The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index; none of the 8 sources its claims cite is checked for support yet.
A fast quantum mechanical algorithm for database search
Open accessAbstract
An unsorted database contains N records, of which just one satisfies a particular property.The problem is to identify that one record.Any classical algorithm, deterministic or probabilistic, will clearly take O (N) steps since on the average it will have to examine a large fraction of the N records.Quantum mechanical systems can do several operations simultaneously due to their wave like properties.This paper gives an O ( JN) step quantum mechanical algorithm for identifying that record.It is within a constant factor of the fastest possible quantum mechanical algorithm.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
19 No basis given · 8 Sources not found · 4 Own interpretation
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This paper gives an O ( JN) step quantum mechanical algorithm for identifying that record.”
§ A fast quantum mechanical algorithm for database search > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: There is a unique state that satisfies the condition C(S)=1.
- The authors state this as an assumption: For any state S, the condition C(S) can be evaluated in unit time.
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 3.1-Let the state vector be as followsfor any one state the amplitude is k, for each of the remaining (N-1) states the amplitude is 1.Let k and 1 be real numbers (in general the amplitudes can be complex).Let k be negative and 1 be positive such that ~< ~N.Then after applying the diffusion transform both k and 1are positive numbers.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“First, it is proved that the system is a valid quantum mechanical system (theorems 1 & 2)”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“As mentioned in the introduction, the algorithm of this paper does not use any Imowledge about the problem.”
§ A fast quantum mechanical algorithm for database search > 114
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“Theorem 1-The matix D is unitary.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The following sections prove that the system discussed in section 3 is indeed a valid quantum mechanical system and that it converges to the desired state with a probability O(l).”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: There is a unique state that satisfies the condition C(S)=1.
- The authors state this as an assumption: For any state S, the condition C(S) can be evaluated in unit time.
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
“Theorem 2 -D can be expressed as D = FRF, where F, the Fourier Transform Matrix and R, the rotation matrix are defined as follows”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“Since the proba-& bility of the system being found in any particular state is proportional to the square of the amplitude, it follows that the probability of the system being in tlhe desired state when k is ~, 1 J2 is k2 = ~.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“In case there is a unique state SV such that C(SV) = 1, the final state is SV with a probability of at least ~. 2”
§ A fast quantum mechanical algorithm for database search > T. Acknowledgments
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
- The authors state this as an assumption: There is a unique state that satisfies the condition C(S)=1.
- The authors state this as an assumption: For any state S, the condition C(S) can be evaluated in unit time.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It can be easily modified to take care of the case when there are multiple states satisfying the condition C(S) = 1 and it is required to return one of these.”
§ A fast quantum mechanical algorithm for database search > 114
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Probably not a substantial claim. 8
- It may state two separate claims as one. 4
- The quote only partly states this claim. 1
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
“Theorem 5-Let the probability of a particular outcome in an experiment be &.Then if the experiment be repeated ~times, the probability that the outcome does not happen even once is less than or equal to e-K.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The change in k ( Ak) after steps (a) and (b) of the algorithm is lower bounded by Ak>~.Also after steps (a) and (b), 1>0.2fi”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It 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
“Using this it immediately follows that there exists a number M less than EN, such that in M repetitions of the loop in step (ii), k wifl become ~.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The most efficient classical algorithm for this is to examine the items in the database one by one.”
§ A fast quantum mechanical algorithm for database search > ------------------------------------------------
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Very recent results [Shor95] have shown the existence of quantum mechanical error corr~ting cod~which enable transmission of data even in the presence of noise”
§ A fast quantum mechanical algorithm for database search > 114
What the sources say
- Not matchedcites [Shor95]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This algorithm, by cleverly making use of some features of the structure of the problem, is the only known algorithm that solves the problem in O (logIV) steps.”
§ A fast quantum mechanical algorithm for database search > 114
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The phase does not have an analog in classical probabilistic algorithms.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably 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
“This illustrates the point that, in quantum mechanics, the complete description of the system requires the amplitudes over all states, just the probabilities is not enough.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“For example Shor's primality testing algorithm [Shor94] for a number N can be viewed as a search of the (N-l) numbers smaller than N to see if any of them is a factor of N.”
