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 2,901–3,000 of 8,792
Quantum Secret Aggregation Utilizing a Network of Agents
Ampatzis, M., & Andronikos, T. (2023) · Cryptography · doi:10.3390/cryptography7010005 · Cited by 11
Quantum Circuit Based on Grover Algorithm to Solve Hamiltonian Cycle Problem
Jiang, J. (2022) · IEEE Eurasia Conference on IOT, Communication and Engineering (ECICE) · doi:10.1109/ecice55674.2022.10042919 · Cited by 10
Supervised learning of random quantum circuits via scalable neural networks
Cantori, S., Vitali, D., & Pilati, S. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acc4e2 · Cited by 12
The Impact of Quantum Supremacy on Cryptography : Implications for Secure Financial Transactions
Dixit, S. (2020) · International Journal of Scientific Research in Computer Science Engineering and Information Technology · doi:10.32628/cseit2064141 · Cited by 10
Grover’s Algorithm with Errors
Ambainis, A., Bačkurs, A., Nahimovs, N., et al. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-36046-6_17 · Cited by 10
The quantum walk search algorithm: factors affecting efficiency
Lovett, N. B., Everitt, M., Heath, R. M., & Kendon, V. M. (2018) · Mathematical Structures in Computer Science · doi:10.1017/s0960129518000051 · Cited by 16
Applying Quantum Algorithm to Speed Up the Solution of Hamiltonian Cycle Problems
Raj, C. V., & Shivakumar, M. S. (2007) · Springer eBooks · doi:10.1007/978-0-387-44641-7_6 · Cited by 10
Query Complexity in Expectation
Kaniewski, J., Lee, T., & de Wolf, R. (2015) · Lecture notes in computer science · doi:10.1007/978-3-662-47672-7_62 · Cited by 14
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
Jeffery, S., Kothari, R., Gall, F. L., & Magniez, F. (2015) · Algorithmica · doi:10.1007/s00453-015-9985-x · Cited by 11
Stronger Methods of Making Quantum Interactive Proofs Perfectly Complete
Kobayashi, H., Gall, F. L., & Nishimura, H. (2015) · SIAM Journal on Computing · doi:10.1137/140971944 · Cited by 10
Universal test for quantum one-way permutations
Kawachi, A., Kobayashi, H., Koshiba, T., & Putra, R. H. (2005) · Theoretical Computer Science · doi:10.1016/j.tcs.2005.07.036 · Cited by 10
Multiple re-encounter approach to radical pair reactions and the role of nonlinear master equations
Clausen, J., Guerreschi, G. G., Tiersch, M., & Briegel, H. J. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4891470 · Cited by 10
High-speed processor for quantum-computing emulation and its applications
Fujishima, M., Saito, K., Onouchi, M., & Hoh, H. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2003.1206362 · Cited by 10
Hirsh, H. (1999) · IEEE Intelligent Systems · doi:10.1109/mis.1999.10014 · Cited by 10
The Analysis of the Concrete Gravity Dam’s Foundation Uplift Pressure under the Function of Typhoon
Zhu, K., Gu, C., Qiu, J., et al. (2016) · Mathematical Problems in Engineering · doi:10.1155/2016/2834192 · Cited by 10
A Server-Assisted Hash-Based Signature Scheme
Buldas, A., Laanoja, R., & Truu, A. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-70290-2_1 · Cited by 10
Design and Optimization of Modular Multiplication for SIDH
Liu, C., Ni, J., Liu, W., Liu, Z., & O'Neill, M. P. (2018) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2018.8351082 · Cited by 10
Milestone Developments in Quantum Information and No-Go Theorems
Sharma, K. K., Gerdt, V. P., & Gerdt, P. V. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-66471-8_39 · Cited by 10
Quantum-Inspired Automatic Clustering Technique Using Ant Colony Optimization Algorithm
Dey, S., Bhattacharyya, S., & Maulik, U. (2018) · Advances in computer and electrical engineering book series · doi:10.4018/978-1-5225-5219-2.ch002 · Cited by 10
