Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining
arXiv:2410.23116 · doi:10.1103/bysj-hjfl
Abstract
Model order reduction encompasses mathematical techniques aimed at reducing the complexity of mathematical models in simulations while retaining the essential characteristics and behaviors of the original model. This is particularly useful in the context of large-scale dynamical systems, which can be computationally expensive to analyze and simulate. Here, we present a model order reduction technique to reduce the time complexity of open quantum systems, grounded in the principle of measurement-adapted coarse-graining. This method, governed by a coarse-graining time scale and the spectral band center , organizes corrections to the lowest-order model which aligns with the RWA Hamiltonian in certain limits, and rigorously justifies the resulting effective quantum master equation (EQME). The focus on calculating to a high degree of accuracy only what can be resolved by the measurement introduces a principled regularization procedure to address singularities and generates low-stiffness models suitable for efficient long-time integration. Furthermore, the availability of the analytical form of the EQME parameters significantly boosts the interpretive capabilities of the method. As a demonstration, we derive the fourth-order EQME for a challenging problem related to the dynamics of a superconducting qubit under high-power dispersive readout in the presence of a continuum of dissipative waveguide modes. This derivation shows that the lowest-order terms align with previous results, while higher-order corrections suggest new phenomena.
References in corpus (42)
- Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
- Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
- Circuit Quantum Electrodynamics
- Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
- Entanglement and non-Markovianity of quantum evolutions
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting
- Dissipation and Ultrastrong Coupling in Circuit QED
- To catch and reverse a quantum jump mid-flight
- Dispersive regime of circuit QED: photon-dependent qubit dephasing and relaxation rates
- Demonstration of Universal Parametric Entangling Gates on a Multi-Qubit Lattice
- High-Fidelity Readout in Circuit Quantum Electrodynamics Using the Jaynes-Cummings Nonlinearity
- Rapid high-fidelity multiplexed readout of superconducting qubits
- Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation
- Qubit-oscillator dynamics in the dispersive regime: analytical theory beyond rotating-wave approximation
- Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
- Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model
- Machine learning non-Markovian quantum dynamics
- Dynamics of Transmon Ionization
- Eternal non-Markovianity: from random unitary to Markov chain realisations
- Pure-state quantum trajectories for general non-Markovian systems do not exist
- Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier
- Cutoff-free Circuit Quantum Electrodynamics
- Non-Markovian dephasing and depolarizing channels
- On the static effective Hamiltonian of a rapidly driven nonlinear system
- Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem
- Quantum non-demolition dispersive readout of a superconducting artificial atom using large photon numbers
- Quantum Trajectories for Realistic Photodetection I: General Formalism
- Generalized rotating-wave approximation to the two-qubit and cavity coupling system
- Lifetime renormalization of weakly anharmonic superconducting qubits: I. Role of number non-conserving terms
- Quantum-tailored machine-learning characterization of a superconducting qubit
- Evading Vacuum Noise: Wigner Projections or Husimi Samples?
- Intrinsic mechanisms for drive-dependent Purcell decay in superconducting quantum circuits
- Protocol for high fidelity readout in the photon blockade regime of circuit QED
- Dynamically enhancing qubit-photon interactions with anti-squeezing
- Cloaking a qubit in a cavity
- On the static effective Lindbladian of the squeezed Kerr oscillator
- DEC-QED: A flux-based 3D electrodynamic modeling approach to superconducting circuits and materials
- Experimental graybox quantum system identification and control
- Qubit readouts enabled by qubit cloaking
- Multi-Axis Control of a Qubit in the Presence of Unknown Non-Markovian Quantum Noise
- Effective Formalism for Open Quantum System Dynamics: Time-coarse-graining Approach