§ A fast quantum mechanical algorithm for database search > 114
What the sources say
- Not matchedcites [Shor94]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“There is also a scheme discussed in [VV86] by which it is possible to modify any algorithm that solves an NPsearch problem with a unique solution and use it to solve an NP-search problem in general.”
§ A fast quantum mechanical algorithm for database search > 114
What the sources say
- Not matchedcites [VV86]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“This operation is one of the things that makes quantum mechanical algorithms more powerful than classical algorithms and forms the basis for most significant quantum mechanical algorithms.”
§ A fast quantum mechanical algorithm for database search > T. Acknowledgments
What the sources say
- Not matchedcites [DJ92]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
The authors state this as an assumption.
There is a unique state that satisfies the condition C(S)=1.
“Let there be a unique state, say Sv, that satisfies the condition C(SV) = 1, whereas for all other states S, C(S) = 0”
“The algorithm as discussed here assumes a unique state that satisfies the desired condition.”
The authors state this as an assumption.
For any state S, the condition C(S) can be evaluated in unit time.
“(assume that for any state S, the condition C(S) can be evaluated in unit time)”
The paper relies on this without support.
There does not exist any sorting on the database that would aid selection of the desired item.
“However, there does not exist any sorting on the database that would aid its selection.”
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
“Symmetric cryptography remains comparatively resilient, yet Grover's algorithm offers a quadratic speed-up for brute-force key search, effectively halving the security margin of symmetric ciphers [13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Similarly, for hash functions, Grover's algorithm [185] can facilitate quantum birthday attack to find collision, thereby necessitating an output of larger size.”
From Zero Trust Architecture (ZTA): A Comprehensive Survey (2022) · cites this paper as [185]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Similarly, Grover’s algorithm concedes a quadratic advantage for mining blocks in certain consensus protocols such as proof of work.”
From Quantum-resistance in blockchain networks (2023) · cites this paper as [71]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Quantum computers will be able to find these nonces quadratically faster using Grover’s algorithm71.”
From Quantum-resistance in blockchain networks (2023) · cites this paper as [71]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This model is realistic given the falling cost of storage, the rise of large-scale surveillance infrastructures, and the expected disruption of quantum algorithms such as Shor's and Grover's [1,2,13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measured
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
“Grover's algorithm provides only a quadratic speedup, effectively halving brute-force resistance. Comparable security margins can be restored by doubling key sizes (for example, AES-128 to AES-256) [13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This explains why AES-256 maintains post-quantum security margins, whereas AES-128 requires upgrading to maintain equivalent protection levels [13,14].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“At the same time, Grover's algorithm shows that symmetric cryptography, though more resilient, also demands doubled key sizes to maintain equivalent margins [13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe 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 this sense, Grover-based optimization algorithms [184] such as Grover Adaptive Search [161] have been proposed.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [184]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The former bound is tight since recent work of Grover [13] shows how to accept the class NP relative to any oracle on a quantum computer in time O (2 n/ 2 ).”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
Experimental — accuracy not yet measuredThe 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 view of Grover's algorithm [13], we know that the constant '1 / 2' in the statement of Theorem 3.5 cannot be improved.”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The former bound is tight since recent work of Grover [13] shows how to accept the class NP relative to any oracle on a quantum computer in time O (2 n/ 2 ).”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Grover’s algorithm [54] is a quantum algorithm for searching in a database, ofering quadratic speedup over classical searching methods.”
From QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation (2023) · cites this paper as [54]
The cited source says what the claim attributes to it.
In the citing paper
“However, quantum machines can recognize this language quadratically faster, in time O ( √ 2 n ), using Grover's algorithm [13].”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
The cited source says what the claim attributes to it.
In the citing paper
“That this was a real possibility is clear from Grover's [13] result, which gives a black-box approach to solving NP -complete problems in square-root as much time as is required classically.”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
The cited source says what the claim attributes to it.
In the citing paper
“Various strategies can be imagined, but a good one (called 'inversion about the average' by Grover [13]) is to perform an oracle-independent unitary transformation so as to change the phase difference into an amplitude difference, leaving the y term with the same sign as all the other terms but a magnitude approximately threefold larger.”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“The HNDL adversary departs from conventional cryptanalysis in its temporal asymmetry. Instead of attempting immediate decryption, the attacker passively collects encrypted traffic or stored archives and defers decryption until sufficient computational resources become available.”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredIn the citing paper
“This algorithm uses a single function evaluation to label the single state which satisfies the function, followed by a series of gates which drive the system into this particular state.”
