Non-Markovian noise affecting superconductng circuits

Electrical circuits containing superconducting elements are one of the leading platforms for building an efficiently working quantum processor. Like any other realistic quantum system, superconducting qubits are open quantum systems, and the deleterious effects of their environment are the major obstacle on the road for reaching fault-tolerant quantum computation. In our work, we describe temporally correlated noise processes, that influence the idle evolution of a superconducting qubit. We model the composite qubit-environment system using quantum circuit theory, and we show how a circuit Hamiltonian can be derived for both longitudinal and transverse noise affecting the qubit. Based on the time-convolutionless projection operator method, we construct a master equation that is capable of capturing non-Markovian behaviour of the reduced system dynamics. By expressing the solution of the master equation in the Kraus representation, we are able to predict non-Markovian phenomena such as revivals of coherence, and also identify the limits of our theory by checking whether complete positivity is respected.