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
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., & Preda, D. (2001) · Science · doi:10.1126/science.1057726 · Cited by 2,056
Measurement-based quantum computation on cluster states
Raussendorf, R., Browne, D. E., & Briegel, H. J. (2003) · Physical Review A · doi:10.1103/physreva.68.022312 · Cited by 1,655
Quantum-inspired evolutionary algorithm for a class of combinatorial optimization
Han, K.-H., & Kim, J.-H. (2002) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2002.804320 · Cited by 1,601
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560
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
Quantum amplitude amplification and estimation
Brassard, G., Høyer, P., Mosca, M., & Tapp, A. (2002) · Contemporary Mathematics · doi:10.1090/conm/305/05215 · Cited by 1,680
Quantum random walks: An introductory overview
Kempe, J. (2003) · Contemporary Physics · doi:10.1080/00107151031000110776 · Cited by 1,413
6G and Beyond: The Future of Wireless Communications Systems
Akyildiz, I. F., Kak, A., & Nie, S. (2020) · IEEE Access · doi:10.1109/access.2020.3010896 · Cited by 1,472
Cleve, R., EKERT, A. K., Macchiavello, C., & Mosca, M. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0164 · Cited by 1,399
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
Bernstein, D. J., & Lange, T. (2017) · Nature · doi:10.1038/nature23461 · Cited by 1,242
Stabilizer Codes and Quantum Error Correction
Gottesman, D. (1997) · arXiv · doi:10.48550/arxiv.quant-ph/9705052 · Cited by 753
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J., Degroote, M., Johnson, P., Kieferová, M., Kivlichan, I., Menke, T., Peropadre, B., Sawaya, N., et al. (n.d.) · OPUS - Open Publications of UTS Scholars (University of Technology Sydney) · Cited by 1,265
The role of relative entropy in quantum information theory
Vedral, V. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.197 · Cited by 1,191
CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM
Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J. M., Schwabe, P., Seiler, G., & Stehle, D. (2018) · 2018 IEEE European Symposium on Security and Privacy (EuroS&P) · doi:10.1109/eurosp.2018.00032 · Cited by 1,192
Machine learning & artificial intelligence in the quantum domain: a review of recent progress
Dunjko, V., & Briegel, H. J. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab406 · Cited by 1,241
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031
Quantum walks: a comprehensive review
Venegas-Andraca, S. E. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0432-5 · Cited by 934
Quantum random walks - an introductory overview
Kempe, J., & Einstein, A. (2003) · Cited by 1,035
Power of data in quantum machine learning
Huang, H.-Y., Broughton, M., Mohseni, M., Babbush, R., Boixo, S., Neven, H., & McClean, J. R. (2021) · Nature Communications · doi:10.1038/s41467-021-22539-9 · Cited by 896
Hamiltonian Simulation by Qubitization
Low, G. H., & Chuang, I. L. (2019) · Quantum · doi:10.22331/q-2019-07-12-163 · Cited by 854
On the role of entanglement in quantum-computational speed-up
Jozsa, R., & Linden, N. (2003) · Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2002.1097 · Cited by 839
Le, P. Q., Dong, F., & Hirota, K. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0177-y · Cited by 797
NEQR: a novel enhanced quantum representation of digital images
Zhang, Y., Lü, K., Gao, Y., & Wang, M. (2013) · Quantum Information Processing · doi:10.1007/s11128-013-0567-z · Cited by 731
Quantum Walk Algorithm for Element Distinctness
Ambainis, A. (2007) · SIAM Journal on Computing · doi:10.1137/s0097539705447311 · Cited by 814
Challenges and opportunities in quantum machine learning
Cerezo, M., Verdon, G., Huang, H.-Y., Cincio, Ł., & Coles, P. J. (2022) · Nature Computational Science · doi:10.1038/s43588-022-00311-3 · Cited by 862
Quantum computing for finance: Overview and prospects
Orús, R., Mugel, S., & Lizaso, E. (2019) · Reviews in Physics · doi:10.1016/j.revip.2019.100028 · Cited by 792
Genetic quantum algorithm and its application to combinatorial optimization problem
Han, K.-H., & Kim, J.-H. (2002) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2000.870809 · Cited by 675
Complexity measures and decision tree complexity: a survey
Buhrman, H., & de Wolf, R. (2002) · Theoretical Computer Science · doi:10.1016/s0304-3975(01)00144-x · Cited by 706
Hamiltonian Simulation by Qubitization
Low, G. H., & Chuang, I. L. (2019) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 714
QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS
AMBAINIS, A. (2003) · International Journal of Quantum Information · doi:10.1142/s0219749903000383 · Cited by 632
Aharonov, D., Ambainis, A., Kempe, J., & Vazirani, U. (2001) · Proceedings of the thirty-third annual ACM symposium on Theory of computing · doi:10.1145/380752.380758 · Cited by 654
Childs, A. M., Kothari, R., & Somma, R. D. (2017) · SIAM Journal on Computing · doi:10.1137/16m1087072 · Cited by 646
Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3313276.3316366 · Cited by 1,070
Quantum lower bounds by polynomials
Beals, R., Buhrman, H., Cleve, R., Mosca, M., & de Wolf, R. (2001) · Journal of the ACM · doi:10.1145/502090.502097 · Cited by 639
Grover’s quantum searching algorithm is optimal
Zalka, C. (1999) · Physical Review A · doi:10.1103/physreva.60.2746 · Cited by 635
Nonlocality and communication complexity
Buhrman, H., Cleve, R., Massar, S., & de Wolf, R. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.665 · Cited by 656
Fernandez-Carames, T. M., & Fraga-Lamas, P. (2020) · IEEE Access · doi:10.1109/access.2020.2968985 · Cited by 607
Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices
Li, G., Ding, Y., & Xie, Y. (2019) · Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems · doi:10.1145/3297858.3304023 · Cited by 594
6G Wireless Communications Networks: A Comprehensive Survey
Alsabah, M. Q., Naser, M. A., Mahmmod, B. M., Abdulhussain, S. H., Eissa, M. R., Al-Baidhani, A., Noordin, N. K., Sait, S. M., Al-Utaibi, K. A., & Hashim, F. (2021) · IEEE Access · doi:10.1109/access.2021.3124812 · Cited by 622
Cybersecurity in an Era with Quantum Computers: Will We Be Ready?
Mosca, M. (2018) · IEEE Security & Privacy · doi:10.1109/msp.2018.3761723 · Cited by 581
Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., & Watrous, J. (2001) · Proceedings of the thirty-third annual ACM symposium on Theory of computing · doi:10.1145/380752.380757 · Cited by 562
Implementation of a quantum search algorithm on a quantum computer
Jones, J. A., Mosca, M., & Hansen, R. H. (1998) · Nature · doi:10.1038/30687 · Cited by 558
Information and computation: Classical and quantum aspects
Galindo, A., & Martin-Delgado, M. A. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.347 · Cited by 563
Coelho, L. D. S. (2009) · Expert Systems with Applications · doi:10.1016/j.eswa.2009.06.044 · Cited by 554
Quantum Computation by Adiabatic Evolution
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (2000) · arXiv · doi:10.48550/arxiv.quant-ph/0001106 · Cited by 536
“The other example is the “Grover problem” [2], which has a single (generalized) n-bit clause with a unique satisfying assignment.”
BackgroundUniversal quantum computation using the discrete-time quantum walk
Lovett, N. B., Cooper, S., Everitt, M., Trevers, M., & Kendon, V. (2010) · Physical Review A · doi:10.1103/physreva.81.042330 · Cited by 510
Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials
Stav, T., Faerman, A., Maguid, E., Oren, D., Kleiner, V., Hasman, E., & Segev, M. (2018) · Science · doi:10.1126/science.aat9042 · Cited by 494
CSIDH: An Efficient Post-Quantum Commutative Group Action
Castryck, W., Lange, T., Martindale, C., Panny, L., & Renes, J. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-03332-3_15 · Cited by 497
Schlosshauer, M. (2019) · Physics Reports · doi:10.1016/j.physrep.2019.10.001 · Cited by 603