From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [9]
In the citing paper
“Here we show how such a computer can be used to implement a fast quantum search algorithm initially developed by Grover. 9, 10”
From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [9]
In the citing paper
“Among other applications Grover's algorithms enable an extremely rapid search over the domain of a binary function to find elements for which this function is satisfied (that is, the function has the value 1).”
From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [9]
In the citing paper
“the ability to efficiently perform Hamiltonian simulation is used in conjunction with another technique known as the quantum phase estimation algorithm (QPEA) 42 for efficiently obtaining the eigen-energies and eigenstates of a quantum system 38 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
In the citing paper
“The Quantum Phase Estimation (QPE) algorithm 38,99 is the natural translation of the FCI procedure to quantum computers 45 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
In the citing paper
“Abrams and Lloyd 38 focused on state preparation in more detail and described concrete initialization procedures.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
In the citing paper
“They pointed out that state preparation is conceptually easier in second quantization, where a Fock state is represented by a simple product state of qubits in {| 0 〉 , | 1 〉} states.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
Citations
Cites
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713
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
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Rapid 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
The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics
Penrose, R., & Gardner, M. (1989) · doi:10.1093/oso/9780198519737.001.0001 · Cited by 2,007
Strengths and Weaknesses of Quantum Computing
Bennett, C. H., Bernstein, E., Brassard, G., & Vazirani, U. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796300933 · Cited by 1,470
On the Power of Quantum Computation
Simon, D. R. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796298637 · Cited by 1,295
Bernstein, 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
Benioff, P. (1980) · Journal of Statistical Physics · doi:10.1007/bf01011339 · Cited by 1,244
The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics
Penrose, R., & Landauer, R. (1990) · Physics Today · doi:10.1063/1.2810599 · Cited by 1,110
Research works printed but not linked: 2
- [9]9. R. Penrose, Shadows of the mind,. Oxford University Press, 1994, pp. 348- 388.
- [14]14. Yao93J A. Yao, Quantum circuit complexip, Proceedings 34th Annual Symposium on Foundations of Computer Science (FOCS), 1993, pp. 352-361.
Cited by
Sorted by citations
Items 901–1,000 of 8,792
Zheng, P., & Huang, J. (2018) · IEEE Transactions on Image Processing · doi:10.1109/tip.2018.2802199 · Cited by 46
Pan, D., Li, K., Ruan, D., Ng, S. X., & Hanzo, L. (2020) · IEEE Access · doi:10.1109/access.2020.3006136 · Cited by 47
Exact and Practical Pattern Matching for Quantum Circuit Optimization
Iten, R., Moyard, R., Metger, T., Sutter, D., & Woerner, S. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3498325 · Cited by 45
Low-Depth Mechanisms for Quantum Optimization
McClean, J. R., Harrigan, M. P., Mohseni, M., Rubin, N. C., Zhang, J., Boixo, S., Smelyanskiy, V., Babbush, R., & Neven, H. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030312 · Cited by 50
Stein, S., Wiebe, N., Ding, Y., Peng, B., Kowalski, K., Baker, N., Ang, J., & Li, A. (2022) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3470496.3527434 · Cited by 60
Quantum Circuit Optimization and Transpilation via Parameterized Circuit Instantiation
Younis, E., & Iancu, C. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00068 · Cited by 46
Error correction optimisation in the presence of X/Z asymmetryPreprint
Evans, Z. W. E., Stephens, A. M., Cole, J. H., & Hollenberg, L. C. L. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0709.3875 · Cited by 50
