Unified linear response theory of quantum electronic circuits

TL;DR

This paper introduces a comprehensive linear response theory for quantum electronic circuits that unifies existing models, enabling accurate analysis across all frequencies and incorporating relaxation and dephasing effects.

Contribution

A novel unified theory that models multi-level quantum systems with a universal RLC circuit, valid at any frequency, including non-unitary effects like relaxation and dephasing.

Findings

Successfully applied to double quantum-dot and Majorana qubits

Enables continuous description from adiabatic to resonant regimes

Facilitates design of hybrid quantum-classical circuits

Abstract

Modelling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic losses, and (ii) semiclassical theory, which captures well dynamic dissipation effects but is only accurate at low frequencies. Here, we develop a unifying theory, valid for arbitrary frequencies, that captures both the quantum behaviour and the non-unitary effects introduced by relaxation and dephasing. The theory allows a multi-level system to be described by a universal small-signal equivalent circuit model, a resonant RLC circuit, whose topology only depends on the number of energy levels. We apply our model to a double quantum-dot charge qubit and a Majorana qubit, showing the capability to continuously describe the systems from adiabatic to resonant and from coherent to incoherent, suggesting new and realistic experiments for improved quantum state readout. Our model will facilitate the design of hybrid quantum-classical circuits and the simulation of qubit control and quantum state readout.