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 3,101–3,200 of 8,792
The Prime state and its quantum relatives
García-Martín, D., Ribas, E., Carrazza, S., et al. (2020) · Quantum · doi:10.22331/q-2020-12-11-371 · Cited by 9
The Three-party Quantum Key Agreement Protocol with Quantum Fourier Transform
Wang, W., Zhou, B.-M., & Zhang, L. (2020) · International Journal of Theoretical Physics · doi:10.1007/s10773-020-04467-4 · Cited by 9
Biasse, J., & Pring, B. (2020) · Journal of Mathematical Cryptology · doi:10.1515/jmc-2020-0080 · Cited by 9
Improving Quantum Search on Simple Graphs by Pretty Good Structured Oracles
Paris, M. G. A., Benedetti, C., & Olivares, S. (2021) · Symmetry · doi:10.3390/sym13010096 · Cited by 9
A Quantum Circuit to Speed-Up the Cryptanalysis of Code-Based Cryptosystems
Perriello, S., Barenghi, A., & Pelosi, G. (2021) · Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering · doi:10.1007/978-3-030-90022-9_25 · Cited by 11
Introduction of Quantum-inspired Evolutionary Algorithm
Han, K.-H., & Kim, J.-H. (2002) · Cited by 9
Quantum Computing for Computer Architects
Metodi, T. S., & Chong, F. T. (2006) · Synthesis lectures on computer architecture · doi:10.2200/s00066ed1v01y200610cac001 · Cited by 11
Oskin, M., Chong, F. T., Chuang, I. L., & Kubiatowicz, J. D. (2003) · ACM SIGARCH Computer Architecture News · doi:10.1145/871656.859661 · Cited by 9
Lower Bounds on the Size of Quantum Automata Accepting Unary Languages
Bertoni, A., Mereghetti, C., & Palano, B. (2003) · Lecture notes in computer science · doi:10.1007/978-3-540-45208-9_8 · Cited by 8
Problem-solving and Quantum Computation
Tarrataca, L. D. T. J., & Wichert, A. (2011) · Cognitive Computation · doi:10.1007/s12559-011-9103-6 · Cited by 9
The NESSIE Project: Towards New Cryptographic Algorithms
Bart Preneel, A. (2002) · Cited by 9
Chamoli, A., & Bhandari, C. M. (2007) · Quantum Information Processing · doi:10.1007/s11128-007-0057-2 · Cited by 9
Hines, P. (2008) · Theoretical Computer Science · doi:10.1016/j.tcs.2008.07.015 · Cited by 9
Quantum Higher Order Singular Value Decomposition
Gu, L., Wang, X., & Zhang, G. (2019) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/smc.2019.8914525 · Cited by 11
Training support vector machines: a quantum-computing perspective
Anguita, D., Ridella, S., Rivieccio, F., & Zunino, R. (2004) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2003.1223936 · Cited by 9
Fault tolerant computation on ensemble quantum computers
Boykin, P. O., Roychowdhury, C. P., Mor, T., & Vatan, F. (2004) · International Conference on Dependable Systems & Networks/Proceedings · doi:10.1109/dsn.2004.1311886 · Cited by 8
A Fixed-Phase Quantum Search Algorithm with More Flexible Behavior
Li, X., & Li, P. (2012) · Journal of Quantum Information Science · doi:10.4236/jqis.2012.22006 · Cited by 9
A quantum algorithm for minimal spanning tree
Aghaei, M. R. S., Zukarnain, Z. A., Mamat, A., & Zainuddin, H. (2008) · International Symposium on Information Technology · doi:10.1109/itsim.2008.4632038 · Cited by 9
Li, L., Thornton, M. A., & Perkowski, M. A. (2006) · Proceedings/Proceedings - International Symposium on Multiple-Valued Logic · doi:10.1109/ismvl.2006.8 · Cited by 9
The Quantum Adversary Method and Classical Formula Size Lower Bounds
Laplante, S., Lee, T., & Szegedy, M. (2005) · IEEE Conference on Computational Complexity (CCC) · doi:10.1109/ccc.2005.29 · Cited by 11
Circuit development using biological components: Principles, models and experimental feasibility
