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An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem

https://doi.org/10.1038/srep00260
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/prop.200610315openalex-snapshot
Factorization of numbers with physical systems
inferredcites →https://doi.org/10.1007/0-387-28979-8openalex-snapshot
Prime Numbers: A Computational Perspective
inferredcites →https://doi.org/10.1007/3-540-49116-3_4openalex-snapshot
Circuit Complexity of Testing Square-Free Numbers
inferredcites →https://doi.org/10.1007/3-540-58691-1_70openalex-snapshot
Open problems in number theoretic complexity, II
inferredcites →https://doi.org/10.1007/978-1-4684-9316-0openalex-snapshot
Prime Numbers
inferredcites →https://doi.org/10.1007/978-1-4757-1779-2openalex-snapshot
A Classical Introduction to Modern Number Theory
inferredcites →https://doi.org/10.1007/978-1-4757-2103-4openalex-snapshot
A Classical Introduction to Modern Number Theory
inferredcites →https://doi.org/10.1007/bf01886518openalex-snapshot
Quantum mechanical computers
inferredcites →https://doi.org/10.1007/bfb0054135openalex-snapshot
A new public-key cryptosystem as secure as factoring
inferredcites →https://doi.org/10.1063/1.881299openalex-snapshot
Information is Physical
inferredcites →https://doi.org/10.1088/1367-2630/13/10/103007openalex-snapshot
Factorization of numbers with Gauss sums: I. Mathematical background
inferredcites →https://doi.org/10.1088/1367-2630/13/10/103008openalex-snapshot
Factorization of numbers with Gauss sums: II. Suggestions for implementation with chirped laser pulses
inferredcites →https://doi.org/10.1088/1367-2630/14/1/013049openalex-snapshot
Factorization of numbers with Gauss sums: III. Algorithms with entanglement
inferredcites →https://doi.org/10.1090/s0273-0979-1992-00284-7openalex-snapshot
Algorithms in algebraic number theory
inferredcites →https://doi.org/10.1103/physreva.75.062303openalex-snapshot
Factorizing numbers with the Gauss sum technique: NMR implementations
inferredcites →https://doi.org/10.1103/physreva.82.042317openalex-snapshot
Quantum phase measurement and Gauss sum factorization of large integers in a superconducting circuit
inferredcites →https://doi.org/10.1103/physrevlett.100.030201openalex-snapshot
Gauss Sum Factorization with Cold Atoms
inferredcites →https://doi.org/10.1103/physrevlett.98.120502openalex-snapshot
NMR Experiment Factors Numbers with Gauss Sums
inferredcites →https://doi.org/10.1103/revmodphys.82.1openalex-snapshot
Quantum algorithms for algebraic problems
inferredcites →https://doi.org/10.1112/plms/s2-42.1.230openalex-snapshot
On Computable Numbers, with an Application to the Entscheidungsproblem
inferredcites →https://doi.org/10.1119/1.1463744openalex-snapshot
Quantum Computation and Quantum Information
inferredcites →https://doi.org/10.1137/s009753970343141xopenalex-snapshot
Quantum Algorithms for Some Hidden Shift Problems
inferredcites →https://doi.org/10.1137/s0097539795293172openalex-snapshot
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
inferredcites →https://doi.org/10.1142/s0129183197000138openalex-snapshot
Primality Test Via Quantum Factorization
inferredcites →https://doi.org/10.1142/s021797920603439xopenalex-snapshot
CHIRPED PULSES, GAUSS SUMS AND THE FACTORIZATION OF NUMBERS
inferredcites →https://doi.org/10.1142/s0219749904000109openalex-snapshot
EXACT QUANTUM FOURIER TRANSFORMS AND DISCRETE LOGARITHM ALGORITHMS
inferredcites →https://doi.org/10.1145/152379.152384openalex-snapshot
A binary algorithm for the Jacobi symbol
inferredcites →https://doi.org/10.1145/167088.167097openalex-snapshot
Quantum complexity theory
inferredcites →https://doi.org/10.1145/230514.230515openalex-snapshot
A short note on Shor's factoring algorithm
inferredcites →https://doi.org/10.1209/0295-5075/84/40006openalex-snapshot
NMR implementation of factoring large numbers with Gauß sums: Suppression of ghost factors
inferredcites →https://doi.org/10.17877/de290r-3047openalex-snapshot
Factorizing numbers with the Gauss sum technique
inferredcites →https://doi.org/10.48550/arxiv.quant-ph/0207131openalex-snapshot
Efficient Quantum Algorithms for Estimating Gauss Sums
inferredcites →https://doi.org/10.5802/jtnb.113openalex-snapshot
Approximatting rings of integers in number fields

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/978-3-032-25291-3_13openalex-snapshot
Reducing the Number of Qubits in Quantum Discrete Logarithms on Elliptic Curves
inferred← citeshttps://doi.org/10.1007/s10773-017-3389-4openalex-snapshot
Decompositions of n-qubit Toffoli Gates with Linear Circuit Complexity
inferred← citeshttps://doi.org/10.1007/s10773-019-04039-1openalex-snapshot
Quantum Binary Search Algorithm
inferred← citeshttps://doi.org/10.1007/s11433-017-9040-3openalex-snapshot
Generic preparation and entanglement detection of equal superposition states
inferred← citeshttps://doi.org/10.1016/j.array.2023.100287openalex-snapshot
General implementation of quantum physics-informed neural networks
inferred← citeshttps://doi.org/10.1016/j.physleta.2015.05.038openalex-snapshot
Factorization with a logarithmic energy spectrum of a two-dimensional potential
inferred← citeshttps://doi.org/10.1038/srep02044openalex-snapshot
Fault-tolerant quantum computation with a soft-decision decoder for error correction and detection by teleportation
inferred← citeshttps://doi.org/10.1038/srep04044openalex-snapshot
Geometry of Quantum Computation with Qudits
inferred← citeshttps://doi.org/10.1038/srep25977openalex-snapshot
Quantum Computation Based on Photons with Three Degrees of Freedom
inferred← citeshttps://doi.org/10.1063/5.0153709openalex-snapshot
Improving the success rate of quantum algorithm attacking RSA encryption system
inferred← citeshttps://doi.org/10.1088/1367-2630/15/2/023037openalex-snapshot
Factorization with a logarithmic energy spectrum
inferred← citeshttps://doi.org/10.1088/1674-1056/adab63openalex-snapshot
Global receptive field transformer decoder method on quantum surface code data and syndrome error correction
inferred← citeshttps://doi.org/10.1103/physreva.104.062606openalex-snapshot
Ghost factors in Gauss-sum factorization with transmon qubits
inferred← citeshttps://doi.org/10.1103/physreva.110.022405openalex-snapshot
Using quantum computers to identify prime numbers via entanglement dynamics
inferred← citeshttps://doi.org/10.1103/physreva.90.052318openalex-snapshot
Resource requirements for a fault-tolerant quantum Fourier transform
inferred← citeshttps://doi.org/10.1103/physreva.97.032344openalex-snapshot
Quantum speedup in solving the maximal-clique problem
inferred← citeshttps://doi.org/10.1126/sciadv.1600093openalex-snapshot
Versatile microwave-driven trapped ion spin system for quantum information processing
inferred← citeshttps://doi.org/10.26421/qic22.9-10-4openalex-snapshot
An exact quantum hidden subgroup algorithm and applications to solvable groups
inferred← citeshttps://doi.org/10.3390/math11194222openalex-snapshot
Large-Scale Simulation of Shor’s Quantum Factoring Algorithm
inferred← citeshttps://doi.org/10.4018/979-8-3693-7673-7.ch004openalex-snapshot
Quantum Computing Principles and Potential in Marketing
inferred← citeshttps://doi.org/10.4236/jqis.2023.133008openalex-snapshot
Leveraging Quantum Computing for the Ising Model to Simulate Two Real Systems: Magnetic Materials and Biological Neural Networks (BNNs)
inferred← citeshttps://doi.org/10.4236/jqis.2023.134008openalex-snapshot
Leveraging Quantum Computing for the Ising Model to Simulate Two Real Systems: Magnetic Materials and Biological Neural Networks (BNNs)
inferred← citeshttps://doi.org/10.48550/arxiv.1304.7516openalex-snapshot
Quantum Circuits for GCD Computation with $O(n \log n)$ Depth and O(n) Ancillae
inferred← citeshttps://doi.org/10.48550/arxiv.1605.04870openalex-snapshot
t-multiple discrete logarithm problem and solving difficulty
inferred← citeshttps://doi.org/10.48550/arxiv.2111.02488openalex-snapshot
A quantum algorithm for computing the Carmichael function
inferred← citeshttps://doi.org/10.48550/arxiv.2308.05047openalex-snapshot
Large-Scale Simulation of Shor's Quantum Factoring Algorithm
inferred← citeshttps://doi.org/10.7498/aps.66.150302openalex-snapshot
Experimental technique for multi-qubit nuclear magnetic resonance system
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