Toolbox for nonreciprocal dispersive models in circuit QED

Abstract

We provide a systematic method for constructing effective dispersive Lindblad master equations to describe weakly anharmonic superconducting circuits coupled by a generic dissipationless nonreciprocal linear system, with effective coupling parameters and decay rates written in terms of the immittance parameters characterizing the coupler. This article extends the foundational work of Solgun et al. (2019) for linear reciprocal couplers described by an impedance response. Notably, we expand the existing toolbox to incorporate nonreciprocal elements, account for direct stray coupling between immittance ports, circumvent potential singularities, and include collective dissipative effects that arise from interactions with external common environments. We illustrate the use of our results with a circuit of weakly anharmonic Josephson junctions coupled to a multiport nonreciprocal environment and a dissipative port. The results obtained here can be used for the design of complex superconducting quantum processors with nontrivial routing of quantum information, as well as analog quantum simulators of condensed matter systems.

41 pages, 13 figures. Comments are welcome. Published version

References in corpus (19)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Suppressing quantum errors by scaling a surface code logical qubit
• Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Black-box superconducting circuit quantization
• Dispersive regime of circuit QED: photon-dependent qubit dephasing and relaxation rates
• Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Blackbox Quantization of Superconducting Circuits using exact Impedance Synthesis
• Observation of Josephson Harmonics in Tunnel Junctions
• Circuit theory for decoherence in superconducting charge qubits
• Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes
• Quantum nonreciprocal interactions via dissipative gauge symmetry
• Passive superconducting circulator on a chip
• Hamiltonian Extrema of an Arbitrary Flux-Biased Josephson Circuit
• Non-additivity of decoherence rates in superconducting qubits
• Direct calculation of the ZZ-interaction rates in the multi-mode circuit-QED

Cited by in corpus (6)

• A Review of Design Concerns in Superconducting Quantum Circuits
• Exact quantization of nonreciprocal quasi-lumped electrical networks
• Balanced cross-Kerr coupling for superconducting qubit readout
• Dissipative phase transition of interacting non-reciprocal fermions
• Microwave Circulation in an Extended Josephson Junction Ring
• Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits