Smoking-gun signatures of non-Markovianity of a superconducting qubit

Abstract

We describe temporally correlated noise processes that influence the idle evolution of a superconducting transmon qubit. To model the composite qubit-environment system we use quantum circuit theory, and we show how a circuit Hamiltonian can be derived for transverse noise affecting the qubit. Based on the time-convolutionless projection operator method, we construct a time-local master equation which, when transformed to its canonical Lindblad form, exhbitis a decay rate that is negative at all times, corresponding to eternally non-Markovian dynamics. By expressing the solution of the master equation in the Kraus representation, we identify two crucial non-Markovian phenomena: periodic revivals of coherence, and the appearance of additional frequencies far from the qubit frequency in the precession of the qubit state. When a single qubit gate acts on the qubit state, these extra frequency terms rotate undesirably and they effectively act as the memory of the state prior to the rotation around the Bloch sphere.

10 pages, 5 figures

References in corpus (12)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Suppressing Charge Noise Decoherence in Superconducting Charge Qubits
• Controlling the spontaneous emission of a superconducting transmon qubit
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Finding the Kraus decomposition from a master equation and vice versa
• Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
• Quantification of memory effects in the spin-boson model
• Blackbox Quantization of Superconducting Circuits using exact Impedance Synthesis
• Circuit theory for decoherence in superconducting charge qubits