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 7,901–8,000 of 8,792
AdaptDQC: Adaptive Distributed Quantum Computing With Quantitative Performance Analysis
Xiang, D., Lu, L., Tan, S., Jia, X., Zhou, Z., Sun, G., Chen, M., & Yin, J. (2025) · IEEE Transactions on Computers · doi:10.1109/tc.2025.3586027 · Cited by 5
A Variational Quantum Classifier for predictive analysis in industrial production
Angelino, A., Landolfi, E., Massa, A. A., & Troiano, A. (2025) · Internet of Things · doi:10.1016/j.iot.2025.101695 · Cited by 2
Optimal quantum sampling on distributed databases
Chen, L., Liu, J., & Yao, P. (2025) · ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) · doi:10.1145/3694906.3743335
Jankowski, B., Szydłowski, K., Niemiec, M., et al. (2025) · Electronics · doi:10.3390/electronics14142905
Hybrid quantum-classical framework for clustering
Lefevre, A. (2025) · Elsevier eBooks · doi:10.1016/b978-0-443-29096-1.00005-2
Post quantum cryptography for data safeguarding
Hussain, M. S., Arockiasamy, K., & Kanimozhi, G. (2025) · Elsevier eBooks · doi:10.1016/b978-0-443-29096-1.00009-x
Quantum computing and Artificial Intelligence: Toward a new computational paradigmPreprint
Fatunmbi, T. O. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5355156
Strengthened Key Method in Transition to Quantum Cryptology
Selvi, F., & Alkan, M. (2025) · Gazi Üniversitesi Fen Bilimleri Dergisi Part C Tasarım ve Teknoloji · doi:10.29109/gujsc.1682989
Kumar, P., Kar, B., & Shen, S.-H. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5366467
Yao, G., Kaur, N., & Gupta, L. (2024) · IEEE Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON) · doi:10.1109/iemcon62851.2024.11093551
Resource-efficient quantum data representation based on Grover’s algorithm
Ji, J., & Bae, J. (2025) · International Journal of Quantum Information · doi:10.1142/s0219749925500182
Accelerating Quantum Circuit Simulations with Data Compression
Xu, L., Sha, E. H. ‐., Song, Y., et al. (2025) · Advanced Quantum Technologies · doi:10.1002/qute.202500223
Quantum-resistant authentication: Securing identity and data against quantum threats
González-Tablas, A. I., Universidad Carlos Ⅲ de Madrid, D. D. I., Vasco, M. I. G., & Universidad Carlos Ⅲ de Madrid, D. D. M. (2025) · AIMS Mathematics · doi:10.3934/math.2025779
The Applications of Quantum Chips in RoboticsPreprint
Yarlagadda, H. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5354846
A Grover-Meets-Simon Approach to Match Vector Boolean Functions
Vénere, M., Barenghi, A., & Pelosi, G. (2025) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2025.3595275
An Unconditionally Secure Encryption Scheme for IoBT Networks
Moltafet, M., Sadjadpour, H. R., & Rezki, Z. (2025) · IEEE Internet of Things Journal · doi:10.1109/jiot.2025.3595493
Waked, H. N., Goyal, S. B., & Ghai, D. (2025) · Springer eBooks · doi:10.1007/978-981-96-4948-8_8
Quantum Computing for Analyzing Microgrid Systems With Uncertainties
Lange, J. M., Chen, J., Li, Y., et al. (2025) · doi:10.1109/itec63604.2025.11098157
Basic circuits for quantum computation
Kalita, G. (2025) · Advances in computers · doi:10.1016/bs.adcom.2025.06.003
Evaluation of quantum contouring algorithms for treatment planning on MR abdominal images
Glenn, R., Netherton, T., Celaya, A., et al. (2025) · Frontiers in Oncology · doi:10.3389/fonc.2025.1553539
A Pedagogical Introduction to the Deutsch and Deutsch-Jozsa AlgorithmsPreprint
Guchhait, A. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5372952
