Theory of qubit noise characterization using the long-time cavity transmission

Abstract

Noise induced decoherence is one of the main threats to large-scale quantum computation. In an attempt to assess the noise affecting a qubit we go beyond the standard steady-state solution of the transmission through a qubit-coupled cavity in input-output theory by including dynamical noise in the description of the system. We solve the quantum Langevin equations exactly for a noise-free system and treat the noise as a perturbation. In the long-time limit the corrections may be written as a sum of convolutions of the noise power spectral density with an integration kernel that depends on external control parameters. Using the convolution theorem, we invert the corrections and obtain relations for the noise spectral density as an integral over measurable quantities. Additionally, we treat the noise exactly in the dispersive regime, and again find that noise characteristics are imprinted in the long-time transmission in convolutions containing the power spectral density.