Gillespie algorithm for quantum jump trajectories

Abstract

The jump unravelling of a quantum master equation decomposes the dynamics of an open quantum system into abrupt jumps, interspersed by periods of coherent dynamics when no jumps occur. Such open quantum systems are ubiquitous in quantum optics and mesoscopic physics, hence the need for efficient techniques for their stochastic simulation. Numerical simulation techniques fall into two main categories. The first splits the evolution into small timesteps and determines stochastically for each step if a jump occurs or not. The second, known as Monte Carlo Wavefunction simulation, is based on the reduction of the norm of an initially pure state in the conditional no-jump evolution. It exploits the fact that the purity of the state is preserved by the finest unraveling of the master equation. In this work, we present an alternative method for the simulation of the quantum jump unraveling, inspired by the classical Gillespie algorithm. The method is particularly well suited for situations in which a large number of trajectories is required for relatively small systems. It allows for non-purity-preserving dynamics, such as the ones generated by partial monitoring and channel merging. We describe the algorithm in detail and discuss relevant limiting cases. To illustrate it, we include four example applications of increasing physical complexity and discuss the performance of the algorithm across regimes of interest for open quantum systems simulation. Publicly available implementations of our code are provided in Julia and Mathematica.

11 pages, 5 figures

References in corpus (11)

• Quantum Simulation
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Continuous quantum measurement and Itô formalism
• Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach
• Signatures of a dissipative phase transition in photon correlation measurements
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Dynamics of a mesoscopic qubit under continuous quantum measurement
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Orthogonal jumps of wavefunction in white-noise potentials
• Diverging current fluctuations in critical Kerr resonators

Cited by in corpus (4)

• QuTiP 5: The Quantum Toolbox in Python
• Parameter estimation for quantum jump unraveling
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
• Quantum Measurement Induced Radiative Processes in Continuously Monitored Optical Environments