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.
Highlights
Quantum computation [1,2] is a most urgent and promising next-generation technique, which overcomes the limit of the Moore law
One of the methods to realize universal quantum computation is based on quantum walks [6,7,8,9,10,11,12,13,14,15], where widgets act as quantum gates
We present a physical realization of a set of the CNOT, Hadamard, and π /4 phase-shift gates with the use of LC electric circuits
Summary
Quantum computation [1,2] is a most urgent and promising next-generation technique, which overcomes the limit of the Moore law. We present a physical realization of a set of the CNOT, Hadamard, and π /4 phase-shift gates with the use of LC electric circuits. IV, we study one-qubit gates made of widgets involving two telegrapher wires They include the phase-shift gate, the mixing gate, the Hadamard gate, and the Pauli gates. 2. (a) Illustration of an electric circuit realizing the mixing gate Um(2ix) marked by a green rectangle It consists of two parallel wires linked by two inductors L .
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