Krishnan, R., & Purdy, C. C. (2007) · Analog Integrated Circuits and Signal Processing · doi:10.1007/s10470-007-9094-0 · Cited by 9
Upper Bounds on Quantum Query Complexity Inspired by the Elitzur-Vaidman Bomb TesterPreprint
Lin, C. Y.-Y., & Lin, H.-H. (2014) · arXiv (Cornell University) · doi:10.4230/lipics.ccc.2015.537 · Cited by 17
Finding Matches between Two Databases on a Quantum ComputerPreprint
Heiligman, M. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0006136 · Cited by 13
Decoherence in Search AlgorithmsPreprint
Abal, G., Donangelo, R., Marquezino, F. D. L., Oliveira, A. C., & Portugal, R. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0912.1523 · Cited by 9
Quantum Complexity: restrictions on algorithms and architecturesPreprint
Shepherd, D. J. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1005.1425 · Cited by 10
High fidelity quantum gates with ions in cryogenic microfabricated ion traps
Chuang, I. L., & Labaziewicz, J. (2008) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 10
Quantum algorithms in group theory
Batty, M., Braunstein, S. L., Duncan, A. J., & Rees, S. (2004) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/349/06356 · Cited by 13
A Grover-based quantum search of optimal order for an unknown number of marked elementsPreprint
Zalka, C. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9902049 · Cited by 9
Sharp error bounds on quantum Boolean summation in various settings
Kwas, M., & Woźniakowski, H. (2003) · Journal of Complexity · doi:10.1016/j.jco.2003.08.004 · Cited by 9
A quantum query algorithm for the graph collision problemPreprint
Gavinsky, D., & Ito, T. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1204.1527 · Cited by 11
Non-Markovian quantum interference in multilevel quantum systems: Exact master equation approach
Chen, Y., You, J. Q., & Yu, T. (2018) · Quantum Information and Computation · doi:10.26421/qic18.15-16 · Cited by 9
Quantum finite automata: survey, status and research directionsPreprint
Bhatia, A. S., & Kumar, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1901.07992 · Cited by 9
Complexity-Theoretic Limitations on Blind Delegated Quantum ComputationPreprint
Aaronson, S., Cojocaru, A., Gheorghiu, A., & Kashefi, E. (2017) · arXiv (Cornell University) · doi:10.4230/lipics.icalp.2019.6 · Cited by 31
Quantum walks and their algorithmic applicationsPreprint
Ambainis, A. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0403120 · Cited by 16
Quantum Walks on the HypercubePreprint
Moore, C., & Russell, A. C. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0104137 · Cited by 9
Quantum Computing and Cryptography: Analysis, Risks, and Recommendations for Decisionmakers
Tibbetts, J. (2019) · doi:10.2172/1566798 · Cited by 5
The Bitcoin Backbone Protocol Against Quantum Adversaries.Preprint
Cojocaru, A., Garay, J. A., Kiayias, A., et al. (2019) · IACR Cryptology ePrint Archive · Cited by 9
Towards Post-Quantum Secure Symmetric Cryptography: A Mathematical Perspective.Preprint
Bogomolec, X., Underhill, J. G., & Kovac, S. A. (2019) · IACR Cryptology ePrint Archive · Cited by 9
Post-Quantum Secure Architectures for Automotive Hardware Secure Modules.Preprint
Wang, W., & Stöttinger, M. (2020) · IACR Cryptology ePrint Archive · Cited by 9
Arithmetic Coding and Blinding Countermeasures for Ring-LWE.Preprint
Saarinen, M.-J. O. (2016) · IACR Cryptology ePrint Archive · Cited by 9
A Digital Quantum Algorithm for Jet Clustering in High-Energy PhysicsPreprint
Pires, D., Bargassa, P., Seixas, J., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.05618 · Cited by 9
