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 8,201–8,300 of 8,792
Patil, P. P., Tembhurne, J. V., & Choudhury, S. J. (2026) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2026.3659640
A Quantum Variational Approach to Phase-Only Pattern Synthesis
Huber, S., & Epping, M. (2026) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2026.3659730 · Cited by 1
A New Key Expansion Scheme for SM4 based on Sponge Construction
Yu, X., Xu, J., Zhang, X., et al. (2025) · IEEE International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom) · doi:10.1109/trustcom66490.2025.00314
Security Issues on Quantum Computing
Srivastava, S., & Yadav, S. (2026) · Algorithms for intelligent systems · doi:10.1007/978-3-032-14156-9_9
Analytical Perspective of Quantum Computing-Based Big Data Security Mechanisms
Kotangale, A., Kumar, M. S., & Bhagat, A. P. (2026) · Lecture notes in networks and systems · doi:10.1007/978-981-96-7526-5_27
Applications of Mathematics and Logics in Quantum Computing
Awasthi, S., & Singh, S. (2026) · Algorithms for intelligent systems · doi:10.1007/978-3-032-14156-9_17
Singh, M. S. I., & Rawal, B. S. (2026) · Springer eBooks · doi:10.1007/978-981-95-2498-3_6
From Classical to Quantum-Safe Security: the Transformative Role of Quantum Technologies
Mobilon, E., Rosolem, J. B., Inga, M., Riveros, L. G. M., Sutili, T., Paixão, A. C. P., Braga, A. M., & Figueiredo, R. C. (2025) · SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC) · doi:10.1109/imoc65414.2025.11365742 · Cited by 1
Case Study: PQC Migration for Android Strongbox Keymaster on Samsung Galaxy Mobile Devices
Lee, S., Jung, H., Heo, N., & Kwon, T. T. (2026) · IEEE Access · doi:10.1109/access.2026.3660949 · Cited by 1
Quantum Cryptographic Primitives based on Parameterised Quantum CircuitsPreprint
Fiorentini, M., Garvin, D., Kondratyev, A., et al. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6114006
Voiding the Search: The Quantum Abyss Engine
Bhushan, K. (2026) · Smart innovation, systems and technologies · doi:10.1007/978-3-032-12830-0_27
A Quantum-Inspired QAOA Solver for Knapsack Problems with 100-Qubit Scalability and 100,000x Speedup
Hou, S.-J., Wang, C.-C., Huang, P.-H., Tu, C.-H., & Hung, S.-H. (2025) · Research in Adaptive and Convergent Systems · doi:10.1145/3769002.3769984
A Quantum Framework for K Coloring of Graphs
Sen, & Mukherjee, S. (2025) · International Conference on Computational Intelligence and Communication Networks · doi:10.1109/cicn67655.2025.11368181 · Cited by 1
Meghazi, I., & Bourreau, E. (2026) · Communications in computer and information science · doi:10.1007/978-3-032-13855-2_7
Positive-unlabeled learning for training an entanglement detector
Nohara, T., Noda, I., & Oyama, S. (2026) · Quantum Machine Intelligence · doi:10.1007/s42484-026-00343-2
A Probabilistic Framework for Forecasting Cryptographic Security Under Quantum and Classical Threats
Rosas-Bustos, J. R., Pecen, M., Thé, J. V. G., et al. (2026) · Symmetry · doi:10.3390/sym18020297
Implementing low-performance-overhead logic locking in SoCs via homomorphic feedback
Ziyang, Y., & IKEDA, M. (2026) · IEICE Electronics Express · doi:10.1587/elex.23.20250738
Wang, S., & Chattopadhyay, A. (2026) · Computer architecture and design methodologies · doi:10.1007/978-981-95-6039-4_1
OTPPM: A One-time Pad-based Password Manager
Min, H., Li, Y., Li, W., et al. (2025) · International Conference on Cyber Security and Information Engineering (ICCSIE) · doi:10.1109/iccsie65832.2025.00033
SoK: Blockchain Consensus in the Quantum Age
