doi:10.1145/3297858.3304023 · Cited by 594
Synthesis of reversible logic circuits
Shende, V., Prasad, A. K., Markov, I. L., & Hayes, J. P. (2003) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2003.811448 · Cited by 567
Quantum Teleportation Between Distant Matter Qubits
Olmschenk, S., Matsukevich, D. N., Maunz, P., Hayes, D., Duan, L.-M., & Monroe, C. (2009) · Science · doi:10.1126/science.1167209 · Cited by 458
Information and computation: Classical and quantum aspects
Galindo, A., & Martin-Delgado, M. A. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.347 · Cited by 563
Design of magnetic coordination complexes for quantum computing
Aromı́, G., Aguilà, D., Gámez, P., Luis, F., & Roubeau, O. (2011) · Chemical Society Reviews · doi:10.1039/c1cs15115k · Cited by 551
Fujii, K. (2009) · Institute of Electrical and Electronics Engineers eBooks · doi:10.1109/9780470544907.ch24 · Cited by 642
Theory of decoherence-free fault-tolerant universal quantum computation
Kempe, J., Bacon, D., Lidar, D. A., & Whaley, K. B. (2001) · Physical Review A · doi:10.1103/physreva.63.042307 · Cited by 550
Realizable Universal Quantum Logic Gates
Sleator, T., & Weinfurter, H. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4087 · Cited by 515
Self-citationUniversal quantum computation using the discrete-time quantum walk
Lovett, N. B., Cooper, S., Everitt, M., Trevers, M., & Kendon, V. (2010) · Physical Review A · doi:10.1103/physreva.81.042330 · Cited by 510
Fault-Tolerant Quantum Computation with Constant Error Rate
Aharonov, D., & Ben-Or, M. (2008) · SIAM Journal on Computing · doi:10.1137/s0097539799359385 · Cited by 513
RevLib: An Online Resource for Reversible Functions and Reversible Circuits
Wille, R., Grosse, D. J., Teuber, L., Dueck, G. W., & Drechsler, R. (2008) · IEEE International Symposium on Multiple-Valued Logic (ISMVL) · doi:10.1109/ismvl.2008.43 · Cited by 509
Experimental comparison of two quantum computing architectures
Linke, N. M., Maslov, D., Roetteler, M., Debnath, S., Figgatt, C., Landsman, K. A., Wright, K., & Monroe, C. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1618020114 · Cited by 508
On the power of quantum computation
Simon, D. R. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365701 · Cited by 491
From Quantum Cellular Automata To Quantum Lattice GasesPreprint
Meyer, D., Qca, F., David, Q., & Meyer, A. (1996) · Cited by 502
Quantum measurements and the Abelian Stabilizer ProblemPreprint
Kitaev, A. (1995) · arXiv (Cornell University) · Cited by 472
Semiclassical Fourier Transform for Quantum Computation
Griffiths, R. B., & Niu, C.-S. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.3228 · Cited by 431
Experimental Realization of Nonadiabatic Holonomic Quantum Computation
Feng, G., Xu, G., & Long, G. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.190501 · Cited by 426
Direct Estimations of Linear and Nonlinear Functionals of a Quantum State
Ekert, A. K., Alves, C. M., Oi, D. K. L., Horodecki, M., Horodecki, P., & Kwek, L. C. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.217901 · Cited by 427
Spin qubits with electrically gated polyoxometalate molecules
Lehmann, J., Gaita‐Ariño, A., Coronado, E., & Loss, D. (2007) · Nature Nanotechnology · doi:10.1038/nnano.2007.110 · Cited by 429
ProjectQ: An open source software framework for quantum computing
Steiger, D. S., Häner, T., & Troyer, M. (2018) · Quantum · doi:10.22331/q-2018-01-31-49 · Cited by 428
Generation of three-qubit entangled states using superconducting phase qubits
Neeley, M., Bialczak, R. C., Lenander, M., Lucero, E. A., Mariantoni, M., O’Connell, A. D., Sank, D., Wang, H., Weides, M. P., Wenner, J., et al. (2010) · Nature · doi:10.1038/nature09418 · Cited by 415
Coecke, B., & Kissinger, A. (2017) · Cambridge University Press eBooks · doi:10.1017/9781316219317 · Cited by 512
Geometric theory of nonlocal two-qubit operations
Zhang, J., Vala, J., Sastry, S., & Whaley, K. B. (2003) · Physical Review A · doi:10.1103/physreva.67.042313 · Cited by 415
Optimal local implementation of nonlocal quantum gates
Eisert, J., Jacobs, K. A., Papadopoulos, P., & Plenio, M. B. (2000) · Physical Review A · doi:10.1103/physreva.62.052317 · Cited by 450
Prospects for Spin-Based Quantum Computing in Quantum Dots
Kloeffel, C., & Loss, D. (2013) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-030212-184248 · Cited by 421
An introduction to quantum computing for non-physicists
Rieffel, E. G., & Polak, W. (2000) · ACM Computing Surveys · doi:10.1145/367701.367709 · Cited by 436
Universal Quantum Computation with Spin- 1 / 2 Pairs and Heisenberg Exchange
Levy, J. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.147902 · Cited by 400
Local Random Quantum Circuits are Approximate Polynomial-Designs
Brandão, F. G. S. L., Harrow, A. W., & Horodecki, M. (2016) · Communications in Mathematical Physics · doi:10.1007/s00220-016-2706-8 · Cited by 404
Multivalued logic gates for quantum computation
Muthukrishnan, A., & Stroud, C. R. (2000) · Physical Review A · doi:10.1103/physreva.62.052309 · Cited by 411
Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer
Jones, J. A., & Mosca, M. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476739 · Cited by 406
Quantum Circuits for General Multiqubit Gates
Möttönen, M., Vartiainen, J. J., Bergholm, V., & Salomaa, M. M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.130502 · Cited by 395
Optimal quantum circuits for general two-qubit gates
Vatan, F., & Williams, C. (2004) · Physical Review A · doi:10.1103/physreva.69.032315 · Cited by 443
Simulating quantum systems on a quantum computer
Zalka, C. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0162 · Cited by 420
Implementation of a Toffoli gate with superconducting circuits
Fedorov, A., Steffen, L., Baur, M., Silva, M. P. D., & Wallraff, A. J. (2011) · Nature · doi:10.1038/nature10713 · Cited by 383
Analog analogue of a digital quantum computation
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.57.2403 · Cited by 389
Quantum coherence and entanglement with ultracold atoms in optical lattices
Bloch, I. (2008) · Nature · doi:10.1038/nature07126 · Cited by 389
An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures
Zulehner, A., Paler, A., & Wille, R. (2018) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2018.2846658 · Cited by 382
Metadata
- Authors
- Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H.
- Affiliations
- AT&T (United States) (US)
- ORCID
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1995-11-01
- Volume
- 52
- Issue
- 5
- Pages
- 3457-3467
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2102008187
- Semantic Scholar
- 59b447f58246fbbdffd5e896f83a3a142eca5cf1
- Cited by
- 4,311
- References
- 52
- Citations by year
- 2026: 201 · 2025: 271 · 2024: 253 · 2023: 271 · 2022: 258 · 2021: 218 · 2020: 200 · 2019: 179 · 2018: 152 · 2017: 125 · 2016: 125 · 2015: 130 · 2014: 119 · 2013: 124 · 2012: 136
- FWCI
- 63.39
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Quantum-Dot Cellular Automata
- Keywords
- quantum gates, XOR gate, gate decomposition, circuit complexity, lower bounds, upper bounds, quantum computing
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