Information Encryption Algorithm Using a Discrete Quantum Map
Сидоренко, А. В., & Vysotskaya, E. A. (2025) · Doklady BGUIR · doi:10.35596/1729-7648-2025-23-3-102-107
Shinde, S., Chandragiri, A., Chaudhari, A., et al. (2025) · doi:10.1109/ginotech63460.2025.11076641
MKV: a new block cipher for the post-quantum cryptography transition
Nguyen, B. C., Nguyen, V. L., Nguyen, T. A., et al. (2025) · Математические вопросы криптографии · doi:10.4213/mvk497
A New Hard Problem for Post-Quantum Cryptography: Q-Problem Primitives
Kara, M., Hammoudeh, M. A. A., & Alamri, S. (2025) · Mathematics · doi:10.3390/math13152410
Braid Group Cryptography: Non-Abelian Defense Against Shor's AlgorithmPreprint
Kundnani, R., Kant, S., & Alam, K. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5391180
A Benchmarking Study of Grover’s Algorithm for Solving Boolean SAT with Quantum Circuits
Jipipob, J. U., & Chongstitvatana, P. (2025) · International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON) · doi:10.1109/ecti-con64996.2025.11100698
Quantum Implementation of Finite State Automata
Puram, V., Karuppasamy, K., George, K. M., et al. (2025) · Lecture notes in networks and systems · doi:10.1007/978-3-031-92608-2_23
Kumar, R., Malhotra, M., & Reddy, C. K. K. (2025) · IGI Global eBooks · doi:10.4018/979-8-3373-3551-3.ch004 · Cited by 1
Enhancing Metaheuristics: The Role of Quantum-Inspired Soft Computing
Das, P., Jain, C., Ansul, Gola, K. K., Kumar, N., & Singh, M. (2025) · Springer eBooks · doi:10.1007/978-3-031-87931-9_8
Analysis and Implementation of Quantum Logic Gates and Circuits
Kumar, D., Raj, B., & Singh, G. (2025) · International Conference on Electronics, AI and Computing (EAIC) · doi:10.1109/eaic66483.2025.11101348
IID-Based QPP-RNG: A Random Number Generator Utilizing Qpp Generated from System Jitter
Kuang, R., & Lou, D. (2025) · International Conference on Communications, Circuits and Systems · doi:10.1109/icccas65806.2025.11102777
Quantum representation of the earth based on the bloch sphere
Li, C., Cao, Z., Lu, D., et al. (2025) · International Journal of Quantum Information · doi:10.1142/s0219749925500224
Quantum Speedups for Multiproposal MCMC
Lin, C., Chen, K.-C., Lemey, P., Suchard, M. A., Holbrook, A. J., & Hsieh, M.-H. (2025) · Bayesian Analysis · doi:10.1214/25-ba1546
The Fine Print of Solving Markov Chains with Analog Quantum Computing
van der Schoot, W., & Neumann, N. M. P. (2025) · Lecture notes in networks and systems · doi:10.1007/978-3-031-92602-0_9
Beamforming Design for RIS-Assisted MIMO Systems with Spatial Channel Correlation
Si, W. (2025) · Communications in computer and information science · doi:10.1007/978-981-95-1331-4_1
Discrete quantum walks with marked vertices and their average vertex mixing matrices
Mohan, A., & Zhan, H. (2025) · Linear Algebra and its Applications · doi:10.1016/j.laa.2025.08.013
Tools to Design Algorithms for Implementing Control Over Quantum Computers
Narasimhan, S., Halloun, J. A., Nieman, K., & Durand, H. (2025) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc63710.2025.11107665
Gupta, A. K., Vaidya, P., & Sonia, S. (2025) · International Conference on Computing for Sustainable Global Development · doi:10.23919/indiacom66777.2025.11115508
203Chapter 8 Quantum computing and blind computing for secure futuristic networks
Dua, A., Aseri, V., Slimani, K., Patel, S., & Singh, A. (2025) · De Gruyter eBooks · doi:10.1515/9783111264349-008