Nash, A., Garcia, C. E. T., Chimal-Dzul, H., et al. (2025) · ACM International Symposium on Blockchain and Secure Critical Infrastructure (BSCI) · doi:10.1145/3709016.3737798
A Classical-Computing Framework for the Simulation of Multiple Spectrotemporally Entangled Photons
Brewster, R. A., Baumgartner, G., & Chembo, Y. K. (2026) · IEEE Access · doi:10.1109/access.2026.3661390
Distributed quantum approximate counting algorithmPreprint
Huang, H., & Qiu, D. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6203465
A Proposal for Rational Quantum Multi‐Secret Sharing
Li, F., Gu, J., & Zhu, S. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.202500891
Quantum annealing and condensed matter physics
Kendon, V. M., & Chancellor, N. (2026) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ae5906
Simulation of E91 Quantum Key Distribution Protocol Using Qiskit
Kadir, N. M., & Hossain, M. A. (2025) · IEEE International Conference on Computing, Applications and Systems (COMPAS) · doi:10.1109/compas67506.2025.11381830
Decoded quantum interferometry under noise
Bu, K., Gu, W., Koh, D. E., & Li, X. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae4536 · Cited by 9
Tang, Y., Cai, Z., Zhang, Y., Gao, Z., & Yu, J. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05085-5
Quantum-Enhanced Modeling and Optimization of Sodium-Ion Batteries
Masemola, K., Nyamupangedengu, C., & Dorrell, D. G. (2025) · SPEC Workshops · doi:10.1109/spec64875.2025.11376854
Al-Dulaimi, M. H., & Al-Dulaimi, S. K. (2025) · CyberSystem journal. · doi:10.57238/csj.2025.1016
Engelsberger, A., Psenickova, M., & Villmann, T. (2026) · Entropy · doi:10.3390/e28020229
A Quaternary Interpretation of Quantum Dynamics (QIQD) Dialogic Computer
Malik, P., & Hilton, K. (2025) · IEEE Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON) · doi:10.1109/iemcon67450.2025.11381037
QRAT: A Reachability Analysis Tool for Quantum Programs
Do, C. M., & OGATA, K. (2026) · Lecture notes in computer science · doi:10.1007/978-981-95-6032-5_2
A Fundamental Concept & Systematic Reviews, Understanding of The Quantum Search Algorithms
Bhatt, A., Chaudhary, S., Kuksal, R., et al. (2025) · doi:10.1109/iscs69371.2025.11386026
Quantum Computing: Principles, Technologies, and Future Directions - A Comprehensive Review
Nagaraju, D., Nimmala, H., Srinivasulu, T., Hemabala, K., & Jayalakshmi, P. (2025) · 2025 IEEE Pune Section International Conference (PuneCon) · doi:10.1109/punecon67554.2025.11378432
Unveiling the Quantum Realm: A Comprehensive Analysis of Quantum Computing
helmy, S. M. A., El-Regaily, S. A., Mahmoud, A. M., et al. (2025) · doi:10.1109/ic-ftai67960.2025.11384159
McHugh, M., & Pahlevanzadeh, B. (2025) · Cyber Research Conference - Ireland (Cyber-RCI) · doi:10.1109/cyber-rci68134.2025.11384979
Quantum algorithm for apprenticeship learning
Ambainis, A., & Lim, D. (2026) · Quantum Machine Intelligence · doi:10.1007/s42484-026-00368-7
Tackling Traveling Salesman Problems with a Cluster-Based Quantum-Classical Optimization
Hussain, S., Sausan, L., Rahman, A., et al. (2025) · International Conference on Information and Communication Technology Convergence (ICTC) · doi:10.1109/ictc66702.2025.11388124
Lee, Y., Merlec, M. M., Jung, J. W., Souihi, S., & In, H. P. (2025) · International Conference on Information and Communication Technology Convergence (ICTC) · doi:10.1109/ictc66702.2025.11388883 · Cited by 1
van der Schoot, W., de Kok, W., & Phillipson, F. (2026) · Communications in computer and information science · doi:10.1007/978-3-032-13852-1_32
