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

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.

Automated summary

Noise-induced decoherence is a major threat to large-scale quantum computation. In order to assess the noise affecting a qubit, we consider dynamical noise in the system description beyond the standard steady-state solution of qubit-coupled cavity transmission in input-output theory. By solving the quantum Langevin equations exactly for a noise-free system and treating the noise as a perturbation, we find that the corrections in the long-time limit can be expressed as convolutions of the noise power spectral density with an integration kernel dependent on external control parameters. Using the convolution theorem, we invert the corrections to obtain relations for the noise spectral density as integrals over measurable quantities. Furthermore, we accurately handle the noise in the dispersive regime and again observe that noise characteristics are present in long-time transmission in convolutions involving the power spectral density.