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arXiv:1911.02250 · Physical Review Research

Electric circuits for universal quantum gates and quantum Fourier transformation

Motohiko Ezawa

Published Jun 3, 2020• 24 citations
arXivHTMLPDF

Abstract

This paper demonstrates that a set of universal quantum gate consisting of the Hadamard, the phase shift and the CNOT gates can be constructed by LC electric circuits. Furthermore, it is possible to perform the quantum Fourier transformation by electric circuits, which is a core algorithm of the Shor integer factorization.
DOI
10.1103/physrevresearch.2.023278

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We propose to simulate quantum gates by LC resonators, where the amplitude and the phase of the voltage describe the quantum state.By controlling the capacitance or inductance of resonators, it is possible to control the phase of the voltage arbitrarily.A set of resonators acts as the phase-shift, the Hadamard, and the CNOT gates.They constitute a set of universal quantum gates.We also discuss an application to an artificial neuron.As an example, we study pattern recognition of numbers and alphabets by evaluating the similarity between an input and the reference pattern.We also study colored pattern recognition by using a complex neural network.
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Abstract There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and two-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. An especially interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than two qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses two-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov and Nam 2018 New J. Phys. 20 033018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n − 18 reported in (Maslov and Nam 2018 New J. Phys. 20 033018) to 6n − 8.