Full-Stack, Real-System Quantum Computer Studies: Architectural Comparisons and Design InsightsPreprint
Murali, P., Linke, N. M., Martonosi, M., Javadi-Abhari, A., Nguyen, N. H., & Alderete, C. H. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.11349 · Cited by 45
Quantum Computing: Vision and Challenges
Gill, S. S., Cetinkaya, O., Marrone, S., Claudino, D., Haunschild, D., Schlote, L., Wu, H., Ottaviani, C., Liu, X., Machupalli, S. P., et al. (2025) · Quantum Computing · doi:10.1016/b978-0-443-29096-1.00008-8 · Cited by 44
Solving SAT (and MaxSAT) with a quantum annealer: Foundations, encodings, and preliminary results
Bian, Z., Chudak, F. A., Macready, W. G., Roy, A., Sebastiani, R., & Varotti, S. (2020) · Information and Computation · doi:10.1016/j.ic.2020.104609 · Cited by 57
Yunakovsky, S. E., Kot, M., Pozhar, N. O., Nabokov, D., Kudinov, M., Guglya, A. P., Kiktenko, E. O., Kolycheva, E., Borisov, A., & Fedorov, A. K. (2021) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-021-00104-z · Cited by 48
The arrow of time in operational formulations of quantum theory
Biagio, A. D., Donà, P., & Carlo Rovelli, C. (2021) · Quantum · doi:10.22331/q-2021-08-09-520 · Cited by 52
Quantum Artificial Intelligence: A Brief Survey
Klusch, M., Lässig, J., Müssig, D., Macaluso, A., & Wilhelm, F. K. (2024) · Künstliche Intell. · doi:10.1007/s13218-024-00871-8 · Cited by 57
Impossibility of a Quantum Speed-Up with a Faulty Oracle
Regev, O., & Schiff, L. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-70575-8_63 · Cited by 47
A note on the switching adiabatic theorem
Elgart, A., & Hagedorn, G. A. (2012) · Journal of Mathematical Physics · doi:10.1063/1.4748968 · Cited by 45
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
Finding spin glass ground states using quantum walks
Callison, A., Chancellor, N., Mintert, F., & Kendon, V. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab5ca2 · Cited by 52
Quantum Computation in Robotic Science and Applications
Petschnigg, C., Brandstötter, M., Pichler, H., Hofbaur, M., & Dieber, B. (2019) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2019.8793768 · Cited by 45
Qraft: reverse your Quantum circuit and know the correct program output
Patel, T., & Tiwari, D. (2021) · International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS) · doi:10.1145/3445814.3446743 · Cited by 52
Vidick, T., & Watrous, J. (2016) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000068 · Cited by 44
Exponential Separation of Quantum and Classical Online Space Complexity
Gall, F. L. (2007) · Theory of Computing Systems · doi:10.1007/s00224-007-9097-3 · Cited by 47
Lower bounds for quantum communication complexityPreprint
Klauck, H. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0106160 · Cited by 44
Mosca, M. (2009) · Springer eBooks · doi:10.1007/978-0-387-30440-3_423 · Cited by 44
A Finite Regime Analysis of Information Set Decoding Algorithms
Baldi, M., Barenghi, A., Chiaraluce, F., Pelosi, G., & Santini, P. (2019) · Algorithms · doi:10.3390/a12100209 · Cited by 43
Accessible and inaccessible quantum coherence in relativistic quantum systems
Harikrishnan, S., Jambulingam, S., Rohde, P. P., & Radhakrishnan, C. (2022) · Physical Review A · doi:10.1103/physreva.105.052403 · Cited by 52
Analysis of the NTRU Post-Quantum Cryptographic Scheme in Constrained IoT Edge Devices
Señor, J., Portilla, J., & Mujica, G. (2022) · IEEE Internet of Things Journal · doi:10.1109/jiot.2022.3162254 · Cited by 43
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
Quantum Random Access Memory for Dummies
Phalak, K., Chatterjee, A., & Ghosh, S. (2023) · Sensors · doi:10.3390/s23177462 · Cited by 55
Tate, R., Moondra, J., Gard, B., Mohler, G., & Gupta, S. (2023) · Quantum · doi:10.22331/q-2023-09-26-1121 · Cited by 59
Quantum Deep Reinforcement Learning for Robot Navigation Tasks
Hohenfeld, H., Heimann, D., Wiebe, F., & Kirchner, F. (2024) · IEEE Access · doi:10.1109/access.2024.3417808 · Cited by 58
A Comprehensive Review of Quantum Circuit Optimization: Current Trends and Future Directions
Karuppasamy, K., Puram, V., Johnson, S., & Thomas, J. P. (2025) · Quantum Reports · doi:10.3390/quantum7010002 · Cited by 45