Rifat, M. R. I., Rahman, M. M., Nayon, M. A. K., Azad, M. S., & Mahdy, M. R. C. (2025) · Engineering Science and Technology an International Journal · doi:10.1016/j.jestch.2025.102167 · Cited by 4
A simple model of quantum walk with a gap in distribution
Machida, T. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04898-0
273Chapter 11 Quantum security in 6G networks
Krishna, K., & Pathak, P. (2025) · De Gruyter eBooks · doi:10.1515/9783111264349-011
Putranto, D. S. C., Wardhani, R. W., & Kim, H. (2025) · IEEE Access · doi:10.1109/access.2025.3601565
AI and Quantum Computing: The Future of Financial Modeling and Risk Assessment
Bhati, S., Thareja, R., & Sharma, S. (2025) · Information systems engineering and management · doi:10.1007/978-3-031-92916-8_21 · Cited by 2
Parallelization of Quantum Algorithms Using Quantum Teleportation
Sysoev, S. S. (2025) · Moscow University Physics Bulletin · doi:10.3103/s002713492570050x
A Statistical Approach to Analyzing the Quantum Alternating Operator Ansatz with Grover Mixer
Bridi, G. A., & Marquezino, F. D. L. (2025) · doi:10.5753/ctd.2025.8022
Hai, V. T., Urbaneja, J., & Ho, L. B. (2025) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw67625.2025.00022
Grover-Diffusion Operator Unicity for the Grover Quantum-Search Algorithm
Dima, M. O., Dima, M. O., Dima, M., et al. (2025) · Physics of Particles and Nuclei · doi:10.1134/s106377962570011x
Babakhel, O., Tabassum, M., & Sharma, T. (2025) · Information systems engineering and management · doi:10.1007/978-3-031-99786-0_7
Wang, C., Lin, Y., & Cheng, L. (2025) · IEEE Transactions on Learning Technologies · doi:10.1109/tlt.2025.3604522
An Optimized Hybrid Quantum-Classical Neural Network Model for Handwritten Digit Classification
Nguyen, V.-Q.-M., Le, T.-K., Bui, T.-T., et al. (2025) · doi:10.1109/icdv66179.2025.11135335
Evaluating the Suitability of IBM Quantum Hardware for Practical Quantum Search
Sajja, J., Abhishek, V., Sumanth, A., et al. (2025) · IEEE Applied Sensing Conference (APSCON) · doi:10.1109/apscon63569.2025.11144201
Secure Two-Party Euclidean Distance Algorithm Based on Quantum Entanglement
Zhang, S., Liu, Z., Wu, Z., et al. (2025) · International Conference on Information Science, Computer Technology and Transportation (ISCTT) · doi:10.1109/isctt66403.2025.11137896
Revisit: Multi‐Tree Approach to Mutable Order‐Preserving Encoding
Bang, J., Chung, D., & Lee, S. (2025) · Electronics Letters · doi:10.1049/ell2.70419
Computação quântica aplicada à hardware reconfigurável com foco em segurança da informação
Fernandes, G. I. A., Filgueiras, G. T., & Gomes, O. D. S. M. (2025) · Simpósio Brasileiro de Cibersegurança (SBSeg) · doi:10.5753/sbseg_estendido.2025.13963
Analysis of two dimensional measurement-free surface code under idling patch
Min, G., & Heo, J. (2025) · IEEE VTS Asia Pacific Wireless Communications Symposium (APWCS) · doi:10.1109/apwcs67981.2025.11151932
ZXNet: ZX Calculus-Driven Graph Neural Network Framework for Quantum Circuit Equivalence Checking
Choudhury, N., Bhave, A., & Basu, K. (2025) · Proceedings - ACM IEEE Design Automation Conference · doi:10.1109/dac63849.2025.11133226
DDRoute: a Novel Depth-Driven Approach to the Qubit Routing Problem
Annechini, A., Vénere, M., Sciuto, D., & Santambrogio, M. D. (2025) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1109/dac63849.2025.11133018 · Cited by 2
A Quantum Virtual Machine for Execution of Oracles
de Muelenaere, U. (2025) · ACM International Symposium on High-Performance Parallel and Distributed Computing (HPDC) · doi:10.1145/3731545.3744150
Parallelisation of Quantum Algorithms Using Quantum Teleportation
Sysoev, S. S. (2025) · Vestnik Moskovskogo Universiteta Seriya 3 Fizika Astronomiya · doi:10.55959/msu0579-9392.80.2530406
Improving Qiskit strategies for circuit synthesis using the Reed-Muller spectrum
Lima, R. B. F., Kowada, L. A. B., & dos Santos, F. G. (2025) · Anais do Seminário Integrado de Software e Hardware (SEMISH) · doi:10.5753/semish.2025.9256
Further applications of the generalized phase kick-back
Ossorio-Castillo, J., Pastor–Díaz, U., & Tornero, J. M. (2025) · International Journal of Modern Physics C · doi:10.1142/s0129183125430053
Quantum Algorithm Mapping Latency Estimation in Three-Dimensional Quantum Architectures
Chen, J., Yao, L., Li, C., Guo, B., & Tsang, K. F. (2025) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2025.3610871
Quantum Amplitude Hash Function for Quantum Evidence Integrity
Lee, D., Shin, H., & Hong, S. (2025) · IEEE Access · doi:10.1109/access.2025.3611342
Q-xApp: A Quantum-Enabled Resource Management Module for Virtualized RAN Architectures
Lee, W., Song, Y., Jang, Y. H., et al. (2025) · IEEE International Conference on Communications workshops · doi:10.1109/iccworkshops67674.2025.11162380
Gonçalves, L. F., Oliveira, I. E. G. D., Caitano, R., Moraes, L., de Figueirêdo, P. H., & Ferraz, J. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04928-x
Hamiltonian Formulation of a Finite-State Automaton
Kwon, Y., & Agha, G. (2025) · Lecture notes in computer science · doi:10.1007/978-3-032-05291-9_13
Method for 3D structure of measurement-free fault tolerant surface codePreprint
Min, G., & Heo, J. (2025) · Research Square · doi:10.21203/rs.3.rs-7596333/v1
Finance in the Quantum Computing Era: A Survey from 2019 to 2024
Andrade-Gorjoux, L. E., Castrejón-Peralta, C., Saavedra-Benavides, J., et al. (2025) · Studies in computational intelligence · doi:10.1007/978-3-031-85614-3_14
Counting with the quantum alternating operator ansatz
Drapeau, J., Banerjee, S., & Kourtis, S. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae57d6 · Cited by 2
Enhancing ROS 2 (robot operating system 2) security with standardized post-quantum cryptosystems
Safdar, U., Qadir, S., & Nazir, M. S. (2025) · International Journal of Information Security · doi:10.1007/s10207-025-01133-w
Quantum Machine Learning: Applications in Electrical Engineering
Rajalakshmi, A., Sajan, M. R., & Krishna, K. (2025) · IFIP advances in information and communication technology · doi:10.1007/978-3-031-98364-1_28
Resource-Efficient Reversible Quantum Circuit for Theta Function in SHA-3
Suh, Y., & Park, Y. (2025) · doi:10.1109/icufn65838.2025.11169923
Quantum Speedup for Pilot Assignment Problems
Mikuriya, T., Ando, K., Yukiyoshi, K., de Abreu, G. T. F., Ishibashi, K., & Ishikawa, N. (2025) · IEEE Vehicular Technology Conference · doi:10.1109/vtc2025-spring65109.2025.11174641
Introduction to Quantum Computing
Thé, J. V. G., Fraser, R. A., & Rosas-Bustos, J. R. (2025) · Springer eBooks · doi:10.1007/978-3-031-98245-3_1
Quantum Data Structures and Encoding
Thé, J. V. G., Fraser, R. A., & Rosas-Bustos, J. R. (2025) · Springer eBooks · doi:10.1007/978-3-031-98245-3_4
Thé, J. V. G., Fraser, R. A., & Rosas-Bustos, J. R. (2025) · Springer eBooks · doi:10.1007/978-3-031-98245-3_8
The efficiency frontier: Classical shadows versus direct quantum measurement
Ma, S., & Liu, J. (2026) · Quantum Machine Intelligence · doi:10.1007/s42484-026-00413-5
Quantum Methods for Boundary Checking in Classical Programs
Guang, Y., Zanotta, P., Zhou, K., Chen, Y., & Ayanzadeh, R. (2025) · International Conference on Mobile Systems, Applications, and Services · doi:10.1145/3711875.3737656
Exploring the use of quantum computers for resilience analysis in critical infrastructure networks
Brockt-Haßauer, C., Shatokhin, V., Jain, A. K., Köpke, C., Stolz, A., Fehling-Kaschek, M., & Buchleitner, A. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04947-8
Dhanu, A. C., Chaitra, P. C., & Manohar, M. (2025) · Lecture notes in networks and systems · doi:10.1007/978-3-032-05802-7_10
On the query complexity of unitary channel certification
Jeon, S., & Oh, C. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01135-5 · Cited by 5
Simple quantum coins enable pretty good state transfer on every hypercube
Zhan, H. (2025) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2024.0418
Compositional Quantum Control Flow with Efficient Compilation in Qunity
Mints, M., Voichick, F., Lampropoulos, L., et al. (2025) · Proceedings of the ACM on Programming Languages · doi:10.1145/3763056
Quantum spatial best-arm identification on a complete bipartite graph
Yamagami, T., Segawa, E., Mihana, T., Röhm, A., Uchida, A., & Horisaki, R. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05189-y
iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
Yin, K., Fang, X., Chen, Z., Hayes, D., Kaur, E., Nejabati, R., Häffner, H., Campbell, W. C., Hudson, E. R., Palsberg, J., et al. (2026) · International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS) · doi:10.1145/3779212.3790177 · Cited by 10
Quantum reservoir computing for predicting and characterizing chaotic maps
Li, Q., Mukhopadhyay, C., Minati, L., & Bayat, A. (2026) · Physical Review Research · doi:10.1103/qwvv-xqfq · Cited by 2
On quantum perceptron learning via quantum search
Sun, X., Roget, M., Molfetta, G. D., & Kadri, H. (2026) · Quantum Machine Intelligence · doi:10.1007/s42484-026-00406-4
Comparing gate and annealing-based quantum computing for configuration-based design tasks
Schiffmann, O., Gopsill, J., & Hicks, B. J. (2025) · Design Science · doi:10.1017/dsj.2025.10028
A new non-commutative key exchange protocol on combinatorial semigroup
Zhang, J., Yang, Y., & Bao, J. (2025) · Automatika · doi:10.1080/00051144.2025.2569114
Full-Phase Distributed Quantum Impossible Differential Cryptanalysis
Zhang, K., Shang, T., Zhang, Y., et al. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-3537-8_3
Quantum Color Image Selective Encryption in HSI Color Space
Song, X., Li, M., & Wang, F. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-1346-8_13
Lion: A New Ring Signature Construction from Lattice Gadget
Li, Y., Luo, P., Chen, X., et al. (2025) · Lecture notes in computer science · doi:10.1007/978-981-95-3540-8_17
Feasibility of Quantum Key Distribution Between Supersonic Aircraft
McKiernan, S., & Collins, R. J. (2025) · IET Quantum Communication · doi:10.1049/qtc2.70018
From Classical to Quantum: Exploring Hashing Techniques for Enhanced Data Security and Efficiency
Saiyed, N., & Mishra, N. C. (2025) · doi:10.1109/eites66543.2025.00028
LaPierre, R. (2025) · The Materials Research Society series · doi:10.1007/978-3-031-90731-9_12
López-García, M., & Cantó, E. (2025) · EURASIP Journal on Information Security · doi:10.1186/s13635-025-00218-2
Naveen, P., Rajalakshmi, S., Abhirami, J. S., Vaissnave, V., Subramanian, S., & Pandiaraj, S. (2025) · Blockchain technologies · doi:10.1007/978-981-96-9148-7_11
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
