Resource requirements for a fault-tolerant quantum Fourier transform

Hayato Goto
Phys. Rev. A 90, 052318 – Published 14 November 2014

Abstract

We investigate resource requirements for a fault-tolerant quantum Fourier transform. The quantum Fourier transform is a basic subroutine for quantum algorithms which provide an exponential speedup over known classical ones, such as Shor's algorithm for factoring. To implement single-qubit rotations required for a quantum Fourier transform in a fault-tolerant manner, we consider two types of approaches: gate synthesis and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation allows one to perform single-qubit rotations for a quantum Fourier transform exactly. It is unknown, however, which approach is better for a quantum Fourier transform. Here we develop a state-distillation method optimized for a quantum Fourier transform and compare this performance with those of state-of-the-art techniques for gate synthesis without and with ancillary states (ancillas). The performance is evaluated with the resource requirement for a quantum Fourier transform. The resource is measured by the total number of π/8 gates denoted by T, which is called the T count. Contrary to the expectation, the T count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is a better approach to a fault-tolerant quantum Fourier transform.

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  • Received 6 August 2014

DOI:https://doi.org/10.1103/PhysRevA.90.052318

©2014 American Physical Society

Authors & Affiliations

Hayato Goto

  • Frontier Research Laboratory, Corporate Research & Development Center, Toshiba Corporation, 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi 212-8582, Japan

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Issue

Vol. 90, Iss. 5 — November 2014

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