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
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
Quantum Hoare Logic with Ghost Variables
Unruh, D. (2019) · ACM/IEEE Symposium on Logic in Computer Science (LICS) · doi:10.1109/lics.2019.8785779 · Cited by 44
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
Double quantum color images encryption scheme based on DQRCI
Wang, L., Ran, Q., & Ma, J. (2019) · Multimedia Tools and Applications · doi:10.1007/s11042-019-08514-z · Cited by 45
Quantum Speedup for Aeroscience and Engineering
Givi, P., Daley, A. J., Mavriplis, D. J., & Malik, M. R. (2020) · AIAA Journal · doi:10.2514/1.j059183 · Cited by 46
Shi, R., & Li, Y.-F. (2022) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2022.3152591 · Cited by 43
Towards quantum template matching
Curtis, D., & MEYER, D. A. (2004) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.506669 · Cited by 43
QASMBench: A Low-level QASM Benchmark Suite for NISQ Evaluation and SimulationPreprint
Li, A., Stein, S., Krishnamoorthy, S., & Ang, J. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.13018 · Cited by 46
Quantum Computing: Principles and Applications
Kanamori, Y., & Yoo, S.-M. (2020) · Journal of international technology and information management · doi:10.58729/1941-6679.1410 · Cited by 46
Multi-car paint shop optimization with quantum annealing
Yarkoni, S., Alekseyenko, A., Streif, M., Dollen, D. V., Neukart, F., & Bäck, T. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00019 · Cited by 43
Quantum support vector machine without iteration
Zhang, R., Wang, J., Jiang, N., & Wang, Z. (2023) · Information Sciences · doi:10.1016/j.ins.2023.03.106 · Cited by 47
An Automata-Based Framework for Verification and Bug Hunting in Quantum Circuits
Chen, Y., Chung, K.-M., Lengál, O., Lin, J.-A., Tsai, W.-L., & Yen, D.-D. (2023) · Proceedings of the ACM on Programming Languages · doi:10.1145/3591270 · Cited by 62
Applications of Neural Network-Based AI in Cryptography
Nitaj, A., & Rachidi, T. (2023) · Cryptography · doi:10.3390/cryptography7030039 · Cited by 49
On the security of the Winternitz one-time signature scheme
Buchmann, J. A., Dahmen, E., Ereth, S., et al. (2013) · International Journal of Applied Cryptography · doi:10.1504/ijact.2013.053435 · Cited by 42
Span-program-based quantum algorithm for evaluating formulas
Reichardt, B. W., & Špalek, R. (2012) · Theory of Computing · doi:10.4086/toc.2012.v008a013 · Cited by 42
An Introduction to Quantum Computing, without the Physics
Nannicini, G. (2020) · SIAM Review · doi:10.1137/18m1170650 · Cited by 46
Turbulent Mixing Simulation via a Quantum Algorithm
Xu, G., Daley, A. J., Givi, P., & Somma, R. D. (2017) · AIAA Journal · doi:10.2514/1.j055896 · Cited by 44
On Finding Quantum Multi-collisions
Liu, Q., & Zhandry, M. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-17659-4_7 · Cited by 57
Wang, W., Jungk, B., Wälde, J., Deng, S., Gupta, N., Szefer, J. M., & Niederhagen, R. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-38471-5_21 · Cited by 43
Acampora, G. (2019) · Quantum Machine Intelligence · doi:10.1007/s42484-019-00006-5 · Cited by 47
Improved Classical and Quantum Algorithms for Subset-Sum
Bonnetain, X., Bricout, R., Schrottenloher, A., & Shen, Y. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-64834-3_22 · Cited by 41
Understanding and compensating for noise on IBM quantum computers
Johnstun, S., & Huele, J.-F. S. V. (2021) · American Journal of Physics · doi:10.1119/10.0006204 · Cited by 41
Time-Efficient Quantum Walks for 3-Distinctness
Belovs, A., Childs, A. M., Jeffery, S., Kothari, R., & Magniez, F. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-39206-1_10 · Cited by 42
Quantum certificate complexity
Aaronson, S. (2004) · Journal of Computer and System Sciences · doi:10.1016/j.jcss.2007.06.020 · Cited by 57
Quantum computing with superconductors
Berggren, K. K. (2004) · Proceedings of the IEEE · doi:10.1109/jproc.2004.833672 · Cited by 42
Multi-universe parallel quantum genetic algorithm its application to blind-source separation
