The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer

Abstract

A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian `hidden subgroup problem' can also be described and analysed as such. We then point out how certain instances of these problems can be solved with only one control qubit, or `flying qubits', instead of entire registers of control qubits.

16 pages, 3 figures, LaTeX2e, to appear in Proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communication (Springer-Verlag)

Cited by in corpus (8)

• Efficient Quantum Algorithms for Estimating Gauss Sums
• Efficient Quantum Algorithms for Shifted Quadratic Character Problems
• Solving Shift Problems and Hidden Coset Problem Using the Fourier Transform
• Amplitude-Aware Lossy Compression for Quantum Circuit Simulation
• Quantum Computing Discrete Logarithms with the Help of a Preprocessed State
• Revisiting Shor's quantum algorithm for computing general discrete logarithms
• Hidden Subhypergroup Problem
• An Improved Query for the Hidden Subgroup Problem