Formal Methods for Quantum Programs: A SurveyPreprint
Chareton, C., Bardin, S., Lee, D.-H., Valiron, B., Vilmart, R., & Xu, Z. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.06493 · Cited by 27
EQC : Ensembled Quantum Computing for Variational Quantum AlgorithmsPreprint
Stein, S., Ding, Y., Wiebe, N., Peng, B., Kowalski, K., Baker, N., Ang, J., & Li, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.14940 · Cited by 9
Quantum counterfeit coin problems
Iwama, K., Nishimura, H., Raymond, R., & Teruyama, J. (2012) · Theoretical Computer Science · doi:10.1016/j.tcs.2012.05.039 · Cited by 17
Surveying Quantum-Proof Blockchain Security: The Era of Exotic Signatures
Naz, R., & Kumar, A. (2024) · International Conference on Distributed Computing and Networking (ICDCN) · doi:10.1145/3631461.3631949 · Cited by 9
Expressive quantum supervised machine learning using Kerr-nonlinear parametric oscillators
Mori, Y., Nakaji, K., Matsuzaki, Y., & Kawabata, S. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00152-5 · Cited by 10
Quantum audio LSB steganography with entanglement-assisted modulation
Hao, C., Yang, X., Ma, Q., et al. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04312-1 · Cited by 8
Quantum circuit implementations of SM4 block cipher optimizing the number of qubits
Luo, Q.-B., Li, Q., Li, X., Yang, G., Shen, J., & Zheng, M. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04394-x · Cited by 8
Quantum Probabilistic Model Checking for Time-Bounded Properties
Jeon, S., Cho, K., Kang, C. G., Lee, J., Oh, H., & Kang, J. (2024) · Proceedings of the ACM on Programming Languages · doi:10.1145/3689731 · Cited by 8
Distributed quantum machine learning via classical communication
Hwang, K., Lim, H., Kim, Y., Park, D. K., & Kim, Y. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad9cb9 · Cited by 9
Quantum Algorithms for the Physical Layer: Potential Applications to Physical Layer Security
Matsumine, T., Ochiai, H., & Shikata, J. (2025) · IEEE Access · doi:10.1109/access.2025.3528443 · Cited by 9
Application of quantum artificial intelligence in healthcare
Goswami, S. A., Dave, S., Patel, K. C. K., & Raval, M. N. (2025) · Elsevier eBooks · doi:10.1016/b978-0-443-29297-2.00007-1 · Cited by 9
Halving the cost of quantum algorithms with randomization
Martyn, J. M., & Rall, P. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01003-2 · Cited by 18
Exploring quantum neural networks for binary classification on MNIST dataset: A swap test approach
Chen, K., Liu, J., & Yan, F. (2025) · Neural Networks · doi:10.1016/j.neunet.2025.107442 · Cited by 9
Mirigaldi, M., Piscopo, V., Martina, M., et al. (2025) · Chips · doi:10.3390/chips4020015 · Cited by 8
Mbimbi, B., Murray, D. E., & Wilson, M. (2025) · Blockchains · doi:10.3390/blockchains3020007 · Cited by 8
An Innovative Algorithm for Attacking Symmetric Ciphers Using D-Wave Quantum Annealing
Pei, Z., Hong, C., Xia, F., & Wang, C. (2025) · Tsinghua Science & Technology · doi:10.26599/tst.2024.9010231 · Cited by 8
Theory and Applications of Quantum Hashing
Ablayev, F. M., Khadiev, K. R., Vasiliev, A., & Ziiatdinov, M. (2025) · Quantum Reports · doi:10.3390/quantum7020024 · Cited by 8
Behera, B. K., Al-Kuwari, S. M., & Farouk, A. (2025) · IEEE Transactions on Artificial Intelligence · doi:10.1109/tai.2025.3572852 · Cited by 17
Gold OPRF: Post-Quantum Oblivious Power-Residue PRF
Yang, Y., Benhamouda, F., Halevi, S., Krawczyk, H., & Rabin, T. (2025) · IEEE Symposium on Security and Privacy (S&P) · doi:10.1109/sp61157.2025.00116 · Cited by 8