Yang, J., Li, B., & Zhuang, Z. (2003) · International Conference on Neural Networks and Signal Processing · doi:10.1109/icnnsp.2003.1279292 · Cited by 42
Evolving Quantum Circuits and Programs Through Genetic Programming
Massey, P., Clark, J. A., & Stepney, S. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24855-2_66 · Cited by 41
Path Integration on a Quantum Computer
Traub, J. F., & Woźniakowski, H. (2002) · Quantum Information Processing · doi:10.1023/a:1023417813916 · Cited by 47
Generalized quantum search with parallelism
Gingrich, R. M., Williams, C. P., & Cerf, N. J. (2000) · Physical Review A · doi:10.1103/physreva.61.052313 · Cited by 44
Improved two-party and multi-party purification protocols
Maneva, E., & Smolin, J. A. (2002) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/305/05220 · Cited by 42
Toward the Impossibility of Perfect Complete Quantum PKE from OWFs
Li, L., Li, Q., Li, X., & Liu, Q. (2025) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.itcs.2025.71 · Cited by 3
Hidden Quantum Markov Models and non-adaptive read-out of many-body statesPreprint
Monràs, A., Beige, A., & Wiesner, K. (2010) · Bristol Research (University of Bristol) · doi:10.48550/arxiv.1002.2337 · Cited by 42
A Quantum Algorithm for finding the MaximumPreprint
Ahuja, A., & Kapoor, S. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9911082 · Cited by 53
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 Variational Quantum Algorithm for Preparing Quantum Gibbs StatesPreprint
Chowdhury, A. C. N., Low, G. H., & Wiebe, N. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.00055 · Cited by 91
Streif, M., Yarkoni, S., Skolik, A., Neukart, F., & Leib, M. (2021) · Physical Review A · doi:10.1103/physreva.104.012403 · Cited by 41
A novel protocol for multiparty quantum key management
Xu, G., Chen, X., Dou, Z., Yang, Y., & Li, Z. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-1021-1 · Cited by 41
Quantum Computing As a Topic in Computer Science Education
Seegerer, S., Michaeli, T., & Romeike, R. (2021) · Workshop in Primary and Secondary Computing Education · doi:10.1145/3481312.3481348 · Cited by 47
DiAdamo, S., O’Meara, C., Cortiana, G., & Bernabé-Moreno, J. (2022) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2022.3185505 · Cited by 41
Towards a Lightweight CRYSTALS-Kyber in FPGAs: an Ultra-lightweight BRAM-free NTT Core
Ni, Z., Khalid, A., Liu, W., & O'Neill, M. P. (2023) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas46773.2023.10181340 · Cited by 46
A Conceptual Architecture for a Quantum-HPC Middleware
Saurabh, N., Jha, S., & Luckow, A. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00023 · Cited by 46
Post-quantum distributed ledger technology: a systematic survey
Parida, N. K., Jatoth, C., Reddy, V. D., Hussain, M. M., & Faizi, J. (2023) · Scientific Reports · doi:10.1038/s41598-023-47331-1 · Cited by 52
Dissipation as a resource for Quantum Reservoir Computing
Sannia, A., Martínez‐Peña, R., Soriano, M. C., Giorgi, G. L., & Zambrini, R. (2024) · Quantum · doi:10.22331/q-2024-03-20-1291 · Cited by 64
A quantum k-nearest neighbors algorithm based on the Euclidean distance estimation
Zardini, E., Blanzieri, E., & Pastorello, D. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00155-2 · Cited by 50
Toward Quantum Federated Learning
Ren, C., Yan, R., Zhu, H., Yu, H., Xu, M., Shen, Y., Xu, Y. H., Xiao, M., Dong, Z. Y., Skoglund, M., et al. (2025) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2025.3552643 · Cited by 93
Toward 6G Authentication and Key Agreement Protocol: A Survey on Hybrid Post Quantum Cryptography
Turnip, T. N., Andersen, B., & Vargas‐Rosales, C. (2025) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2025.3567439 · Cited by 51
Quantum algorithm design using dynamic learning
Behrman, E., Steck, J. E., Kumar, P., & Walsh, K. A. (2008) · Quantum Information and Computation · doi:10.26421/qic8.1-2-2 · Cited by 41
Tractable simulation of error correction with honest approximations to realistic fault models
Puzzuoli, D., Granade, C., Haas, H., Criger, B., Magesan, E., & Cory, D. G. (2014) · Physical Review A · doi:10.1103/physreva.89.022306 · Cited by 46
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Babar, Z., Botsinis, P., Alanis, D., Ng, S. X., & Hanzo, L. (2015) · IEEE Access · doi:10.1109/access.2015.2405533 · Cited by 42
Deleting a marked state in quantum database in a duality computing mode
Liu, Y. (2013) · Chinese Science Bulletin · doi:10.1007/s11434-013-5925-9 · Cited by 41
Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions
Ezra, E. E., & Sharir, M. (2007) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2007.10 · Cited by 45
Search by Quantum Walks on Two-Dimensional Grid without Amplitude Amplification
Ambainis, A., Bačkurs, A., Nahimovs, N., Ozols, R., & Rivosh, A. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-35656-8_7 · Cited by 41
INFORMATION IN COMPUTER SCIENCE
Dunn, J. M. (2008) · Elsevier eBooks · doi:10.1016/b978-0-444-51726-5.50019-4 · Cited by 39
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
Zulehner, A., & Wille, R. (2019) · Design, Automation, and Test in Europe · doi:10.23919/date.2019.8714836 · Cited by 41
Zhang, J., Yu, Y., Fan, S., et al. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-45388-6_2 · Cited by 41
Improved quantum algorithm for A-optimal projection
Pan, S., Wan, L., Liu, H., Wang, Q.-L., Qin, S., Wen, Q., & Gao, F. (2020) · Physical Review A · doi:10.1103/physreva.102.052402 · 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
Probabilistic nonunitary gate in imaginary time evolution
Liu, T., Liu, J.-G., & Fan, H. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03145-6 · Cited by 44
Quantum-Enhanced Grid of the Future: A Primer
Eskandarpour, R., Ghosh, K., Khodaei, A., Paaso, E. A., & Zhang, L. (2020) · IEEE Access · doi:10.1109/access.2020.3031595 · Cited by 43
Speeding-up the decision making of a learning agent using an ion trap quantum processor
Sriarunothai, T., Wölk, S., Giri, G., Friis, N., Dunjko, V., Briegel, H., & Wunderlich, C. (2019) · MPG.PuRe (Max Planck Society) · Cited by 41
An area law for 2d frustration-free spin systems
Anshu, A., Arad, I., & Gosset, D. (2022) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3519935.3519962 · Cited by 59
Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection
Cui, J., Xiong, Y., Ng, S. X., & Hanzo, L. (2022) · IEEE Transactions on Communications · doi:10.1109/tcomm.2022.3185287 · Cited by 47
Quantum permutation pad for universal quantum-safe cryptography
Kuang, R., & Barbeau, M. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03557-y · Cited by 45
Group leaders optimization algorithm
Daskin, A., & Kais, S. (2011) · Molecular Physics · doi:10.1080/00268976.2011.552444 · Cited by 41
A better lower bound for quantum algorithms searching an ordered list
Ambainis, A. (2003) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sffcs.1999.814606 · Cited by 49
Sublinear quantum algorithms for training linear and kernel-based classifiersPreprint
Li, T., Chakrabarti, S., & Wu, X. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.02276 · Cited by 53
Daskin, A., & Kais, S. (2016) · Cited by 41
Metadata
- Authors
- Grover, L. K.
- Affiliations
- AT&T (United States) (US)
- Corresponding author
- Grover, Lov K.
- Venue
- Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96
- Publisher
- ACM Press
- Published
- 1996
- Pages
- 212-219
- OpenAlex
- W2084652510
- Semantic Scholar
- 298d799da82395a64a3bda38ef9d2a4646828ccb
- Cited by
- 8,830
- References
- 24
- Citations by year
- 2026: 664 · 2025: 1066 · 2024: 896 · 2023: 841 · 2022: 674 · 2021: 655 · 2020: 529 · 2019: 423 · 2018: 288 · 2017: 283 · 2016: 219 · 2015: 221 · 2014: 184 · 2013: 161 · 2012: 158
- FWCI
- 36.24
- Type
- conference paper
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Symposium on Theory of Computing (STOC) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum search, unsorted database search, Grover's algorithm, quantum algorithms, time complexity, quantum parallelism, lower bounds
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 2026-10-21, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-21 (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