Quantum computing: A taxonomy, systematic review and future directions
Gill, S. S., Kumar, A., Singh, H., Singh, M., Kaur, K., Usman, M., & Buyya, R. (2021) · Software Practice and Experience · doi:10.1002/spe.3039 · Cited by 579
Han, K.-H., & Kim, J.-H. (2004) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2004.823467 · Cited by 485
Towards a quantum programming language
Selinger, P. (2004) · Mathematical Structures in Computer Science · doi:10.1017/s0960129504004256 · Cited by 459
Demonstration of Blind Quantum Computing
Barz, S., Kashefi, E., Broadbent, A., Fitzsimons, J. F., Zeilinger, A., & Walther, P. (2012) · Science · doi:10.1126/science.1214707 · Cited by 475
Variational Quantum Computation of Excited States
Higgott, O., Wang, D., & Brierley, S. (2019) · Quantum · doi:10.22331/q-2019-07-01-156 · Cited by 463
Random Oracles in a Quantum World
Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., & Zhandry, M. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-25385-0_3 · Cited by 507
Ascon v1.2: Lightweight Authenticated Encryption and Hashing
Dobraunig, C., Eichlseder, M., Mendel, F., & Schläffer, M. (2021) · Journal of Cryptology · doi:10.1007/s00145-021-09398-9 · Cited by 478
Quantum walks: a comprehensive reviewPreprint
Venegas-Andraca, S. E. (2012) · Cited by 533
Quantum optimization of maximum independent set using Rydberg atom arrays
Ebadi, S., Keesling, A., Cain, M., Wang, T. T., Levine, H., Bluvstein, D., Semeghini, G., Omran, A., Liu, J.-G., Samajdar, R., et al. (2022) · Science · doi:10.1126/science.abo6587 · Cited by 430
ProjectQ: An open source software framework for quantum computing
Steiger, D. S., Häner, T., & Troyer, M. (2018) · Quantum · doi:10.22331/q-2018-01-31-49 · Cited by 428
Deterministic generation of a cluster state of entangled photons
Schwartz, I., Cogan, D., Schmidgall, E. R., Don, Y., Gantz, L., Kenneth, O., Lindner, N. H., & Gershoni, D. (2016) · Science · doi:10.1126/science.aah4758 · Cited by 428
A review on Quantum Approximate Optimization Algorithm and its variants
Blekos, K., Brand, D., Ceschini, A., Chou, C.-H., Li, R.-H., Pandya, K., & Summer, A. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.03.002 · Cited by 563
Status report on the third round of the NIST Post-Quantum Cryptography Standardization process
Alagic, G., Apon, D., Cooper, D. A., Dang, Q. H., Dang, T., Kelsey, J. M., Lichtinger, J., Liu, Y.-K., Miller, C. A., Moody, D., et al. (2022) · doi:10.6028/nist.ir.8413 · Cited by 492
An introduction to quantum computing for non-physicists
Rieffel, E. G., & Polak, W. (2000) · ACM Computing Surveys · doi:10.1145/367701.367709 · Cited by 436
Quantum machine learning: a classical perspective
Ciliberto, C., Herbster, M., Ialongo, A. D., Pontil, M., Rocchetto, A., Severini, S., & Wossnig, L. (2018) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2017.0551 · Cited by 518
Quantum vs. classical communication and computation
Buhrman, H., Cleve, R., & Wigderson, A. (1998) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/276698.276713 · Cited by 428
Simulating quantum systems on a quantum computer
Zalka, C. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0162 · Cited by 420
Wireless Myths, Realities, and Futures: From 3G/4G to Optical and Quantum Wireless
Hanzo, L., Haas, H., Imre, S., O'Brien, D. C., Rupp, M., & Gyöngyösi, L. (2012) · Proceedings of the IEEE · doi:10.1109/jproc.2012.2189788 · Cited by 391
Analog analogue of a digital quantum computation
Farhi, E., & Gutmann, S. (1998) · Physical Review A · doi:10.1103/physreva.57.2403 · Cited by 389
Zero Trust Architecture (ZTA): A Comprehensive Survey
Syed, N. F., Shah, S. W., Shaghaghi, A., Anwar, A., Baig, Z., & Doss, R. (2022) · IEEE Access · doi:10.1109/access.2022.3174679 · Cited by 406
“Similarly, for hash functions, Grover’s algorithm [185] can facilitate quantum birthday attack to find collision, thereby necessitating an output of larger size.”