A Universe Built of Information
Glattfelder, J. B. (2019) · The frontiers collection · doi:10.1007/978-3-030-03633-1_13 · Cited by 12
Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks
Osawa, S., Simon, D. S., & Sergienko, A. V. (2019) · Entropy · doi:10.3390/e21090853 · Cited by 10
Locking the Design of Building Blocks for Quantum Circuits
Saeed, S. M., Wille, R., & Karri, R. (2019) · ACM Transactions on Embedded Computing Systems · doi:10.1145/3358184 · Cited by 10
Davies, P. C. W., & Australian Centre For Astrobiology (2004) · Cited by 10
Verifiable Quantum Key Exchange with Authentication
Shi, R., Liu, B., & Zhang, M. (2021) · International Journal of Theoretical Physics · doi:10.1007/s10773-020-04681-0 · Cited by 10
Ephemeral Keys Authenticated with Merkle Trees and Their Use in IoT Applications
Zajac, P. (2021) · Sensors · doi:10.3390/s21062036 · Cited by 15
Recent Progress in Code-Based Cryptography
Cayrel, P.-L., Alaoui, S. M. E. Y., Hoffmann, G., Meziani, M., & Niebuhr, R. (2011) · Communications in computer and information science · doi:10.1007/978-3-642-23141-4_3 · Cited by 12
Tree search and quantum computation
Tarrataca, L., & Wichert, A. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0212-z · Cited by 15
An implementation of compact genetic algorithm on a quantum computer
Yingchareonthawornchai, S., Aporntewan, C., & Chongstitvatana, P. (2012) · doi:10.1109/jcsse.2012.6261939 · Cited by 10
Quantum Switching Networks with Classical Routing
Ratan, R., Shukla, M. K., & Oruç, A. Y. (2007) · Conference on Information Sciences and Systems · doi:10.1109/ciss.2007.4298416 · Cited by 10
From gauge transformations to topology computation in quantum lattice gas automata
MEYER, D. A. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/35/323 · Cited by 10
Natural Quantum Operational Semantics with Predicates
Sawerwain, M., & Gielerak, R. (2008) · International Journal of Applied Mathematics and Computer Science · doi:10.2478/v10006-008-0031-x · Cited by 10
Alternation in Quantum Programming: From Superposition of Data to Superposition of ProgramsPreprint
Ying, M., Yu, N., & Feng, Y. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.5172 · Cited by 21
Quantum Domain Theory - Definitions and ApplicationsPreprint
Kashefi, E. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0306077 · Cited by 10
Quantum search for multiple items using parallel queriesPreprint
Grover, L. K., & Radhakrishnan, J. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0407217 · Cited by 10
Self-citationApplications of the Adversary Method in Quantum Query AlgorithmsPreprint
Belovs, A. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.3858 · Cited by 20
Round Elimination in Exact Communication ComplexityPreprint
Briët, J., Buhrman, H., Leung, D., et al. (2015) · arXiv (Cornell University) · doi:10.4230/lipics.tqc.2015.206 · Cited by 10
Image Processing in Quantum ComputersPreprint
Dendukuri, A., & Luu, K. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1812.11042 · Cited by 18
On The Hardness of Approximate and Exact (Bichromatic) Maximum Inner ProductPreprint
Chen, L. (2018) · arXiv (Cornell University) · doi:10.4230/lipics.ccc.2018.14 · Cited by 11
Quantum Walks On GraphsPreprint
Aharonov, D., Ambainis, A., Kempe, J., & Vazirani, U. V. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0012090 · Cited by 57
On Bitcoin Security in the Presence of Broken Crypto Primitives.Preprint
Giechaskiel, I., Cremers, C. J. F., & Rasmussen, K. (2016) · IACR Cryptology ePrint Archive · Cited by 10
Quantum Proofs for Classical TheoremsPreprint
Drucker, A., & de Wolf, R. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0910.3376 · Cited by 10
