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Quantum algorithms for algebraic problems (Q3077033)

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Language	Label	Description	Also known as
English	Quantum algorithms for algebraic problems	scientific article

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scholarly article

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Quantum algorithms for algebraic problems (English)

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zbMATH Open document ID

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10.1103/RevModPhys.82.1

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Andrew M. Childs

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Reviews of Modern Physics

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publication date

21 February 2011

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full work available at URL

https://arxiv.org/abs/0812.0380

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Mathematics Subject Classification ID

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zbMATH DE Number

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MaRDI profile type

MaRDI publication profile

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Quantum Computability

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Counting points on curves and Abelian varieties over finite fields

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Fault-Tolerant Quantum Computation with Constant Error Rate

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A polynomial quantum algorithm for approximating the Jones polynomial

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Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation

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Quantum Walk Algorithm for Element Distinctness

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Fast Monte Carlo algorithms for permutation groups

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Reversing quantum dynamics with near-optimal quantum and classical fidelity

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Quantum lower bounds by polynomials

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Strengths and Weaknesses of Quantum Computing

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Quantum Complexity Theory

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On the computational complexity of the general discrete Fourier transform

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Noise-tolerant learning, the parity problem, and the statistical query model

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Approximate Counting and Quantum Computation

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A new universal and fault-tolerant quantum basis

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Spatial search and the Dirac equation

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Fast generalized Fourier transforms

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The query complexity of order-finding

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Quantum algorithms revisited

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Sharp quantum versus classical query complexity separations

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Quantum theory, the Church–Turing principle and the universal quantum computer

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Quantum computational networks

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Rapid solution of problems by quantum computation

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Efficient Computation of the Fourier Transform on Finite Groups

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New directions in cryptography

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Quantum Query Complexity of Some Graph Problems

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On quantum algorithms for noncommutative hidden subgroups

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The quantum query complexity of the hidden subgroup problem is polynomial

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A modular functor which is universal for quantum computation

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Topological quantum computation

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Simulation of topological field theories by quantum computers

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Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve

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Quantum mechanical algorithms for the nonabelian hidden subgroup problem

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Fast quantum algorithms for computing the unit group and class group of a number field

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Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem

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The Hidden Subgroup Problem and Quantum Computation Using Group Representations

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Efficient discrete approximations of quantum gates

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A ‘Pretty Good’ Measurement for Distinguishing Quantum States

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Group-theoretic algorithms and graph isomorphism

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Statistical decision theory for quantum systems

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EFFICIENT QUANTUM ALGORITHMS FOR SOME INSTANCES OF THE NON-ABELIAN HIDDEN SUBGROUP PROBLEM

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On the computational complexity of the Jones and Tutte polynomials

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Bounds for the adiabatic approximation with applications to quantum computation

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A polynomial invariant for knots via von Neumann algebras

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Quantum computation in algebraic number theory: Hallgren's efficient quantum algorithm for solving Pell's equation.

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State models and the Jones polynomial

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Quantum computation of zeta functions of curves

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Hardness of approximating the shortest vector problem in lattices

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Quantum computations: algorithms and error correction

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Algebraic aspects of cryptography. With an appendix on hyperelliptic curves by Alfred J. Menezes, Yi-Hong Wu, and Robert J. Zuccherato

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The quantum query complexity of the abelian hidden subgroup problem

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A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem

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Factoring polynomials with rational coefficients

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Integer Programming with a Fixed Number of Variables

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Universal Quantum Simulators

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Isomorphism of graphs of bounded valence can be tested in polynomial time

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Quantum complexity of testing group commutativity

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Quantum Algorithms for the Triangle Problem

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The Relationship Between Breaking the Diffie--Hellman Protocol and Computing Discrete Logarithms

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The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant

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Generic quantum Fourier transforms

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The Power of Strong Fourier Sampling: Quantum Algorithms for Affine Groups and Hidden Shifts

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The Symmetric Group Defies Strong Fourier Sampling

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EXACT QUANTUM FOURIER TRANSFORMS AND DISCRETE LOGARITHM ALGORITHMS

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Is code equivalence easy to decide?

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Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields

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Reliable quantum computers

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Probabilistic algorithm for testing primality

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Random measurement bases, quantum state distinction and applications to the hidden subgroup problem

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New lattice-based cryptographic constructions

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Quantum Computation and Lattice Problems

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A method for obtaining digital signatures and public-key cryptosystems

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Fast Fourier analysis for abelian group extensions

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Classical and quantum function reconstruction via character evaluation

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A hierarchy of polynomial time lattice basis reduction algorithms

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Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p

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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

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On the Power of Quantum Computation

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Quantum algorithms for weighing matrices and quadratic residues

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Optimal phase estimation in quantum networks

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Quantum Algorithms for Some Hidden Shift Problems

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Counting curves and their projections

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Quantum simulations of classical random walks and undirected graph connectivity

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Quantum field theory and the Jones polynomial

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Optimum testing of multiple hypotheses in quantum detection theory

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Simulating quantum systems on a quantum computer

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Mathematics(1 entry)

mardi Publication:3077033

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