Variational Quantum Algorithms in the era of Early Fault Tolerance
Dangwal, S., Vittal, S., Seifert, L. M., Chong, F. T., & Ravi, G. S. (2025) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3695053.3731112 · Cited by 13
Xiao, Y., Yang, L., Shu, C., Du, Y., & Song, Y. (2025) · Physics of Fluids · doi:10.1063/5.0273328 · Cited by 8
Srivastava, A. K., Sharma, S., Hussain, S., Ghosh, S., & Sharma, N. (2025) · International Conference on Communication, Security and Artificial Intelligence (ICCSAI) · doi:10.1109/iccsai64074.2025.11064720 · Cited by 11
Revythi, M., & Κούκιου, Γ. (2025) · Machine Learning and Knowledge Extraction · doi:10.3390/make7030075 · Cited by 11
Realization of an untrusted intermediate relay architecture using a quantum dot single-photon source
Zou, M., He, Y.-M., Huang, Y., Zhao, J.-Y., Li, B.-C., Guo, Y.-P., Ding, X., Xu, M.-C., Liu, R., Zou, G.-Y., et al. (2025) · Nature Physics · doi:10.1038/s41567-025-03005-5 · Cited by 8
Campbell, C., Chen, H., Luk, W., & Fan, H. (2025) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1109/dac63849.2025.11133316 · Cited by 8
Quantum and quantum-inspired computing in civil engineering
Ploennigs, J., Smarsly, K., Berger, M., Dragos, K., & Kliesch, M. (2025) · Advanced Engineering Informatics · doi:10.1016/j.aei.2025.103960 · Cited by 12
Quantum cryptography and data protection for medical devices before and after they meet Q-Day
Freyer, O., Ostermann, M., Minssen, T., & Gilbert, S. (2025) · npj Digital Medicine · doi:10.1038/s41746-025-02082-3 · Cited by 16
Khan, M. A., Noor, F., Javaid, S., & Żywiołek, J. (2025) · Discover Internet of Things · doi:10.1007/s43926-025-00238-x · Cited by 16
Variational Quantum Computing for Quantum Simulation: Principles, Implementations, and Challenges
Galvão, L. Q., de Souza, A. B. M., Moret, M. A., & Cruz, C. (2025) · Brazilian Journal of Physics · doi:10.1007/s13538-025-01946-z · Cited by 8
Quantum Pattern Search with Closed Match
Zhou, R., Shen, C., Xiao, T.-R., et al. (2013) · International Journal of Theoretical Physics · doi:10.1007/s10773-013-1710-4 · Cited by 8
Role of Entanglement in Quantum Neural Networks (QNN)
Singh, M. P., & Rajput, B. S. (2015) · Journal of Modern Physics · doi:10.4236/jmp.2015.613196 · Cited by 8
QKD-Based Quantum Private Query Protocol in the Single-Photon Interference Communication System
Liu, B., Gao, Z., Xiao, D., Huang, W., Zhang, Z.-Q., Li, Y., & Xu, B. (2019) · IEEE Access · doi:10.1109/access.2019.2930548 · Cited by 8
$Q|SI\rangle $ : a quantum programming environment
Guan, J., Ying, M., Duan, R., et al. (2017) · Scientia Sinica Informationis · doi:10.1360/n112017-00095 · Cited by 8
Quantum Optimization of Resource Distribution Management for Multi-Task, Multi-Subtasks
Gaily, S. E., & Imre, S. (2019) · Híradástechnika/Infocommunications journal · doi:10.36244/icj.2019.4.7 · Cited by 8
Sajeev, V., Vyshnavi, A. M. H., & Namboori, P. K. K. (2020) · International Conference for Emerging Technology (INCET) · doi:10.1109/incet49848.2020.9154041 · Cited by 8
HORSIC+: An Efficient Post-Quantum Few-Time Signature Scheme
Lee, J., & Park, Y. (2021) · Applied Sciences · doi:10.3390/app11167350 · Cited by 14
Noise-Aware Quantum Amplitude Estimation
Herbert, S., Williams, I., Guichard, R., & Ng, D. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3476929 · Cited by 17
Quantum Search Algorithm for Weighted Solutions
Seo, Y., Kang, Y., & Heo, J. (2022) · IEEE Access · doi:10.1109/access.2022.3149351 · Cited by 8