The Urgency of Change: Climate and Environmental Challenges in the Quantum Era
Kumar, G. S., Maheshwari, G. U., Kumar, B. A., Dinola, A. A., & Jenita, P. (2026) · Springer eBooks · doi:10.1007/978-3-032-15188-9_1
The Gilles Brassard Laboratory: An Open Research Platform for Secure Quantum-Era Communications
Dierick, A., Rakotondrainibe, L., & Pisane, J. (2026) · Communications in computer and information science · doi:10.1007/978-3-032-13852-1_9
Gupta, A., & Mittal, S. (2026) · IEEE International Conference on AI in Cybersecurity (ICAIC) · doi:10.1109/icaic67076.2026.11395745
Quantum-Inspired Algorithms for Large-Scale Data Analytics: A Tensor Network Approach
Jarsania, J., & Chavda, C. (2026) · Computing and Communication Workshop and Conference · doi:10.1109/ccwc67433.2026.11393744
Design of novel multi-valued quantum adder circuit
Cheng, J.-X., Chen, J., Du, W.-B., et al. (2026) · Modern Physics Letters A · doi:10.1142/s0217732326500938
Larasati, H. T., & Choi, B.-S. (2026) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-026-00483-1 · Cited by 1
Quantum key-recovery attacks on FBC algorithm
Zhu, Y.-Y., Cai, B., Gao, F., et al. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05098-0
Constructing an enhanced variant of Hill cipher based on 2D hyper chaotic map over GF(2n)
Lu, Y., & Liu, H. (2026) · International Journal of Modern Physics C · doi:10.1142/s0129183127500719
Quantum-Resistant Networks using Post-Quantum Cryptography
Jin, X., Chandra, N. K., Azari, M., et al. (2025) · IEEE International Conference on Trust, Privacy and Security in Intelligent Systems and Applications (TPS-ISA) · doi:10.1109/tps-isa67132.2025.00072
1.2 Quantum Computing – Toward Large-Scale Fault-Tolerant Quantum Computing
Riel, H. (2026) · Digest of technical papers/Digest of technical papers - IEEE International Solid-State Circuits Conference · doi:10.1109/isscc49663.2026.11409084
Quantum Optimization of Event-Driven Neuromorphic Systems
Dour, S. (2026) · Advances in computational intelligence and robotics book series · doi:10.4018/979-8-3373-7779-7.ch012
D'ArQ: A QOC Framework with Causality-Aware Grouping and Basis Selection
Lee, C., Kim, H. J., Choi, S., Kim, Y., & Ro, W. W. (2026) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca68181.2026.11408534
The absolute zeta function with respect to a bipartite walk on a bipartite graph
Akahori, J., Konno, N., Sato, I., Tamura, Y., & Zhang, X. (2026) · Quantum Studies Mathematics and Foundations · doi:10.1007/s40509-026-00385-y
Alam, S., Verma, D., Jain, A., et al. (2025) · doi:10.1109/aisummit66170.2025.11411098
Revolutionizing Image Processing with Quantum Algorithms: Encoding, Enhancement and Recognition
Sood, S., Kalra, A., & Singh, G. (2025) · doi:10.1109/aisummit66170.2025.11410633
Quantum-Resistant Cryptographic Models for Next-Gen Cybersecurity
Chhibber, N., Rastogi, A., Mahida, A., et al. (2025) · doi:10.1109/apcit65661.2025.11410884
CLINE: Improving Control Flow Compilation of Quantum Programs with Control Line Encoding
Wu, A., Lu, L., Yin, J., Leng, J., & Guo, M. (2026) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca68181.2026.11408609 · Cited by 1
Quantum-Assisted Big Data Analytics for Ultra-High-Dimensional Datasets
Meruga, V. B. (2025) · Asia Pacific Conference on Innovation in Technology (APCIT) · doi:10.1109/apcit65661.2025.11411655
DC-MBQC: A Distributed Compilation Framework for Measurement-Based Quantum Computing
Xue, Y., Yang, R., Liang, Z., & Li, T. (2026) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca68181.2026.11408612
