Lifetime renormalization of weakly anharmonic superconducting qubits: I. Role of number non-conserving terms

Abstract

The dynamics of a weakly anharmonic superconducting qubit in a complex electromagnetic environment is generally well-described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue is a limiting factor in the optimization of superconducting qubit readout schemes. We claim here that an effective master equation with drive-power dependent parameters is an efficient approach to model such quantum dynamics. In this sequence of papers, we derive effective master equations, whose parameters exhibit nonlinear dependence on the excitation level of the circuit as well as the electromagnetic environment of the qubit. We show that the number non-conserving terms in the qubit nonlinearity generally lead to a renormalization of dissipative parameters of the effective master equation, while the number conserving terms give rise to a renormalization of the system frequencies. Here, in Part I, we consider the excitation-relaxation dynamics of a transmon qubit that is prepared in a certain initial state, but is not driven otherwise. A unitary transformation technique is introduced to study the renormalization of i) qubit relaxation due to coupling to a generic bath and ii) Purcell decay. Analytic expressions are provided for the dependence of the nonlinear dissipative terms on the details of the electromagnetic environment of the qubit. The perturbation technique based on unitary transformations developed here is generalized to the continuously driven case in Part II.

arXiv comment20 pages, 5 figures, 4 tables and 38 references

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Cited by in corpus (22)

• Circuit Quantum Electrodynamics
• First-principles analysis of cross-resonance gate operation
• Dynamics of Transmon Ionization
• Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem
• Reservoir Computing Approach to Quantum State Measurement
• Quantum non-demolition dispersive readout of a superconducting artificial atom using large photon numbers
• Accurate methods for the analysis of strong-drive effects in parametric gates
• Mitigating off-resonant error in the cross-resonance gate
• Photon-noise-tolerant dispersive readout of a superconducting qubit using a nonlinear Purcell filter
• Intrinsic mechanisms for drive-dependent Purcell decay in superconducting quantum circuits
• Optimization of the resonator-induced phase gate for superconducting qubits
• Algebraic canonical quantization of lumped superconducting networks
• A Multi-Qubit Quantum Gate Using the Zeno Effect
• Qubit readouts enabled by qubit cloaking
• Noise reduction in qubit readout with a two-mode squeezed interferometer
• Minimizing the discrimination time for quantum states of an artificial atom
• Practical Trainable Temporal Postprocessor for Multistate Quantum Measurement
• Variational Quantum Gate Optimization at the Pulse Level
• GPU-accelerated Effective Hamiltonian Calculator
• Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining
• Time-dependent Schrieffer-Wolff-Lindblad Perturbation Theory: measurement-induced dephasing and second-order Stark shift in dispersive readout
• Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits