Electric circuits for universal quantum gates and quantum Fourier transformation

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 Schrödinger 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.

arXiv comment10 pages, 9 figures

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• Topological Toda lattice and nonlinear bulk-edge correspondence
• Universal quantum gates, artificial neurons and pattern recognition simulated by \textit{LC} resonators
• Variational Quantum Support Vector Machine based on $\Gamma$ matrix expansion and Variational Universal-Quantum-State Generator
• Dirac formulation for universal quantum gates and Shor's integer factorization in high-frequency electric circuits
• Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing
• Quantum signatures of chaos in a cavity-QED-based stimulated Raman adiabatic passage
• Nonlinear Anderson localization in Toda lattices