Upper bounds on quantum query complexity inspired by the elitzur-vaidman bomb testerPreprint
Lin, C. Y.-Y., & Lin, H.-H. (2015) · arXiv (Cornell University) · doi:10.5555/2833227.2833254 · Cited by 12
Foundational Patterns for Efficient Quantum ComputingPreprint
Gilliam, A., Venci, C., Muralidharan, S., Dorum, V., May, E. F., Narasimhan, R., & Gonciulea, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.11513 · Cited by 10
Span programs and quantum query algorithms.Preprint
Reichardt, B. W. (2010) · Electronic colloquium on computational complexity · Cited by 10
Sharma, S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.10453 · Cited by 12
Image Compression and Classification Using Qubits and Quantum Deep LearningPreprint
Mohsen, A., & Tiwari, M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.05476 · Cited by 18
NISQ-HHL: Portfolio Optimization for Near-Term Quantum HardwarePreprint
Yalovetzky, R., Minssen, P., Herman, D., & Pistoia, M. (2021) · arXiv (Cornell University) · Cited by 11
Position Papers for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking
Lougovski, P., Parekh, O., Broz, J., Byrd, M., Chembo, Y. K., de Jong, W. A., Figueroa, E. V., Humble, T. S., Larson, J. M., Quiroz, G., et al. (2023) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · doi:10.2172/2283320 · Cited by 10
Withdrawn: Advancements in Quantum Computing and AI May Impact PQC Migration TimelinesPreprint
Campbell, R., Diffie, W., & Robinson, C. R. (2024) · Preprints.org · doi:10.20944/preprints202402.1299.v1 · Cited by 10
Hybrid Quantum-Classical Heuristic to Solve Large-Scale Integer Linear Programs
Svensson, M., Andersson, M., Grönkvist, M., Vikstål, P., Dubhashi, D., Ferrini, G., & Johansson, G. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.20.034062 · Cited by 15
Formal semantics of a classical-quantum language
Deng, Y., & Feng, Y. (2022) · Theoretical Computer Science · doi:10.1016/j.tcs.2022.02.017 · Cited by 9
Chen, Y., & Stade, Y. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-44245-2_9 · Cited by 10
High-speed train timetable optimization based on space–time network model and quantum simulator
Xu, H.-Z., Chen, J., Zhang, X., Lu, T.-E., Gao, T., Wen, K., & Ma, Y. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04170-3 · Cited by 9
M&M’S: Mix and Match Attacks on Schnorr-Type Blind Signatures with Repetition
Do, K., Hanzlik, L., & Paracucchi, E. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-58751-1_13 · Cited by 9
Quantum Control Machine: The Limits of Control Flow in Quantum Programming
Yuan, C., Villanyi, A., & Carbin, M. (2024) · Proceedings of the ACM on Programming Languages · doi:10.1145/3649811 · Cited by 24
Quantum and Classical Query Complexities of Functions of Matrices
Montanaro, A., & Shao, C. (2024) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3618260.3649665 · Cited by 17
Multiparty Quantum Key Agreement Based on d$d$‐dimensional Bell States
Shu, Y., Bai, C., Hong, W., et al. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202400204 · Cited by 9
Joshi, M., Mishra, M. K., & Karthikeyan, S. (2024) · International Journal of Theoretical Physics · doi:10.1007/s10773-024-05751-3 · Cited by 9
Implementing Grover’s on AES-based AEAD schemes
Mandal, S., Anand, R., Rahman, M., Sarkar, S., & Isobe, T. (2024) · Scientific Reports · doi:10.1038/s41598-024-69188-8 · Cited by 9
Al-Bayaty, A., & Perkowski, M. A. (2024) · Entropy · doi:10.3390/e26100843 · Cited by 10
Evaluating Quantum Optimization for Dynamic Self-Reliant Community Detection
Bucher, D., Porawski, D., Wimmer, B., et al. (2024) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2024.3483657 · Cited by 9
A threshold changeable dynamic quantum secret sharing scheme with cheating identification
