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Quantum Information Processing

Quantum QR decomposition in the computational basis

  • 01-08-2020
Published in:
Authors
Guangsheng Ma
Hongbo Li
Jiman Zhao
Published in
Quantum Information Processing | Issue 8/2020

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Abstract

In this paper, we propose a quantum algorithm for approximating the QR decomposition of any \(N\times N\) matrix with a running time \(O(\frac{1}{\epsilon ^2}\) \(N^{2.5}\text {polylog}(N))\), where \(\epsilon \) is the desired precision. This quantum algorithm provides a polynomial speedup over the best classical algorithm, which has a running time \(O(N^3)\). Our quantum algorithm utilizes the quantum computation in the computational basis (QCCB) and a setting of updatable quantum memory. We further present a systematic approach to applying the QCCB to simulate any quantum algorithm. By this approach, the simulation time does not exceed \(O(N^2\text {polylog}(N))\) times the running time of the quantum algorithm originally designed with the amplitude encoding method, where N is the size of the problem.

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previous article A low failure rate quantum algorithm for searching maximum or minimum
next article Encoding qubits into harmonic-oscillator modes via quantum walks in phase space
Title
Quantum QR decomposition in the computational basis
Authors
Guangsheng Ma
Hongbo Li
Jiman Zhao
Publication date
01-08-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02777-4
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