Seyhan, K., Akleylek, S., & Dursun, A. F. (2026) · Karadeniz Fen Bilimleri Dergisi · doi:10.31466/kfbd.1695525
Schrödinger’s bug: a survey on quantum software debugging
Rosa, E. C. R., & de Santiago, R. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05114-3
Introduction to quantum cryptography and postquantum cryptography for securing IIoT platforms
Alakesan, C., John, Y. M. M., Sathiyamurthi, P., et al. (2026) · Elsevier eBooks · doi:10.1016/b978-0-443-38349-6.00016-6
Post-Quantum Secure Peer-to-Peer VPN Protocol
Kumari, P., Yadav, S., & Misra, R. N. (2025) · IEEE International Conference on Big Data (BigData) · doi:10.1109/bigdata66926.2025.11402568
Open QBench: A benchmarking framework for evaluating quantum computing platforms
Wojciechowski, K., Kurowski, K., Slysz, M., & Pecyna, T. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05115-2 · Cited by 2
Quantum Safe Lattice-Based Lightweight Authentication Protocol
Seyhan, K., Akleylek, S., & Dursun, A. F. (2026) · International Informatics and Software Engineering Conference (IISEC) · doi:10.1109/iisec69317.2026.11418483
Kumar, M., & Perkowski, M. A. (2025) · Quantum Information and Computation · doi:10.2478/qic-2025-0038
Subtrajectory Clustering with Machine Learning on Quantum Computers
Bishop, W., Leal, E., & Gruenwald, L. (2025) · IEEE ... International Conference on Data Mining workshops · doi:10.1109/icdmw69685.2025.00263
Simulating Quantum Attacks on Classical Cryptography with CUDA-Q
Yılmaz, E., & Özbudak, E. K. (2026) · International Informatics and Software Engineering Conference (IISEC) · doi:10.1109/iisec69317.2026.11418518
Post-Quantum DLT Framework for Secure Financial Transactions in Banking Applications
Pandey, A., Ghosh, D., Bagchi, P., et al. (2026) · doi:10.1109/comsnets67989.2026.11418232
TreeVQA: A Tree-Structured Execution Framework for Shot Reduction in Variational Quantum Algorithms
Hou, Y., Bharadwaj, D., & Ravi, G. S. (2026) · International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS) · doi:10.1145/3779212.3790239
Wang, C., Lin, Y., Ou, C., & Shih, J.-D. (2025) · Quantum Information and Computation · doi:10.2478/qic-2025-0037
Liu, Y., Tao, Y.-H., Lan, J.-R., & Fei, S.-M. (2025) · Quantum Information and Computation · doi:10.2478/qic-2025-0031 · Cited by 1
No-go theorem for generic simulation of qubit channels with finite classical resources
Naik, S. G., Zartab, M., Gisin, N., & Banik, M. (2026) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2025.0831 · Cited by 1
Knowledge Graphs and Quantum Computing: First Blood
Tzitzikas, Y., & Kondylakis, H. (2026) · Lecture notes in computer science · doi:10.1007/978-981-95-5009-8_1
On Encoding Big Knowledge Graphs as Quantum States and on Running Grover’s Algorithm
Theodorakis, G., Touloupakis, M., & Tzitzikas, Y. (2026) · Lecture notes in computer science · doi:10.1007/978-981-95-5009-8_37
Forhad, M. S., Hassan, M. A. M., Fahim, M. F. H., & Sardar, T. H. (2026) · Elsevier eBooks · doi:10.1016/b978-0-443-33172-5.00008-x
Sun, C., Mahfuz, N. M., & Wang, Y. (2026) · IEEE Transactions on Dependable and Secure Computing · doi:10.1109/tdsc.2026.3674809 · Cited by 1
QED: Quantum-Enhanced Diagnosis for Faults in Networked Grids
Tarakeshwar, K., & Venkatesan, N. (2025) · Advances in Science and Engineering Technology International Conferences (ASET) · doi:10.1109/aset66891.2025.11427898
A Secure Quantum Group Blind Signature Based on Entanglement Swapping
Xing, K., Lu, R., Zhong, J., et al. (2025) · doi:10.1109/aicsip65423.2025.11427262