Li, F., Wu, Q., Lin, C., et al. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04572-x · Cited by 9
Three-party quantum dialogue based on Grover’s algorithm with identity dual authentication
Pan, T.-J., Zhou, R., & Zhang, X. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04570-z · Cited by 9
Quantum-Position-Locked Loop: New Concept for Collaborative Beam Forming for UAV Swarm
Arya, S., & Wang, Y. N. (2024) · IEEE Wireless Communications Letters · doi:10.1109/lwc.2024.3508657 · Cited by 9
Cyber Security and Data Ownership
Vrana, J. (2024) · Springer eBooks · doi:10.1007/978-3-030-48200-8_79-1 · Cited by 10
Optimizing quantum machine learning for proactive cybersecurity
Rosa-Remedios, C., & Caballero‐Gil, P. (2024) · Optimization and Engineering · doi:10.1007/s11081-024-09934-z · Cited by 13
An invitation to the sample complexity of quantum hypothesis testing
Cheng, H., Datta, N., Liu, N., Nuradha, T., Salzmann, R., & Wilde, M. M. (2025) · npj Quantum Information · doi:10.1038/s41534-025-00980-8 · Cited by 23
Qu-Trefoil: Large-Scale Quantum Circuit Simulator Working on FPGA With SATA Storages
Wei, K., Amano, H., Niwase, R., et al. (2024) · IEEE Transactions on Computers · doi:10.1109/tc.2024.3521546 · Cited by 9
Quantum data encoding as a distinct abstraction layer in the design of quantum circuits
Agliardi, G., & Prati, E. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/ada6f8 · Cited by 9
Hype or Heuristic? Quantum Reinforcement Learning for Join Order Optimisation
Franz, M., Winker, T., Groppe, S., & Mauerer, W. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00055 · Cited by 18
Optimizing Quantum Circuits, Fast and Slow
Xu, A., Molavi, A., Tannu, S. S., & Albarghouthi, A. (2024) · International Conference on Architectural Support for Programming Languages and Operating Systems · doi:10.1145/3669940.3707240 · Cited by 24
Eisinger, J., Gauderis, W., de Huybrecht, L., & Wiggins, G. A. (2025) · Entropy · doi:10.3390/e27040433 · Cited by 9
AutoQ 2.0: From Verification of Quantum Circuits to Verification of Quantum Programs
Chen, Y., Chung, K.-M., Hsieh, M.-H., Huang, W., Lengál, O., Lin, J.-A., & Tsai, W.-L. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-90660-2_5 · Cited by 9
Zecchi, A. A., Sanavio, C., Perotto, S., & Sauro Succi, A. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/addeea · Cited by 9
Security Attacks Abusing Pulse-Level Quantum Circuits
Xu, C., & Szefer, J. M. (2025) · Springer eBooks · doi:10.1007/978-3-032-09303-5_11 · Cited by 16
Xia, S., Zhao, J., Zhang, F., & Guo, X. (2025) · Proceedings of the ACM on software engineering. · doi:10.1145/3728926 · Cited by 9
Alzahrani, A. I. A. (2025) · The Journal of Supercomputing · doi:10.1007/s11227-025-07682-0 · Cited by 9
Kebande, V. R. (2025) · Wiley Interdisciplinary Reviews Forensic Science · doi:10.1002/wfs2.70013 · Cited by 9
Quantum-Resilient Cryptography: A Survey on Classical and Quantum Algorithms
Sharath, H. A., Vrindavanam, J., V, Dana, S., & Prasad, S. N. (2025) · IEEE Access · doi:10.1109/access.2025.3612982 · Cited by 13
A Survey of Quantum Deep Reinforcement Learning for Resource Allocation in Future Wireless Networks
Astiti, N. M. E. P., & Lee, B. M. (2025) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2025.3638435 · Cited by 15
Quantum random walks on congested lattices and the effect of dephasing
Motes, K. R., Gilchrist, A., & Rohde, P. P. (2016) · Scientific Reports · doi:10.1038/srep19864 · Cited by 10
Quantum Competition Network Model Based On Quantum Entanglement
Zhong, Y., & Yuan, C.-Q. (2012) · Journal of Computers · doi:10.4304/jcp.7.9.2312-2317 · Cited by 9
Can quantum search accelerate evolutionary algorithms?
Johannsen, D., Kurur, P. P., & Lengler, J. (2010) · Genetic and Evolutionary Computation Conference (GECCO) · doi:10.1145/1830483.1830746 · Cited by 9
Multicasting in Quantum Switching Networks
Shukla, M. K., & Oruç, A. Y. (2010) · IEEE Transactions on Computers · doi:10.1109/tc.2010.52 · Cited by 9
Selected Privacy-Preserving Protocols
de Oliveira, F. B. (2016) · Springer eBooks · doi:10.1007/978-3-319-40718-0_6 · Cited by 9
Sun, H.-W., Zhang, L., Zuo, H.-J., Zhang, K., & Ma, C. (2018) · International Journal of Theoretical Physics · doi:10.1007/s10773-018-3791-6 · Cited by 9
Generating Student Interest in Quantum Computing
Uhlig, R. P., Dey, P. P., Jawad, S. K., et al. (2019) · 2022 IEEE Frontiers in Education Conference (FIE) · doi:10.1109/fie43999.2019.9028378 · Cited by 9
A quantum procedure for map generation
Wootton, J. R. (2020) · IEEE Conference on Games (CoG) · doi:10.1109/cog47356.2020.9231571 · Cited by 10
A Review on Fundamentals of Ternary Reversible Logic Circuits
Rani, P. M. N., & Thangkhiew, P. L. (2020) · International Conference on Computational Performance Evaluation (ComPE) · doi:10.1109/compe49325.2020.9200021 · Cited by 9
Quantum Maximum Likelihood Decoding for Linear Block Codes
Jung, H.-W., Kang, J., & Ha, J. (2020) · International Conference on Information and Communication Technology Convergence (ICTC) · doi:10.1109/ictc49870.2020.9289350 · Cited by 9
An ant colony based mapping of quantum circuits to nearest neighbor architectures
Bhattacharjee, A., Bandyopadhyay, C., Mukherjee, A., Wille, R., Drechsler, R., & Rahaman, H. (2021) · Integration · doi:10.1016/j.vlsi.2020.12.002 · Cited by 9
Ghosh, I. (2021) · Resonance · doi:10.1007/s12045-021-1168-2 · Cited by 10
Universal quantum state preparation via revised greedy algorithm
He, R.-H., Liu, H.-D., Wang, S., Wu, J., Nie, S.-S., & Wang, Z.-M. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac1dfe · Cited by 8
Constrained Quantum Optimization for Resource Distribution Management
Gaily, S. E., & Imre, S. (2021) · International Journal of Advanced Computer Science and Applications · doi:10.14569/ijacsa.2021.0120806 · Cited by 9
Quantum security of Grain-128/Grain-128a stream cipher against HHL algorithm
Liu, W., & Gao, J. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03275-x · Cited by 9
Applications of the Lambert–Tsallis Wq function in quantum photonic Gaussian boson sampling
Mendes, F. V., Lima, C., & Ramos, R. V. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03559-w · Cited by 10
A novel quantum image watermarking scheme for tamper localization and self-recovery
Wang, M., Yang, H.-M., Jiang, D., et al. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03619-1 · Cited by 9
Hitting times of quantum and classical random walks in potential spaces
Varsamis, G. D., Karafyllidis, I. G., & Sirakoulis, G. C. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128119 · Cited by 9
Quantum generative adversarial networks based on Rényi divergences
Liu, L., Song, T., Sun, Z., & Lei, J. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128169 · Cited by 9
A Review of Developments in Superconducting Quantum Processors
Mamgain, A., Khaire, S. S., Singhal, U., Ahmad, I., Patel, L., Helambe, K. D., Majumder, S., Singh, V., & Suri, B. (2022) · Journal of the Indian Institute of Science · doi:10.1007/s41745-022-00330-z · Cited by 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
