Bit-flip errors in dissipative cat qubits: second-order perturbation theory

• URL: http://arxiv.org/abs/2407.17299v2
• Date: Mon, 27 Jan 2025 14:05:57 GMT
• Title: Bit-flip errors in dissipative cat qubits: second-order perturbation theory
• Authors: Kirill S. Dubovitskii,
• Abstract summary: We develop a second-order perturbation theory on top of a nonlinear dissipative Lindbladian.<n>We derive an analytical expression for the exponentially small bit-flip rate due to single-photon loss.<n>We also apply our scheme to other perturbations, such as frequency detuning and the Z gate, and find the corresponding bit-flip rates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Dissipative cat qubits are known for the exponential suppression of the bit-flip rate. However, there is significant discrepancy between experimental measurements and analytical predictions of the strength of the bit-flip suppression. In this paper we resolve this discrepancy for some of the perturbations, by developing a second-order perturbation theory on top of a nonlinear dissipative Lindbladian. Following this scheme, we derive an analytical expression for the exponentially small bit-flip rate due to single-photon loss, which shows good agreement with numerical simulations. We also apply our scheme to other perturbations, such as frequency detuning and the Z gate, and find the corresponding bit-flip rates, which also show good agreement with the numerical simulation.

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