arXiv subjects

Peter L. Walters

Publications and source records attributed to Peter L. Walters.

10 recordsLinked to original sources

arXiv2024

Variational quantum algorithm for non-Markovian quantum dynamics

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.

quant-ph↗

arXiv2024

Exact decomposition of non-Markovian dynamics in open quantum systems

In this work, we developed a rigorous procedure for mapping the exact non-Markovian propagator to the generalized Lindblad form. It allows us to extract the negative decay rate that is the indicator of the non-Markovian effect. As a consequence, we can investigate the influence of the non-Markovian bath on the system's properties such as coherence and equilibrium state distribution. The understanding of the non-Markovian contribution to the dynamical process points to the possibility of leveraging non-Markovianity for quantum control.

quant-ph↗

arXiv2024

Polynomial time and space quantum algorithm for the simulation of non-Markovian quantum dynamics

In this work, we developed an efficient quantum algorithm for the simulation of non-Markovian quantum dynamics, based on the Feynman path integral formulation. The algorithm scales polynomially with the number of native gates and the number of qubits, and has no classical overhead. It demonstrates the quantum advantage by overcoming the exponential cost on classical computers. In addition, the algorithm is efficient regardless of whether the temporal entanglement due to non-Markovianity is low or high, making it a unified framework for simulating non-Markovian dynamics in open quantum system.

quant-ph↗

arXiv2024

Ensemble Variational Quantum Algorithm for Non-Markovian Quantum Dynamics

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.

quant-ph↗

arXiv2023

A tensor network representation of path integrals: Implementation and analysis

Tensors with finite correlation afford very compact tensor network representations. A novel tensor network-based decomposition of real-time path integral simulations involving Feynman-Vernon influence functional is introduced. In this tensor network path integral (TNPI) technique, the finite temporarily non-local interactions introduced by the influence functional can be captured very efficiently using matrix product state representation for the path amplitude (PA) tensor. We illustrate this particular TNPI method through various realistic examples, including a charge transfer reaction and an exciton transfer in a dimer. We also show how it is readily applied to systems with greater than two states by simulating a 7-site model of FMO and a molecular wire model. The augmented propagator (AP) TNPI utilizes the symmetries of the problem, leading to accelerated convergence and dramatic reductions of computational effort. We also introduce an approximate method that speeds up propagation beyond the non-local memory length. Furthermore, the structure imposed by the tensor network representation of the PA tensor naturally suggests other factorizations that make simulations for extended systems more efficient. These factorizations would be the subject of future explorations. The flexibility of the AP-TNPI framework makes it a promising new addition to the family of path integral methods for non-equilibrium quantum dynamics.

physics.chem-ph↗

arXiv2023

Impact of solvent on state-to-state population transport in multistate systems using coherences

Understanding the pathways taken by a quantum particle during a transport process is an enormous challenge. There are broadly two different aspects of the problem that affect the route taken. First is obviously the couplings between the various sites, which translates into the intrinsic "strength" of a state-to-state channel. Apart from the inter-state couplings, the solvents affecting the energies of the state, and their relative coupling strengths and time-scales form the second factor. This impact of dissipative media is significantly more difficult to analyze. Building on recently derived relations between coherences and population derivatives, we present an analysis of the transport that allows us to account for both the effects in a rigorous manner. We demonstrate the richness hidden behind the transport even for a relatively simple system, a 4-site coarse-grained model of the Fenna-Matthews-Olson complex. The effect of the local dissipative media is highly non-trivial. We show that while the impact on the total site population may be small, there are dramatic changes to the pathway taken by the transport process. The ability to untangle the dynamics at a greater granularity opens up possibilities in terms of design of novel systems with an eye towards quantum control.

physics.chem-ph↗

arXiv2023

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Challenges persist in numerically simulating these systems both in parameterizing them and following their dynamics over long periods of time. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneties in the Fenna-Matthews-Olson (FMO) complex. We investigate the dynamics of FMO with an exact treatment of various theoretical spectral densities. Because FMO has Hamiltonian elements that connect most of the bacteriochlorophyll sites together, it becomes difficult to rigorously identify the energy transport pathways in the complex. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some of the pathways.

physics.chem-ph↗

arXiv2022

Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations

The recently introduced multisite tensor network path integral (MS-TNPI) allows simulation of extended quantum systems coupled to dissipative media. We use MS-TNPI to simulate the exciton transport and the absorption spectrum of a B850 bacteriochlorophyll (BChl) ring. The MS-TNPI network is extended to account for the ring topology of the B850 system. Accurate molecular dynamics-based description of the molecular vibrations and the protein scaffold is incorporated through the framework of Feynman-Vernon influence functional. To relate the present work with the excitonic picture, an exploration of the absorption spectrum is done by simulating it using approximate and topologically consistent transition dipole moment vectors. Comparison of these numerically exact MS-TNPI absorption spectra are shown with second-order cumulant approximations. The effect of temperature on both the exact and the approximate spectra is also explored.

physics.chem-ph↗

arXiv2022

Effect of Temperature Gradient on Quantum Transport

The recently introduced multisite tensor network path integral (MS-TNPI) method [Bose and Walters, J. Chem. Phys., 2022, 156, 24101.] for simulation of quantum dynamics of extended systems has been shown to be effective in studying one-dimensional systems. Quantum transport in these systems are typically studied at a constant temperature. However, temperature seems to be a very obvious parameter that can be spatially changed to control the quantum transport. Here, MS-TNPI is used to study ``non-equilibrium'' effects of an externally imposed temperature gradient on the quantum transport in one-dimensional extended quantum systems.

physics.chem-ph↗

arXiv2021

A Multisite Decomposition of the Tensor Network Path Integrals

Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the non-equilibrium dynamics of extended quantum systems coupled with local dissipative environments. In this work, we extend the tensor network path integral (TNPI) framework to efficiently simulate such extended systems. The Feynman-Vernon influence functional is a popular approach used to account for the effect of environments on the dynamics of the system. In order to facilitate the incorporation of the influence functional into a multisite framework (MS-TNPI), we combine a matrix product state (MPS) decomposition of the reduced density tensor of the system along the sites with a corresponding tensor network representation of the time axis to construct an efficient 2D tensor network. The 2D MS-TNPI network, when contracted, yields the time-dependent reduced density tensor of the extended system as an MPS. The algorithm presented is independent of the system Hamiltonian. We outline an iteration scheme to take the simulation beyond the non-Markovian memory introduced by solvents. Applications to spin chains coupled to local harmonic baths are presented; we consider the Ising, XXZ and the Heisenberg models, demonstrating that the presence of local environments can often dissipate the entanglement between the sites. We discuss three factors causing the system to transition from a coherent oscillatory dynamics to a fully incoherent dynamics. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.

quant-ph↗