Konar, D., Bhattacharyya, S., Dey, S., et al. (2022) · Applied Intelligence · doi:10.1007/s10489-021-03108-5 · Cited by 8
Laskar, M. R., Mondal, S., & Dutta, A. K. (2022) · IEEE Transactions on Communications · doi:10.1109/tcomm.2022.3167057 · Cited by 8
Manikanta, G., Mani, A., Singh, H. P., et al. (2022) · Energy Systems · doi:10.1007/s12667-022-00517-4 · Cited by 8
Quantum-enhanced filter: QFilter
Atchade-Adelomou, P., & Alonso-Linaje, G. (2022) · Soft Computing · doi:10.1007/s00500-022-07190-w · Cited by 13
Quantum reinforcement learning method and application based on value function
Liu, Y.-P., Jia, Q., & Wang, X. (2022) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2022.08.061 · Cited by 8
Quantum Geometric Transformation Based on QIRHSI Quantum Color images
Song, X., Chen, G., El‐Latif, A. A. A., et al. (2023) · IEEE Access · doi:10.1109/access.2023.3247507 · Cited by 8
Nakagawa, Y. O., Chen, J., Sudo, S., Ohnishi, Y., & Mizukami, W. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c01176 · Cited by 9
Non-uniformity and Quantum Advice in the Quantum Random Oracle Model
Liu, Q. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-30545-0_5 · Cited by 8
Optimized Implementation and Analysis of CHAM in Quantum Computing
Yang, Y., Jang, K., Baksi, A., et al. (2023) · Applied Sciences · doi:10.3390/app13085156 · Cited by 8
Symmetry-adapted encodings for qubit number reduction by point-group and other Boolean symmetries
Picozzi, D., & Tennyson, J. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/acd86c · Cited by 10
Coherence and entanglement in Grover and Harrow–Hassidim–Lloyd algorithm
Feng, C., Chen, L., & Zhao, L. (2023) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2023.129048 · Cited by 8
QContext: Context-Aware Decomposition for Quantum Gates
Liu, J., Bowman, M., Gokhale, P., Dangwal, S., Larson, J. M., Chong, F. T., & Hovland, P. (2023) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas46773.2023.10181370 · Cited by 8
Prakash, P. M. (2023) · Optical and Quantum Electronics · doi:10.1007/s11082-023-05347-x · Cited by 8
RetractedQuantum Algorithm for Estimating Largest Eigenvalues
Nghiem, N. A., & Wei, T.-C. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.129138 · Cited by 20
DISQ: Dynamic Iteration Skipping for Variational Quantum Algorithms
Zhang, J., Wang, H., Ravi, G. S., Chong, F. T., Han, S., Mueller, F., & Chen, Y. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00120 · Cited by 12
Quantum Speed-Up for Multidimensional (Zero Correlation) Linear Distinguishers
Hosoyamada, A. (2023) · Lecture notes in computer science · doi:10.1007/978-981-99-8727-6_11 · Cited by 10
Quantum Computers: The Need for a New Cryptographic Strategy
Hale, B., Bindel, N., & Bossuyt, D. L. V. (2023) · Springer optimization and its applications · doi:10.1007/978-3-031-39542-0_7 · Cited by 8
Implementation of Database Search with Quantum Computing: Grover's Algorithm vs Linear Search
Khurana, S., & Nene, M. J. (2023) · International Conference on Ambient Intelligence, Knowledge Informatics and Industrial Electronics (AIKIIE) · doi:10.1109/aikiie60097.2023.10389962 · Cited by 9
An efficient quantum algorithm for ensemble classification using bagging
Macaluso, A., Clissa, L., Lodi, S., & Sartori, C. (2024) · IET Quantum Communication · doi:10.1049/qtc2.12087 · Cited by 8
Accelerating Quantum Algorithms with Precomputation
Huggins, W. J., & McClean, J. R. (2024) · Quantum · doi:10.22331/q-2024-02-22-1264 · Cited by 8
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
