Integrating Self-Initialized\nLocal Thermalizing Lindblad\nOperators for Variational Quantum Algorithm with Quantum Jump: Implementation\nand Performance

Quantum computing holds great potential for simulating\nquantum\nsystems, such as molecular systems, due to its inherent ability to\nrepresent and manipulate quantum states. However, simulating nonunitary\ndynamics of open quantum systems on a quantum computer is still challenging.\nHere, we present a scheme denoted as VQS-QJ-LTLME, which adopts the\ntrajectory average of quantum jump Monte Carlo wave function variational\nevolution to evolve the system’s density matrix and local thermalizing\nLindblad operators to describe the system-environment interactions.\nThis combination allows the quantum circuit to be initialized after\na period of evolution, thereby eliminating the accumulation of errors.\nThe VQS-QJ-LTLME algorithm requires only log<sub>2</sub>(<i>n</i>) qubits for system size <i>n</i> and holds a time complexity\nof O(Tn3), making it particularly suitable for operation\non noisy intermediate-scale quantum devices. To accelerate the Monte\nCarlo sampling process in VQS-QJ-LTLME, we introduce an efficient\nsampling method, named No-evolution sampling (NES). The VQS-QJ-LTLME\naided by NES requires simulating only <i>n</i><sup>3</sup> + 1 trajectories on quantum computers, and then makes 10<sup>6</sup> to 10<sup>7</sup> samplings on classical computers in a few seconds.\nTo demonstrate the performance of the VQS-QJ-LTLME algorithm, we simulate\nthe dynamics of a two-level spin-boson model and a four-level reduced\nFenna–Matthews–Olson system with real superconducting\nquantum computers and classical simulators. It is shown that the simulations\nproduced by VQS-QJ-LTLME algorithm align closely with those obtained\nfrom the purely classical methods.