Digital Quantum Simulation of the Lindblad Master Equation and Its Nonlinear Extensions via Quantum Trajectory Averaging
arXiv:2504.00121 · doi:10.1103/q33r-j5tl
Abstract
Since precisely controlling dissipation in realistic environments is challenging, digital simulation of the Lindblad master equation (LME) is of great significance for understanding nonequilibrium dynamics in open quantum systems. However, achieving long-time simulations for complex systems with multiple dissipation channels remains a major challenge, both theoretically and experimentally. Here, we propose a 1-dilation digital scheme for simulating the LME based on quantum trajectory averaging without postselection. By rigorously matching the stochasticity inherent in quantum trajectories with the probabilistic outcomes of quantum measurements, our method effectively translates the classically established quantum jump algorithm into executable quantum circuits. A key advantage of our method is that it overcomes the exponential suppression of success probability seen in some existing postselection-dependent schemes, especially for long-time evolution or systems with numerous jump operators. Moreover, the scheme can be extended to a 2-dilation framework for the nonlinear LME with postselection, bridging the full LME and non-Hermitian Hamiltonian dynamics. This extended scheme provides a digital approach for exploring the interplay between non-Hermitian Hamiltonians and dissipative terms within a monitored quantum dynamics framework.
13 pages, 6 figures
References in corpus (33)
- The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
- Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
- Quantum trajectories and open many-body quantum systems
- Preparation of Entangled States by Quantum Markov Processes
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- A short introduction to the Lindblad Master Equation
- Toward the first quantum simulation with quantum speedup
- Theory of variational quantum simulation
- Variational quantum simulation of general processes
- Quantum simulation of open-system dynamical maps with trapped ions
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
- Digital quantum simulation of open quantum systems using quantum imaginary time evolution
- Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
- A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex
- Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
- Simulating Open Quantum Systems Using Hamiltonian Simulations
- Experimental simulation of open quantum system dynamics via Trotterization
- Localization in open quantum systems
- Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
- Signatures of many-body localization in steady states of open quantum systems
- Dissipation induced extended-localized transition
- Engineering Dissipative Quasicrystals
- Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
- Absence of measurement-induced entanglement transition due to feedback-induced skin effect
- Pontryagin-Optimal Control of a non-Hermitian Qubit
- Dynamical Transition due to Feedback-induced Skin Effect
- Experimental repetitive quantum channel simulation
- Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices
- Lindbladian dynamics with loss of quantum jumps
- Singular value decomposition quantum algorithm for quantum biology
- Dynamical Signatures of Liouvillian Flat Band
- Exponentially reduced circuit depths in Lindbladian simulation
- Breakdown of Measurement-Induced Phase Transitions Under Information Loss