Adaptive Rotating-Wave Approximation for Driven Open Quantum Systems

Abstract

We present a numerical method to approximate the long-time asymptotic solution ${\rho }_{\infty }(t)$ to the Lindblad master equation for an open quantum system under the influence of an external drive. The proposed scheme uses perturbation theory to rank individual drive terms according to their dynamical relevance, and adaptively determines an effective Hamiltonian. In the constructed rotating frame, ${\rho }_{\infty }$ is approximated by a time-independent, nonequilibrium steady-state. This steady-state can be computed with much better numerical efficiency than asymptotic long-time evolution of the system in the lab frame. We illustrate the use of this method by simulating recent transmission measurements of the heavy-fluxonium device, for which ordinary time-dependent simulations are severely challenging due to the presence of metastable states with lifetimes of the order of milliseconds.

13 pages, 7 figures

References in corpus (30)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Charge insensitive qubit design derived from the Cooper pair box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Microwave photonics with superconducting quantum circuits
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Quantum computing with trapped ions
• Decoherence in Josephson Qubits from Dielectric Loss
• Quantum Logic Gates in Optical Lattices
• Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
• Multi-valued Logic Gates for Quantum Computation
• Effective operator formalism for open quantum systems
• Nonlinear response of the vacuum Rabi resonance
• Demonstrating a Driven Reset Protocol of a Superconducting Qubit
• Implementing optimal control pulse shaping for improved single-qubit gates
• Protected gates for superconducting qubits
• Collective quantum jumps of Rydberg atoms
• Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
• Critical dynamical properties of a first-order dissipative phase transition
• Circuit QED with fluxonium qubits: theory of the dispersive regime
• Realization of a $\Lambda$ system with metastable states of a capacitively-shunted fluxonium
• Perturbative approach to Markovian open quantum systems
• Circuit QED and engineering charge based superconducting qubits
• Asymptotic Floquet states of open quantum systems: The role of interaction
• Driven open quantum systems and Floquet stroboscopic dynamics
• Floquet theorem for open systems and its applications
• Dynamic steady-state of periodically-driven quantum systems
• Completely positive approximate solutions of driven open quantum systems
• Non-adiabatic effects in periodically driven-dissipative open quantum systems

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• Observation and stabilization of photonic Fock states in a hot radio-frequency resonator
• Exact solution of time-dependent Lindblad equations with closed algebras
• Fixing the rotating-wave approximation for strongly-detuned quantum oscillators
• Non-perturbative analytical diagonalization of Hamiltonians with application to coupling suppression and enhancement in cQED
• Flux qubit-based detector of microwave photons
• GPU-accelerated Effective Hamiltonian Calculator
• Conditions for Time-Independence of N-level Systems under the Rotating Wave Approximation (RWA) and Dipole Selection Rules