Physical Constraints on Quantum Circuits

Abstract

The physical constraints underlying the concept of quantum circuit are considered. In particular it is shown that the point of departure for their modeling starts from the interconnection of the components into a classical network, followed by quantization of the latter, and not by the interconnection of already quantized components. The procedure is straightforward for lossless networks but cannot be worked out in presence of resistors for the impossibility of constructing a Lagrangian function. However the difficulty is circumvented by distinguishing thermal from radiative resistors, the former being the usual ones, the latter being realized by semi-infinite LC transmission lines, for which the Lagrangian exists. In the complex plane s = σ + jω the impedance of a thermal resistor is Z(s) = R in the entire plane while that of a radiative resistor is Rsign(σ), so that the latter is lossless and does not dissipate energy but conveys it to the infinity. Comparison with Lindblad approach shows that the resistor fits into it in the RHP. Radiative resistors make evolution reversible, which is not true for a physical system including thermal.