Low-rank optimal control of quantum devices
arXiv:2508.18114 · doi:10.1103/v383-2vss
Abstract
We demonstrate that the control protocols of quantum information devices can be simulated by assuming a low-rank ansatz for the density matrix. The rationale underlying this assumption is that quantum information protocols, by design, operate in a regime of nearly pure quantum states. Within the low-rank assumption, the simulation of these protocols is considerably faster than solving the full Lindblad master equation. This advantage can be used to increase the accuracy of the simulation by avoiding uncontrolled approximations, and to streamline protocol optimization. We benchmark our approach on the optimization of the transmon qubit dispersive readout in a realistic transmon-resonator-filter model. With Hilbert space dimension , assuming a rank as low as we achieve a nearly 100-fold speedup compared to full master equation integration while accurately reproducing all relevant observables. By combining the low-rank approximation with a compact pulse parametrization and gradient-free optimization, we obtain state-of-the-art readout assignment errors for a 40 ns readout pulse schedule, while comfortably running on a laptop and not relying on the rotating-wave approximation. Our approach is broadly applicable to most quantum control protocols, including quantum gates, state preparation, and fast reset operations. This establishes low-rank methods as a general tool for optimal control across diverse quantum platforms.
8 pages, 3 figures
References in corpus (69)
- Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
- Circuit Quantum Electrodynamics
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- Suppressing quantum errors by scaling a surface code logical qubit
- Quantum error correction below the surface code threshold
- A short introduction to the Lindblad Master Equation
- Optimal control technique for Many Body Quantum Systems dynamics
- Real-time quantum error correction beyond break-even
- Chopped random-basis quantum optimization
- Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits
- Fast Reset and Suppressing Spontaneous Emission of a Superconducting Qubit
- Rapid high-fidelity multiplexed readout of superconducting qubits
- Controlling open quantum systems: Tools, achievements, and limitations
- Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
- Realization of high-fidelity CZ and ZZ-free iSWAP gates with a tunable coupler
- Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
- A positive tensor network approach for simulating open quantum many-body systems
- Leakage reduction in fast superconducting qubit gates via optimal control
- Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
- Suppression of crosstalk in superconducting qubits using dynamical decoupling
- Fast readout and reset of a superconducting qubit coupled to a resonator with an intrinsic Purcell filter
- High-Fidelity, Frequency-Flexible Two-Qubit Fluxonium Gates with a Transmon Coupler
- Optimal control of open quantum systems: cooperative effects of driving and dissipation
- Gated conditional displacement readout of superconducting qubits
- Speedup for quantum optimal control from automatic differentiation based on graphics processing units
- Optimal Control for Generating Quantum Gates in Open Dissipative Systems
- Removing leakage-induced correlated errors in superconducting quantum error correction
- Krotov: A Python implementation of Krotov's method for quantum optimal control
- An information theoretical analysis of quantum optimal control
- Rapid Driven Reset of a Qubit Readout Resonator
- Dynamics of Transmon Ionization
- Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
- Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier
- Measurement-Induced State Transitions in a Superconducting Qubit: Within the Rotating Wave Approximation
- Pulsed reset protocol for fixed-frequency superconducting qubits
- General method for extracting the quantum efficiency of dispersive qubit readout in circuit QED
- Optimized controlled Z gates for two superconducting qubits coupled through a resonator
- Reducing leakage of single-qubit gates for superconducting quantum processors using analytical control pulse envelopes
- Measurement-Induced Transmon Ionization
- Optimizing quantum gates towards the scale of logical qubits
- Enhancing Dispersive Readout of Superconducting Qubits Through Dynamic Control of the Dispersive Shift: Experiment and Theory
- Efficient, stabilized two-qubit gates on a trapped-ion quantum computer
- Robust control and optimal Rydberg states for neutral atom two-qubit gates
- Qubit Measurement by Multichannel Driving
- Resonator reset in circuit QED by optimal control for large open quantum systems
- Model-based Optimization of Superconducting Qubit Readout
- Optimal control of families of quantum gates
- Low rank approximation for the numerical simulation of high dimensional Lindblad and Riccati equations
- Optimal Control of Quantum Measurement
- Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits
- Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
- QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
- Problem-free time-dependent variational principle for open quantum systems
- Learning How to Dynamically Decouple
- Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
- Reinforcement learning pulses for transmon qubit entangling gates
- Optimal control in large open quantum systems: the case of transmon readout and reset
- Adaptive variational low-rank dynamics for open quantum systems
- Optimization of decoder priors for accurate quantum error correction
- Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits
- Enhanced Qubit Readout via Reinforcement Learning
- Qubit readouts enabled by qubit cloaking
- Information Theoretical Limits for Quantum Optimal Control Solutions: Error Scaling of Noisy Channels
- Locally purified density operators for noisy quantum circuits
- Non-stochastic matrix Schrödinger equation for open systems
- Designing fast quantum gates using optimal control with a reinforcement-learning ansatz
- Balanced cross-Kerr coupling for superconducting qubit readout
- Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems