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
Items 801–900 of 1,008
Automated window-based partitioning of quantum circuits
Nikahd, E., Mohammadzadeh, N., Sedighi, M., & Zamani, M. S. (2020) · Physica Scripta · doi:10.1088/1402-4896/abd57c · Cited by 46
Measurement-Free Fault-Tolerant Quantum Error Correction in Near-Term Devices
Heußen, S., Locher, D. F., & Müller, M. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.010333 · Cited by 53
Roy, S., Sethi, P., Topolancik, J., & Vollmer, F. (2011) · Advances in Optical Technologies · doi:10.1155/2012/727206 · Cited by 43
Reversible Circuit Optimization Via Leaving the Boolean Domain
Maslov, D. A., & Saeedi, M. (2011) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2011.2105555 · Cited by 44
Wang, T.-J., & Wang, C. X. (2014) · Physical Review A · doi:10.1103/physreva.90.052310 · Cited by 44
Wei, H., & Long, G. L. (2015) · Scientific Reports · doi:10.1038/srep12918 · Cited by 43
Make it reversible: Efficient embedding of non-reversible functions
Zulehner, A., & Wille, R. (2017) · Design, Automation, and Test in Europe · doi:10.23919/date.2017.7927033 · Cited by 44
Programming quantum computers using design automation
Soeken, M., Häner, T., & Roetteler, M. (2018) · Design, Automation, and Test in Europe · doi:10.23919/date.2018.8341993 · Cited by 49
Efficient decomposition methods for controlled-Rn using a single ancillary qubit
Kim, T., & Choi, B.-S. (2018) · Scientific Reports · doi:10.1038/s41598-018-23764-x · Cited by 64
Li, M., Guo, F.-Q., Jin, Z., Yan, L.-L., Liang, E., & Su, S. (2021) · Physical Review A · doi:10.1103/physreva.103.062607 · Cited by 43
Implementation of efficient quantum search algorithms on NISQ computers
Zhang, K., Rao, P., Yu, K., Lim, H., & Korepin, V. E. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03165-2 · Cited by 49
Xiao, Y., Zou, X., & Guo, G. (2007) · Physical Review A · doi:10.1103/physreva.75.054303 · Cited by 44
Macroscopic Einstein-Podolsky-Rosen pairs in superconducting circuits
Wei, L. F., Liu, Y.-X., Storcz, M. J., & Nori, F. (2006) · Physical Review A · doi:10.1103/physreva.73.052307 · Cited by 44
Experimental simulation of anyonic fractional statistics with an NMR quantum-information processor
Feng, G., Long, G., & Laflamme, R. (2013) · Physical Review A · doi:10.1103/physreva.88.022305 · Cited by 44
Programmable Networks for Quantum Algorithms
Schuch, N., & Siewert, J. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.027902 · Cited by 44
Simplification of Toffoli networks via templates
Maslov, D., Dueck, G. W., & Miller, D. M. (2003) · doi:10.5555/942808.943941 · Cited by 44
How to Convert the Flavor of a Quantum Bit Commitment
Crépeau, C., Légaré, F., & Salvail, L. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44987-6_5 · Cited by 44
Electron spins in quantum dots for spintronics and quantum computation
Engel, H., Recher, P., & Loss, D. (2001) · Solid State Communications · doi:10.1016/s0038-1098(01)00110-7 · Cited by 44
Parametrized discrete phase-space functions
Opatrný, T., Welsch, D. ‐., & Bužek, V. (1996) · Physical Review A · doi:10.1103/physreva.53.3822 · Cited by 44
Quantum Carry-Save ArithmeticPreprint
Gossett, P. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9808061 · Cited by 44
Kissinger, A. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1203.0202 · Cited by 67
Quantum algorithms for approximate function loading
Marin-Sanchez, G., Gonzalez-Conde, J., & Sanz, M. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033114 · Cited by 55
Phase flip code with semiconductor spin qubits
van Riggelen, F., Lawrie, W. I. L., Rimbach-Russ, M., Hendrickx, N. W., Sammak, A., Rispler, M., Terhal, B. M., Scappucci, G., & Veldhorst, M. (2022) · npj Quantum Information · doi:10.1038/s41534-022-00639-8 · Cited by 44
Equivalence Checking in Multi-level Quantum Systems
Niemann, P., Wille, R., & Drechsler, R. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-08494-7_16 · Cited by 42
Fermion parity measurement and control in Majorana circuit quantum electrodynamics
Yavilberg, K., Ginossar, E., & Grosfeld, E. (2015) · Physical Review B · doi:10.1103/physrevb.92.075143 · Cited by 44
Coupling superconducting flux qubits at optimal point via dynamic decoupling with the quantum bus
Wang, Y.-D., Kemp, A., & Semba, K. (2009) · Physical Review B · doi:10.1103/physrevb.79.024502 · Cited by 43
A review of procedures to evolve quantum algorithms
Gepp, A., & Stocks, P. (2009) · Genetic Programming and Evolvable Machines · doi:10.1007/s10710-009-9080-7 · Cited by 42
FPGA-Based Circuit Model Emulation of Quantum Algorithms
Aminian, M., Saeedi, M., Zamani, M. S., & Sedighi, M. (2008) · IEEE Computer Society Annual Symposium on VLSI · doi:10.1109/isvlsi.2008.43 · Cited by 43
Control of valley dynamics in silicon quantum dots in the presence of an interface step
Boross, P., Széchenyi, G., Culcer, D., & Pályi, A. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.035438 · Cited by 43
Qudit-Basis Universal Quantum Computation Using χ(2) Interactions
Niu, M. Y., Chuang, I. L., & Shapiro, J. H. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.160502 · Cited by 42
Quantum circuit design for several morphological image processing methods
Li, P., Shi, T., Lu, A., & Wang, B. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2479-z · Cited by 47
A Variational Algorithm for Quantum Neural Networks
Macaluso, A., Clissa, L., Lodi, S., & Sartori, C. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-50433-5_45 · Cited by 45
On-chip path encoded photonic quantum Toffoli gate
Li, M., Li, C., Chen, Y., Feng, L., Yan, L., Zhang, Q., Bao, J., Liu, B., Ren, X., Wang, J., et al. (2022) · Photonics Research · doi:10.1364/prj.452539 · Cited by 44
Manipulating two-spin coherences and qubit pairs
Rau, A. R. P. (2000) · Physical Review A · doi:10.1103/physreva.61.032301 · Cited by 39
Heuristic methods to use don’t cares in automated design of reversible and quantum logic circuits
Mohammadi, M., & Eshghi, M. (2008) · Quantum Information Processing · doi:10.1007/s11128-008-0081-x · Cited by 43
Chakraborty, A. (2005) · International Conference on VLSI Design · doi:10.1109/icvd.2005.158 · Cited by 43
Optimal Multiqubit Operations for Josephson Charge Qubits
Niskanen, A. O., Vartiainen, J. J., & Salomaa, M. M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.197901 · Cited by 43
Quantum Teleportation of a Three-Particle Entangled State
Jin-Ming, L., & Guang-Can, G. (2002) · Chinese Physics Letters · doi:10.1088/0256-307x/19/4/303 · Cited by 43
Error-free quantum communication through noisy channels
Sørensen, A. S., & Mølmer, K. (1998) · Physical Review A · doi:10.1103/physreva.58.2745 · Cited by 40
Highly Efficient Processing of Multi-photon States
Lin, Q., & He, B. (2015) · Scientific Reports · doi:10.1038/srep12792 · Cited by 42
Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach
Weggemans, J. R., Urech, A., Rausch, A., Spreeuw, R. J. C., Boucherie, R. J., Schreck, F., Schoutens, K., Minář, J., & Speelman, F. (2022) · Quantum · doi:10.22331/q-2022-04-13-687 · Cited by 49
Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems
Illa, M., & A, M. J. S. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.221003 · Cited by 42
Approximating Many-Body Quantum States with Quantum Circuits and Measurements
Piroli, L., Styliaris, G., & Cirac, J. I. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.230401 · Cited by 69
Conditions for optimal construction of two-qubit nonlocal gates
Zhang, Y.-S., Ye, M.-Y., & Guo, G. (2005) · Physical Review A · doi:10.1103/physreva.71.062331 · Cited by 43
From Truth Tables to Programming Languages: Progress in the Design of Reversible Circuits
Drechsler, R., & Wille, R. (2011) · IEEE International Symposium on Multiple-Valued Logic (ISMVL) · doi:10.1109/ismvl.2011.40 · Cited by 41
A fast quantum circuit for addition with few qubits
Takahashi, Y., & Kunihiro, N. (2008) · Quantum Information and Computation · doi:10.26421/qic8.6-7-5 · Cited by 42
Liquid marble interaction gate for collision-based computing
Draper, T. C., Fullarton, C., Phillips, N., Costello, B. D. L., & Adamatzky, A. (2017) · Materials Today · doi:10.1016/j.mattod.2017.09.004 · Cited by 42
An Introduction to Quantum Computing, without the Physics
Nannicini, G. (2020) · SIAM Review · doi:10.1137/18m1170650 · Cited by 46
Bilinear interpolation method for quantum images based on quantum Fourier transform
Li, P., & Liu, X. (2018) · International Journal of Quantum Information · doi:10.1142/s0219749918500314 · Cited by 42
A quantum computational compiler and design tool for technology-specific targets
Smith, K. N., & Thornton, M. A. (2019) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3307650.3322262 · Cited by 42
MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES
Raussendorf, R. (2009) · International Journal of Quantum Information · doi:10.1142/s0219749909005699 · Cited by 47
Automatic Quantum Computer Programming: A Genetic Programming Approach (Genetic Programming)
Spector, L. C. (2006) · Springer eBooks · Cited by 44
Clifford algebras and universal sets of quantum gates
Vlasov, A. Y. (2001) · Physical Review A · doi:10.1103/physreva.63.054302 · Cited by 45
Fate of the cluster state on the square lattice in a magnetic field
Kalis, H., Klagges, D., Orús, R., & Schmidt, K. P. (2012) · Physical Review A · doi:10.1103/physreva.86.022317 · Cited by 45
Quantified synthesis of reversible logic
Wille, R., Le, H. M., Dueck, G. W., & Grosse, D. J. (2008) · Design, Automation, and Test in Europe · doi:10.1145/1403375.1403620 · Cited by 42
Five quantum register error correction code for higher spin systems
Chau, H. F. (1997) · Physical Review A · doi:10.1103/physreva.56.r1 · Cited by 47
Zou, X., Zhang, S. L., Li, K., & Guo, G. (2007) · Physical Review A · doi:10.1103/physreva.75.034302 · Cited by 42
Quantum-information processing in bosonic lattices
Ionicioiu, R., & Zanardi, P. (2002) · Physical Review A · doi:10.1103/physreva.66.050301 · Cited by 41
Depth-Optimal Quantum Circuit Placement for Arbitrary TopologiesPreprint
Bhattacharjee, D., & Chattopadhyay, A. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1703.08540 · Cited by 51
Black-box Hamiltonian simulation and unitary implementation
Berry, D. W., & Childs, A. M. (2012) · Quantum Information and Computation · doi:10.26421/qic12.1-2 · Cited by 41
A shared-cube approach to ESOP-based synthesis of reversible logic
Nayeem, N. M., & Rice, J. (2011) · Facta universitatis - series Electronics and Energetics · doi:10.2298/fuee1103385n · Cited by 41
Continuous-variable and hybrid quantum gates
Wang, X. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 41
Han, Y., Cao, C., Fan, L., & Zhang, R. (2021) · Optics Express · doi:10.1364/oe.426325 · Cited by 41
Warren, C., Fernández-Pendás, J., Ahmed, S., Abad, T., Bengtsson, A., Biznárová, J., Debnath, K., Gu, X. Q., Križan, C., Osman, A., et al. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00711-x · Cited by 42
Deterministic Hyperparallel Control Gates with Weak Kerr Effects
Du, F., Fan, G., Ren, X., & Ma, M. (2023) · Advanced Quantum Technologies · doi:10.1002/qute.202300201 · Cited by 41
Quantum-enhanced greedy combinatorial optimization solver
Dupont, M., Evert, B., Hodson, M. J., Sundar, B., Jeffrey, S., Yamaguchi, Y., Feng, D., Maciejewski, F. B., Hadfield, S., Alam, M. S., et al. (2023) · Science Advances · doi:10.1126/sciadv.adi0487 · Cited by 54
Efficient quantum amplitude encoding of polynomial functions
Gonzalez-Conde, J., Watts, T. W., Rodriguez-Grasa, P., & Sanz, M. (2024) · Quantum · doi:10.22331/q-2024-03-21-1297 · Cited by 42
Symmetry criteria for quantum simulability of effective interactions
Zimborás, Z., Zeier, R., Schulte‐Herbrüggen, T., & Burgarth, D. K. (2015) · Physical Review A · doi:10.1103/physreva.92.042309 · Cited by 44
Incoherent noise and quantum information processing
Boulant, N., Emerson, J., Havel, T. F., Cory, D. G., & Furuta, S. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1773161 · Cited by 41
Stochastic Liouville equation approach for the effect of noise in quantum computations
Cheng, Y., & Silbey, R. (2004) · Physical Review A · doi:10.1103/physreva.69.052325 · Cited by 40
Symmetry and Subspace Controllability for Spin Networks With a Single-Node Control
Wang, X., Pemberton-Ross, P. J., & Schirmer, S. G. (2012) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2012.2202057 · Cited by 41
Quantum circuits employing roots of the Pauli matrices
Soeken, M., Miller, D. M., & Drechsler, R. (2013) · Physical Review A · doi:10.1103/physreva.88.042322 · Cited by 41
Wei, H., & Long, G. L. (2015) · Physical Review A · doi:10.1103/physreva.91.032324 · Cited by 41
Quantum Image Filtering in the Spatial Domain
Yuan, S., Mao, X., Zhou, J., & Wang, X. (2017) · International Journal of Theoretical Physics · doi:10.1007/s10773-017-3403-x · Cited by 41
Normal form for single-qutrit Clifford+ T operators and synthesis of single-qutrit gates
Prakash, S., Jain, A., Kapur, B., & Seth, S. (2018) · Physical Review A · doi:10.1103/physreva.98.032304 · Cited by 41
Resource-Efficient Quantum Computing by Breaking Abstractions
Shi, Y., Gokhale, P., Murali, P., Baker, J. M., Duckering, C., Ding, Y., Brown, N. C., Chamberland, C., Javadi-Abhari, A., Cross, A. W., et al. (2020) · Proceedings of the IEEE · doi:10.1109/jproc.2020.2994765 · Cited by 49
The trapped-ion qubit tool box
Ozeri, R. (2011) · Contemporary Physics · doi:10.1080/00107514.2011.603578 · Cited by 42
A Family of Optimal Packings in Grassmannian Manifolds
Shor, P. W., & Sloane, N. J. A. (1998) · Journal of Algebraic Combinatorics · doi:10.1023/a:1008608404829 · Cited by 41
Self-citationReiss, T. O., Khaneja, N., & Glaser, S. J. (2003) · Journal of Magnetic Resonance · doi:10.1016/s1090-7807(03)00245-3 · Cited by 41
Analogies and differences between quantum and stochastic automata
Bertoni, A., & Carpentieri, M. (2001) · Theoretical Computer Science · doi:10.1016/s0304-3975(00)00154-7 · Cited by 43
Construction and Implementation of NMR Quantum Logic Gates for Two Spin Systems
Price, M. D., Somaroo, S. S., Tseng, C.-H., Gore, J. C., Fahmy, A. F., Havel, T. F., & Cory, D. G. (1999) · Journal of Magnetic Resonance · doi:10.1006/jmre.1999.1851 · Cited by 39
Polynomial simulations of decohered quantum computers
Aharonov, D., & Ben-Or, M. (2002) · Proceedings of 37th Conference on Foundations of Computer Science · doi:10.1109/sfcs.1996.548463 · Cited by 41
Two-qubit Projective Measurements are Universal for Quantum ComputationPreprint
Leung, D. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0111122 · Cited by 45
Quantum computation with Kerr-nonlinear photonic crystalsPreprint
Azuma, H. (2006) · Cited by 42
Daskin, A., & Kais, S. (2016) · Cited by 41
Quantum pixel representations and compression for N-dimensional images
Amankwah, M. G., Camps, D., Bethel, E. W., Beeumen, R. V., & Perciano, T. (2022) · Scientific Reports · doi:10.1038/s41598-022-11024-y · Cited by 50
Robust control and optimal Rydberg states for neutral atom two-qubit gates
Mohan, M., de Keijzer, R., & Kokkelmans, S. J. J. M. F. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.033052 · Cited by 40
Jiang, G., Yuan, J.-B., Liu, W., & Wei, H. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.21.014001 · Cited by 40
Lattice Boltzmann–Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
Sanavio, C., & Succi, S. (2024) · AVS Quantum Science · doi:10.1116/5.0195549 · Cited by 42
A two-tier scheme for greyscale quantum image watermarking and recovery
Iliyasu, A. M., Le, P. Q., Yan, F., Sun, B., Garcia, J. A. S., Dong, F., & Hirota, K. (2013) · International Journal of Innovative Computing and Applications · doi:10.1504/ijica.2013.053179 · Cited by 40
Design automation and design space exploration for quantum computers
Soeken, M., Roetteler, M., Wiebe, N., & Micheli, G. D. (2017) · Design, Automation, and Test in Europe · doi:10.23919/date.2017.7927035 · Cited by 43
Quantum image median filtering in the spatial domain
Li, P., Liu, X., & Xiao, H. Y. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1826-9 · Cited by 40
LUT-Based Hierarchical Reversible Logic Synthesis
Soeken, M., Roetteler, M., Wiebe, N., & Micheli, G. D. (2018) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2018.2859251 · Cited by 61
Logic Synthesis for Established and Emerging Computing
Testa, E., Soeken, M., Amar, L. G., & Micheli, G. D. (2018) · Proceedings of the IEEE · doi:10.1109/jproc.2018.2869760 · Cited by 40
Protocol for a resonantly driven three-qubit Toffoli gate with silicon spin qubits
Gullans, M. J., & Petta, J. R. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.085419 · Cited by 40
Cao, C., Han, Y., Zhang, L., Fan, L., Duan, Y., & Zhang, R. (2019) · Advanced Quantum Technologies · doi:10.1002/qute.201900081 · Cited by 39
Bais, F. A., & Farmer, J. D. (2008) · Elsevier eBooks · doi:10.1016/b978-0-444-51726-5.50020-0 · Cited by 54
Quantum strategies of quantum measurements
Li, C., Zhang, Y.-S., Huang, Y., & Guo, G. (2001) · Physics Letters A · doi:10.1016/s0375-9601(01)00072-x · Cited by 40
Quantum entanglement via nilpotent polynomials
Mandilara, A., Akulin, V. M., Smilga, A. V., & Viola, L. (2006) · Physical Review A · doi:10.1103/physreva.74.022331 · Cited by 41
QIRHSI: novel quantum image representation based on HSI color space model
Chen, G., Song, X., Venegas-Andraca, S. E., & El‐Latif, A. A. A. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03337-0 · Cited by 39
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
