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Quantum computation may well be performed with the use of electric circuits.Especially, the Schr\"{o}dinger equation can be simulated by the lumped-elementmodel of transmission lines, which is applicable to low-frequency electriccircuits. In this paper, we show that the Dirac equation is simulated by thedistributed-element model, which is applicable to high-frequency electriccircuits. Then, a set of universal quantum gates (the Hadamard, phase-shift andCNOT gates) are constructed by networks made of transmission lines. Wedemonstrate Shor's prime factorization based on electric circuits. It will bepossible to simulate any quantum algorithms simply by designing networks ofmetallic wires.

Dirac formulation for universal quantum gates and Shor's integer factorization in high-frequency electric circuits