Path integrals offer a robust approach for simulating open quantum dynamics with advancements transcending initial system size limitations. However, accurately modeling systems governed by mechanisms that do not conserve the number of quantum particles, such as lossy cavity modes, remains a challenge. We present a method to incorporate such empirical source and drain mechanisms within a path integral framework using quantum master equations. This technique facilitates rigorous inclusion of bath degrees of freedom while accommodating empirical time scales via Lindbladian dynamics. Computational costs are primarily driven by the path integral method with minimal overhead from Lindbladian terms. We use it to study exciton transport in a four-site Fenna-Matthews-Olson model, examining the potential loss of the exciton to the reaction center. This path integral Lindblad method promises an enhanced ability to simulate dynamics and will be fundamental to simulation of spectra in diverse quantum processes in open systems.
Path integrals offer a robust approach for simulating open quantum dynamics with advancements transcending initial system size limitations. However, accurately modeling systems governed by mechanisms that do not conserve the number of quantum particles, such as lossy cavity modes, remains a challenge. We present a method to incorporate such empirical source and drain mechanisms within a path integral framework using quantum master equations. This technique facilitates rigorous inclusion of bath degrees of freedom while accommodating empirical time scales via Lindbladian dynamics. Computational costs are primarily driven by the path integral method with minimal overhead from Lindbladian terms. We use it to study exciton transport in a four-site Fenna-Matthews-Olson model, examining the potential loss of the exciton to the reaction center. This path integral Lindblad method promises an enhanced ability to simulate dynamics and will be fundamental to simulation of spectra in diverse quantum processes in open systems.
Analyzing routes of transport for open quantum systems with non-equilibrium initial conditions is extremely challenging. The state-to-state approach [A. Bose, and P.L. Walters, J. Chem. Theory Comput. 2023, 19, 15, 4828-4836] has proven to be a useful method for understanding transport mechanisms in quantum systems interacting with dissipative thermal baths, and has been recently extended to non-Hermitian systems to account for empirical loss. These non-Hermitian descriptions are, however, not capable of describing empirical processes of more general nature, including but not limited to a variety of pumping processes. We extend the state-to-state analysis to account for Lindbladian descriptions of generic dissipative, pumping and decohering processes acting on a system which is exchanging energy with a thermal bath. This Lindblad state-to-state method can elucidate routes of transport in systems coupled to a bath and additionally acted upon by Lindblad jump operators. The method is demonstrated using examples of excitonic aggregates subject to incoherent pumping and draining processes. Using this new state-to-state formalism, we demonstrate the establishment of steady-state excitonic currents across molecular aggregates, yielding a different first-principles approach to quantifying the same.
The time evolution of Markovian open quantum systems is governed by Lindblad master equations, whose solution can be formally written as the Lindbladian exponential acting on the initial density matrix. By expanding this Lindbladian exponential into the Taylor series, we propose a generic method for integrating Lindblad master equations. In this method, the series is truncated, retaining a finite number of terms, and the iterative actions of Lindbladian on the density matrix follow the corresponding master equation. Our method offers significant improvements in numerical efficiencies both in memory cost and computation time, especially for systems with many degrees of freedom. Moreover, our proposed method can be integrated seamlessly with tensor networks. Two illustrative examples, a two-level system exhibiting damped Rabi oscillations and a driven dissipative Heisenberg chain, are used to demonstrate the validity of our method. The superiority of our method is benchmarked with detailed performance tests.
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.
We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves two significant advancements. First, we employ a repetition of unitary gates on a set of n system qubits and, remarkably, only a single ancillary bath qubit representing the environment. It follows that, for the typical case of m locality of the Lindblad operators, we reach an exponential improvement of the number of ancilla in terms of m and up to a polynomial improvement in ancilla overhead for large n with respect to other approaches. Although stochasticity is introduced, requiring multiple circuit realizations, the sampling overhead is independent of the system size. Second, we show that, under fixed accuracy conditions, our algorithm enables a reduction in the number of Trotter steps compared to other approaches, substantially decreasing circuit depth. These advancements hold particular significance for near-term quantum computers, where minimizing both width and depth is critical due to inherent noise in their dynamics. Published by the American Physical Society 2024
Quantum computing offers promising new avenues for tackling the long-standing challenge of simulating the quantum dynamics of complex chemical systems, particularly open quantum systems coupled to external baths. However, simulating such nonunitary dynamics on quantum computers is challenging since quantum circuits are specifically designed to carry out unitary transformations. Furthermore, chemical systems are often strongly coupled to the surrounding environment, rendering the dynamics non-Markovian and beyond the scope of Markovian quantum master equations like Lindblad or Redfield. In this work, we introduce a quantum algorithm designed to simulate non-Markovian dynamics of open quantum systems. Our approach enables the implementation of arbitrary quantum master equations on noisy intermediate-scale quantum (NISQ) computers. We illustrate the method as applied in conjunction with the numerically exact hierarchical equations of motion (HEOM) method. The effectiveness of the resulting quantum HEOM algorithm is demonstrated as applied to simulations of the non-Lindbladian electronic energy and charge transfer dynamics in models of the carotenoid-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran and the Fenna–Matthews–Olson complex.
The path integral Lindblad dynamics (PILD) method [A. Bose, J. Phys. Chem. Lett. 15(12), 3363-3368 (2024)] had been introduced as a way of incorporating the impact of certain empirical processes like pumps and drains on the dynamics of quantum systems interacting with thermal environments. The method being based on the time-translational invariance of the Nakajima-Zwanzig memory kernel, however, was not able to account for time-dependent external fields. In this communication, we give an alternate, simpler formulation of PILD, that allows us to go beyond this limitation. It does not require the evaluation of the non-Markovian memory kernel directly, and consequently can be applied to Floquet systems as well.