Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators

Abstract

The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna−Matthews−Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.

An ensemble variational quantum algorithm for non-Markovian quantum dynamics

“…We have demonstrated its feasibility on NISQ devices for the spinboson model. Compared to other methods of simulating non-Markovian quantum dynamics on quantum computers, [59][60][61][62][63] this variational-EACP approach takes advantage of the strength of the both sides: sampling Monte Carlo points on a classical computer and evaluating the wavefunction overlap on a quantum machine. The Monte Carlo sampling of the thermal distribution can be performed efficiently on a classical computer with linear computational cost regarding the number of Monte Carlo points.…”

“…[54][55][56][57][58] On the other hand, the development of quantum algorithms for non-Markovian time evolution is still in its infancy. Notable works include the method of locally indivisible maps, 59 the ensembles of Lindblad trajectories, 60 the construction of superoperators from the generalized quantum master equation 61 and the Feynman-Vernon influence functional, 62 and the path-integral-based algorithm. 63 In this work, we present a non-Markovian quantum algorithm with a NISQ-friendly focus, the time-dependent variational algorithm (TDVA).…”

Simulating Chemistry on Bosonic Quantum Devices

“…Since many systems of chemical interest are coupled to their surrounding environment, the simulation of open quantum systems on quantum computers has recently gained much attention. ,− Most of these simulations are based on the Lindblad equation which relies on the Born–Markov approximation in the system-environment weak coupling limit. ,, Developing quantum algorithms for numerically exact quantum dynamics applied to the regime beyond this weak coupling may involve either doing part of the computations on a classical computer or resorting to more qubits to represent the environmental degrees of freedom. For example, to simulate the dynamics of the spin-boson model, the current qubit-based quantum algorithm developed for the formally exact generalized quantum master equation (GQME) approach − relies on a classical computer to solve the underlying exact memory kernel due to the limited computational resources of current NISQ devices .…”