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arXiv:2403.04885

Ensemble Variational Quantum Algorithm for Non-Markovian Quantum Dynamics

Peter Walters, Joachim Tsakanikas, Fei Wang

Published Mar 7, 2024• 0 citations
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Abstract

Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of simulating non-Markovian dynamics on NISQ devices. We used a quantum system linearly coupled to its harmonic bath as the model Hamiltonian. The non-Markovianity is captured by introducing auxiliary variables from the bath trajectories. With Monte Carlo sampling of the bath degrees of freedom, finite temperature dynamics is produced. We validated the algorithm on the simulator and demonstrated its performance on the IBM quantum device. The framework developed is naturally adapted to any anharmonic bath with non-linear coupling to the system, and is also well suited for simulating spin chain dynamics in a dissipative environment.

DOI
10.48550/arxiv.2403.04885

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Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of simulating non-Markovian dynamics on NISQ devices. We used a quantum system linearly coupled to its harmonic bath as the model Hamiltonian. The non-Markovianity is captured by introducing auxiliary variables from the bath trajectories. With Monte Carlo sampling of the bath degrees of freedom, finite temperature dynamics is produced. We validated the algorithm on the simulator and demonstrated its performance on the IBM quantum device. The framework developed is naturally adapted to any anharmonic bath with non-linear coupling to the system, and is also well suited for simulating spin chain dynamics in a dissipative environment.
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The simulation of non-Markovian quantum dynamics plays an important role in the understanding of charge and exciton dynamics in the condensed phase environment, and yet it remains computationally expensive on classical computers. We have developed a variational quantum algorithm that is capable of simulating non-Markovian quantum dynamics. The algorithm captures the non-Markovian effect by employing the Ehrenfect trajectories in the path integral formulation and the Monte Carlo sampling of the thermal distribution. We tested the algorithm with the spin-boson model on the quantum simulator and the results match well with the exact ones. The algorithm naturally fits into the parallel computing platform of the NISQ devices and is well suited for anharmonic system-bath interactions and multi-state systems.
The simulation of non-Markovian quantum dynamics plays an important role in the understanding of charge and exciton dynamics in the condensed phase environment, yet such a simulation remains computationally expensive on classical computers. In this work, we develop a variational quantum algorithm that is capable of simulating non-Markovian quantum dynamics on quantum computers. The algorithm captures the non-Markovian effect by employing the Ehrenfest trajectories and Monte Carlo sampling of their thermal distribution. We test the algorithm with the spin-boson model on the quantum simulator, and the results match quantitatively with the exact ones. The algorithm naturally fits into the parallel computing platform of the NISQ devices and can be extended to anharmonic system-bath interactions and multistate systems.
Research in open quantum system dynamics has received growing interest in recent years, and its ongoing investigation has uncovered many intriguing physics departing from closed systems. A particularly useful application of the open quantum system theory is to simulate quantum dynamical processes in condensed phase materials. As the quantum degree of freedom is constantly under the influence of its thermal environment, the accurate description of the dynamics often requires non-Markovian time evolution at finite temperature. Such calculation is usually quite challenging on classical computers as extensive memory storage is required. In this work, we focus on a quantum system linearly coupled to its harmonic bath and present a path integral based quantum algorithm that time-evolves the reduced density matrix under finite temperature non-Markovian dynamics. To treat the nonunitary time evolution, the Sz.-Nagy dilation scheme is used for the conversion to unitary dynamics that can be implementable on gate-based quantum computers. The modified Hadamard test is then used to retrieve all the information of the reduced density matrix. Complexity analysis shows that the memory requirement has exponential reduction on the quantum machine whereas the runtime complexity stays roughly the same as for the classical computer. It points to the possibility of using this algorithm to simulate multilevel and multisite non-Markovian quantum dynamics that are beyond the reach of classical computers. The algorithm makes no ad hoc assumptions and extends naturally beyond Markovian and weak coupling regimes. We validated the algorithm on the quantum simulator with the spin-boson model and demonstrated its excellent agreement with the classical computer benchmark. Published by the American Physical Society 2024
Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum XYXYXY model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.
Simulating non-Markovian open quantum dynamics is crucial for understanding complex quantum systems, yet it poses significant challenges for standard quantum hardware. These challenges stem from the non-Hermitian nature of such dynamics, which results in nonunitary evolution, as well as constraints imposed by limited quantum resources. To address this, we propose a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in systems coupled to non-Markovian environments. Our approach includes formulating a non-Markovian Stochastic Schrödinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. We then employ variational quantum simulation to capture the nonunitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated dissiaptive dynamics in the spin-boson model (SBM) and excitation energy transfer processes in both a prototype dimer system and the biologically relevant Fenna-Matthews-Olson (FMO) complex.