Towards robust variational quantum simulation of Lindblad dynamics via stochastic Magnus expansion
arXiv:2503.22099 · doi:10.1103/yyln-q22s
Abstract
In this paper, we introduce a novel and general framework for the variational quantum simulation of Lindblad equations. Building on the close relationship between the unraveled Lindblad dynamics, stochastic Magnus integrators, and variational quantum simulation, we propose a high-order scheme for solving the quantum state diffusion equation using exponential integrators. This formulation facilitates the simulation of wavefunction trajectories within the established framework of variational quantum algorithms for time evolution. Our algorithm significantly enhances robustness in two key aspects: the stability of the simulation with large time steps, and the reduction in the number of quantum trajectories required to accurately simulate the Lindblad dynamics in terms of the ensemble average. We demonstrate the effectiveness of our algorithm through numerical examples in both classical and quantum implementations, including the transverse-field Ising model (TFIM) with damping, the Fenna-Matthews-Olson (FMO) complex, and the radical pair model (RPM). The simulation accuracy can be systematically improved, and the algorithm remains reliable even in highly oscillatory regimes. These methods are expected to be applicable to a broader class of open quantum systems beyond the specific models considered in this study.
29 pages, 12 figures
References in corpus (35)
- Quantum Error Correction for Quantum Memories
- The Magnus expansion and some of its applications
- Evaluating analytic gradients on quantum hardware
- Hamiltonian Simulation by Qubitization
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Efficient quantum algorithms for simulating sparse Hamiltonians
- Variational ansatz-based quantum simulation of imaginary time evolution
- Theory of variational quantum simulation
- Sustained Quantum Coherence and Entanglement in the Avian Compass
- Non-perturbative treatment of non-Markovian dynamics of open quantum systems
- Quantum master equation for electron transport through quantum dots and single molecules
- Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
- Digital quantum simulation of open quantum systems using quantum imaginary time evolution
- Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
- Ancilla-free quantum error correction codes for quantum metrology
- Sufficient conditions for the convergence of the Magnus expansion
- A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex
- Hamiltonian variational ansatz without barren plateaus
- Quantum Coherence and Entanglement in the Avian Compass
- Convergence of the Magnus series
- Resilience of quantum random access memory to generic noise
- Single-ancilla ground state preparation via Lindbladians
- Simulating Open Quantum Systems Using Hamiltonian Simulations
- A stochastic approach to open quantum systems
- Open systems with error bounds: spin boson model with spectral density variations
- Variational Quantum Time Evolution without the Quantum Geometric Tensor
- Magnetic Sensitivity and Entanglement Dynamics of the Chemical Compass
- Adaptive variational simulation for open quantum systems
- Quantum Simulation of the Radical Pair Dynamics of the Avian Compass
- Exponential Integrators for Stochastic Schrödinger Equation
- Simulation of open quantum systems via low-depth convex unitary evolutions
- On the functional window of the avian compass
- Singular value decomposition quantum algorithm for quantum biology
- Adaptive low-rank approximation and denoised Monte-Carlo approach for high-dimensional Lindblad equations
- Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians