A fast quantum mechanical algorithm for database search
1996/05/29 by Lov K. Grover, Grover, Lov K. · 468 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #DNA and Biological Computing #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9605043
8 pages, single postscript file. This is an updated version of a paper that was originally presented at STOC 1996. The algorithm is the same; however, the proof has been simplified by using a new interpretation termed "inversion about average." Also a few recently discovered insights have been added. Journal Ref.: Proceedings, 28th Annual ACM Symposium on the Theory of Computing (STOC), May 1996, pages 212-219
openalex publication_date 1996/05/29 · arxiv created 1996/11/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Abstract
Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a 50% probability, any classical algorithm (whether deterministic or probabilistic) will need to look at a minimum of N/2 names. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only O(sqrt(N)) steps. The algorithm is within a small constant factor of the fastest possible quantum mechanical algorithm.
Citations
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- OneAdapt: Adaptive Compilation for Resource-Constrained Photonic One-Way Quantum Computing
- Construction of Boolean Logic Gates Using QFT-Based Adder Architecture
- Towards Datalog on Quantum Annealers: Compiling Recursive Logic Programs with Bottom-up Semantics to 2-local Ising Models
- Efficient Depth--Ancilla Tradeoffs for Hamming Weight Computation and Symmetric Boolean Functions
- NEBULA: A Language - Independent Specification for Opaque Rotating Refresh Tokens
- Resource Reduction in Multiparty Quantum Secret Sharing of both Classical and Quantum Information under Noisy Scenario
- Quantum walk search for exceptional configurations on one- and two-dimensional lattice with extra long-range edges of Hanoi network of degree four
- Quantum algorithm for reducing amplitudes in order to search and filter data
- Efficient Algorithms for Isogeny Computation on Hyperelliptic Curves: Their Applications in Post-Quantum Cryptography
- Quantum Speedup for Sampling Random Spanning Trees
- Quantum Search with In-Place Queries
- Quantum Simulation-Based Optimization for Cooling System Design
- Quantum-Enhanced Weight Optimization for Neural Networks Using Grover's Algorithm
- Enhancing LLM-based Quantum Code Generation with Multi-Agent Optimization and Quantum Error Correction
- Refinement orders for quantum programs
- Speedup Chip Yield Analysis by Improved Quantum Bayesian Inference
- Quantum Adaptive Self-Attention for Quantum Transformer Models
- On the Convergence of Markov Chain Distribution within Quantum Walk Circuit Subspace
- Scalable Circuit Cutting: A Framework for Combined Gate and Wire Cuts Using Gate Groups
- Diagonal-Budgeted Trotterization for Efficient Quantum Hamiltonian Simulation
- Asymptotic optimality of Grover-Radhakrishnan-Korepin algorithm
- PQ-CAN: A Framework for Simulating Post-Quantum Cryptography in Embedded Systems
- Fine-Grained Complexity via Quantum Natural Proofs
- A Novel Quantum Fourier Ordinary Differential Equation Solver for Solving Linear and Nonlinear Partial Differential Equations
- An Adaptive Weighted QITE-VQE Algorithm for Combinatorial Optimization Problems
- A Hybrid Chaos-Based Cryptographic Framework for Post-Quantum Secure Communications
- IF-QAOA: A Penalty-Free Approach to Accelerating Constrained Quantum Optimization
- Continuous-Variable Quantum Encoding Techniques: A Comparative Study of Embedding Techniques and Their Impact on Machine Learning Performance
- Efficient quantum detectable weak Byzantine agreement with optimal fault-tolerant bound
- Evaluating Mutation Techniques in Genetic Algorithm-Based Quantum Circuit Synthesis
- AriaQuanta: A Quantum Software for Quantum Computing
- Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction
- Quantum walk with coherent multiple translations induces fast quantum gate operations
- Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
- Implementation of Shor Algorithm: Factoring a 4096-Bit Integer Under Specific Constraints
- Structured search algorithm: A quantum leap
- Q-GEAR: Improving quantum simulation framework
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