Electric circuits for universal quantum gates and quantum Fourier transformation

TL;DR

This paper demonstrates how electric circuits can be used to simulate universal quantum gates and quantum Fourier transformation, enabling potential hardware for quantum computation using classical electrical components.

Contribution

It proposes a physical realization of universal quantum gates and the quantum Fourier transform using electric circuits, specifically LC circuits and mixing bridges.

Findings

Simulation of quantum gates with electric circuits.

Implementation of the quantum Fourier transform components.

Potential for universal quantum computation with classical circuits.

Abstract

Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional $LC$ electric circuit can simulate a Schr\"{o}dinger equation and hence a quantum walk. Especially, we propose a physical realization of a set of universal quantum gates consisting of the CNOT, Hadamard and $\pi /4$ phase-shift gates with the use of telegrapher wires and mixing bridges. Furthermore, we construct the $\pi /2^{n}$ phase-shift gate for an arbitrary integer $n$, which is an essential element to perform the quantum Fourier transformation and prime factorization based on the Shor algorithm. Our results will open a way to universal quantum computation based on electric circuits.