BackgroundAn Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures
Zulehner, A., Paler, A., & Wille, R. (2018) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2018.2846658 · Cited by 382
Quantum Reinforcement Learning
Dong, D., Chen, C., Li, H., & Tarn, T.-J. (2008) · IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) · doi:10.1109/tsmcb.2008.925743 · Cited by 410
Verified quantum information scrambling
Landsman, K. A., Figgatt, C., Schuster, T., Linke, N. M., Yoshida, B., Yao, N. Y., & Monroe, C. (2019) · Nature · doi:10.1038/s41586-019-0952-6 · Cited by 368
A Quantum Algorithm for Finding the Minimum
Durr, C., & Hoyer, P. (1996) · arXiv · doi:10.48550/arxiv.quant-ph/9607014 · Cited by 359
Operating Quantum States in Single Magnetic Molecules: Implementation of Grover’s Quantum Algorithm
Godfrin, C., Ferhat, A., Ballou, R., Klyatskaya, S. V., Ruben, M., Wernsdorfer, W., & Balestro, F. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.187702 · Cited by 373
Quantum information processing and communication
Zoller, P., Beth, T., Binosi, D., Blatt, R., Briegel, H. J., Bruss, D., Calarco, T., Cirac, J. I., Deutsch, D., Eisert, J., et al. (2005) · The European Physical Journal D · doi:10.1140/epjd/e2005-00251-1 · Cited by 356
Moore, C., & Mertens, S. (2011) · doi:10.1093/acprof:oso/9780199233212.001.0001 · Cited by 358
On the power of quantum finite state automata
Kondacs, A., & Watrous, J. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1997.646094 · Cited by 356
Quantum algorithms for algebraic problems
Childs, A. M., & van Dam, W. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1 · Cited by 344
Breaking Symmetric Cryptosystems Using Quantum Period Finding
Kaplan, M. A., Leurent, G., Leverrier, A., & Naya‐Plasencia, M. (2016) · Lecture notes in computer science · doi:10.1007/978-3-662-53008-5_8 · Cited by 347
Quantum Lower Bounds by Quantum Arguments
Ambainis, A. (2002) · Journal of Computer and System Sciences · doi:10.1006/jcss.2002.1826 · Cited by 424
Quantum annealing for industry applications: introduction and review
Yarkoni, S., Raponi, E., Bäck, T., & Schmitt, S. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac8c54 · Cited by 341
Strawberry Fields: A Software Platform for Photonic Quantum Computing
Killoran, N., Izaac, J., Quesada, N., Bergholm, V., Amy, M., & Weedbrook, C. (2019) · Quantum · doi:10.22331/q-2019-03-11-129 · Cited by 395
Quantum lower bounds for the collision and the element distinctness problems
Aaronson, S., & Shi, Y. (2004) · Journal of the ACM · doi:10.1145/1008731.1008735 · Cited by 356
Kavokin, A. V., Baumberg, J. J., Malpuech, G., & Laussy, F. P. (2017) · doi:10.1093/oso/9780198782995.001.0001 · Cited by 326
The status of the P versus NP problem
Fortnow, L. (2009) · Communications of the ACM · doi:10.1145/1562164.1562186 · Cited by 330
Bos, J. W., Costello, C., Ducas, L., Mironov, I., Naehrig, M., Nikolaenko, V., Raghunathan, A., & Stebila, D. (2016) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/2976749.2978425 · Cited by 338
Fernández‐Caramés, T. M. (2019) · IEEE Internet of Things Journal · doi:10.1109/jiot.2019.2958788 · Cited by 358
A survey of quantum image representations
Yan, F., Iliyasu, A. M., & Venegas-Andraca, S. E. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-1195-6 · Cited by 308
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
Valiant, L. G. (2002) · SIAM Journal on Computing · doi:10.1137/s0097539700377025 · Cited by 311
Magnetic qubits as hardware for quantum computers
Tejada, J., Chudnovsky, E. M., del Barco, E., Hernández, J. M., & Spiller, T. P. (2001) · Nanotechnology · doi:10.1088/0957-4484/12/2/323 · Cited by 308
Quantum Machine Learning: What Quantum Computing Means to Data Mining
Wittek, P. (2014) · Cited by 319
Status report on the third round of the NIST Post-Quantum Cryptography Standardization process
Alagic, G., Apon, D., Cooper, D., Dang, Q., Dang, T., Kelsey, J., Lichtinger, J., Liu, Y.-K., Miller, C., Moody, D., et al. (2022) · doi:10.6028/nist.ir.8413-upd1 · Cited by 301
Applying Grover’s Algorithm to AES: Quantum Resource Estimates
Grassl, M., Langenberg, B., Roetteler, M., & Steinwandt, R. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-29360-8_3 · Cited by 299
Random Walks: A Review of Algorithms and Applications
Xia, F., Liu, J., Nie, H., Fu, Y., Wan, L., & Kong, X. (2020) · IEEE Transactions on Emerging Topics in Computational Intelligence · doi:10.1109/tetci.2019.2952908 · Cited by 295
Magniez, F., Nayak, A., Roland, J., & Santha, M. (2011) · SIAM Journal on Computing · doi:10.1137/090745854 · Cited by 294
Herman, D., Googin, C., Liu, X., Sun, Y., Galda, A., Safro, I., Pistoia, M., & Alexeev, Y. (2023) · Nature Reviews Physics · doi:10.1038/s42254-023-00603-1 · Cited by 361
Processing images in entangled quantum systems
Venegas-Andraca, S. E., & Ball, J. L. (2009) · Quantum Information Processing · doi:10.1007/s11128-009-0123-z · Cited by 290
Global Entanglement in Multiparticle SystemsPreprint
MEYER, D. A., Wallach, N. R., & Wallach, M. (2001) · Cited by 319
Ventura, D. A. (2000) · Information Sciences · doi:10.1016/s0020-0255(99)00101-2 · Cited by 292
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