FitQT: a fully integrated and trainable quantum transformer for scalable natural language processing
Pham, L., & Le, A. T. (2026) · Engineering Research Express · doi:10.1088/2631-8695/ae5507
Lattice-based certificateless linearly homomorphic signature scheme
Wang, L., & Tian, K. (2026) · Annals of Telecommunications · doi:10.1007/s12243-026-01169-6
Quantum Heuristic Approach to Vehicle Routing Problem
Kim, J. S., Lee, D., & Ahn, C. W. (2026) · Mathematics · doi:10.3390/math14061026
Yapı Mühendisliğinde Kuantum Hesaplama: Gelecek Uygulamalar İçin Teorik Bir Çerçeve
Kolcu, F. (2026) · Özgür Yayınları eBooks · doi:10.58830/ozgur.pub1267.c5161
Future-Proofing Quantum Networks
Rajkumar, S., & Kavitha, K. (2026) · Advances in computational intelligence and robotics book series · doi:10.4018/979-8-2600-0547-7.ch004
Quantum algorithms for scheduling problems: a survey
Werner, T., & Ullinger, F. (2026) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-026-00494-y
Couveignes, J.-M., & Lercier, R. (2026) · Journal of Complexity · doi:10.1016/j.jco.2026.102046
Ashok Raj, R., & Maruthanayagam, D. (2026) · International Journal of Scientific Research in Computer Science Engineering and Information Technology · doi:10.32628/cseit26121332
Can Quantum Neural Networks Estimate the Redshifted Global Hi 21-cm Signal Parameters?
Gowtham, A., Tripathi, A., & Datta, A. (2026) · SN Computer Science · doi:10.1007/s42979-026-04874-0
A Quantum-Search-Based Algorithm for the 0-1 Knapsack Problem
Stepanenko, K. A. (2025) · Russian Microelectronics · doi:10.1134/s1063739725602000
Chudakov, A. S., Borschevskaia, N. A., Fastovets, D. V., et al. (2025) · Russian Microelectronics · doi:10.1134/s1063739725601584
Decoding the surface code with a spatio-temporal transformer
Joo, R. S. (2026) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-026-00492-0
Dudas, J., Carles, B., Gouzien, É., Grollier, J., & Marković, D. (2026) · Scientific Reports · doi:10.1038/s41598-026-45038-7 · Cited by 1
Santo, A. D., & Lanziani, G. (2026) · Research Square · doi:10.21203/rs.3.rs-9156135/v1
Modeling and Simulation of Quantum Dot Grover States with Cryogenic LNA and LC-Qubit Dynamics
Vats, D., Singh, G., & Kumar, R. (2025) · International Conference on Electrical, Electronics, Communication and Computers (ELEXCOM) · doi:10.1109/elexcom67950.2025.11451232
An Improved Ion-Shuttling Approach for QCCD Architectures
Wu, T.-Y., & Wang, T.-C. (2026) · International Symposium on Physical Design · doi:10.1145/3764386.3779585
Design and FPGA-Based Implementation of a Quantum-Inspired Single-Qubit Circuit
Ketan, Shikha, Goel, V., Vats, D., & Singh, A. K. (2025) · International Conference on Electrical, Electronics, Communication and Computers (ELEXCOM) · doi:10.1109/elexcom67950.2025.11451321
Intrication de champs quantiques mesoscopiques pour les communications quantiques
Blandino, R. (2013) · theses.fr (ABES) · doi:10.70675/badf3d87ze734z436bzbee9z20a3a882954b
Encrypted e-archives and secure delivery via electronic ledger
Zivkovic, M., Milošević, D., & Stanišević, I. (2026) · Serbian Journal of Electrical Engineering · doi:10.2298/sjee2601073z
Insights on Quantum Software Functional Size Measurement: Key Concepts, Challenges and Motivations
Hacaloğlu, T., Soubra, H., Adel, Y., et al. (2025) · doi:10.1109/gcet68529.2025.11450896
Manipulation de champs quantiques mésoscopiques
Ferreyrol, F. (2011) · theses.fr (ABES) · doi:10.70675/d5e86e52z01efz448dz9b72z6df2453fe3f1
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
