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arXiv:2111.02897 · New Journal of Physics

Strategies to simulate dephasing-assisted quantum transport on digital quantum computers

Federico Gallina, Matteo Bruschi, Barbara Fresch

Published Feb 1, 2022• 14 citations
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Abstract

Abstract Simulating charge and energy transfer in extended molecular networks requires an effective model to include the environment because it significantly affects the quantum dynamics. A prototypical effect known as environment-assisted quantum transport (ENAQT) consists in the enhancement of the transfer efficiency by the interaction with an environment. A simple description of this phenomenon is obtained by a quantum master equation describing a quantum walk over the molecular network in the presence of inter-site decoherence. We consider the problem of simulating the dynamics underlying ENAQT in a digital quantum computer. Two different quantum algorithms are introduced, the first one based on stochastic Hamiltonians and the second one based on a collision scheme. We test both algorithms by simulating ENAQT in a small molecular network on a quantum computer emulator and provide a comparative analysis of the two approaches. Both algorithms can be implemented in a memory efficient encoding with the number of required qubits scaling logarithmically with the size of the simulated system while the number of gates increases quadratically. We discuss the algorithmic quantum trajectories generated by the two simulation strategies showing that they realize distinct unravellings of the site-dephasing master equation. In our approach, the non-unitary dynamics of the open system is obtained through effective representations of the environment, paving the way to digital quantum simulations of quantum transport influenced by structured environments.

DOI
10.1088/1367-2630/ac512f

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Abstract Simulating charge and energy transfer in extended molecular networks requires an effective model to include the environment because it significantly affects the quantum dynamics. A prototypical effect known as environment-assisted quantum transport (ENAQT) consists in the enhancement of the transfer efficiency by the interaction with an environment. A simple description of this phenomenon is obtained by a quantum master equation describing a quantum walk over the molecular network in the presence of inter-site decoherence. We consider the problem of simulating the dynamics underlying ENAQT in a digital quantum computer. Two different quantum algorithms are introduced, the first one based on stochastic Hamiltonians and the second one based on a collision scheme. We test both algorithms by simulating ENAQT in a small molecular network on a quantum computer emulator and provide a comparative analysis of the two approaches. Both algorithms can be implemented in a memory efficient encoding with the number of required qubits scaling logarithmically with the size of the simulated system while the number of gates increases quadratically. We discuss the algorithmic quantum trajectories generated by the two simulation strategies showing that they realize distinct unravellings of the site-dephasing master equation. In our approach, the non-unitary dynamics of the open system is obtained through effective representations of the environment, paving the way to digital quantum simulations of quantum transport influenced by structured environments.
Environment assisted quantum transport (ENAQT) has been found to increase efficiency of energy transfer in open quantum systems. Chemical complexes like the photosynthetic Fenna-Mathews-Olson (FMO) complex exhibit such phenomenon. ENAQT in the FMO complex has been simulated on analog quantum simulators. However, digital quantum simulators are universal models for quantum simulation and offer greater flexibility over analog simulations. Here we develop the theoretical framework for digital quantum simulation of ENAQT in open quantum systems with tunable bath coupling. The main challenge in developing theoretical models for digital quantum simulation is that the solutions to the quantum master equation are unknown. We give an exact analytical solution for the Lindblad master equation for ENAQT and develop time evolution operators and evolution equation to solve the system. We apply the evolution equation to give a theoretical model for digital quantum simulation of the FMO complex and reproduce the high efficiency and temperature dependence of the dynamics in the complex
Abstract Quantum effects such as the environment assisted quantum transport (ENAQT) displayed in photosynthetic Fenna–Mathews–Olson (FMO) complex has been simulated on analog quantum simulators. Digital quantum simulations offer greater universality and flexibility over analog simulations. However, digital quantum simulations of open quantum systems face a theoretical challenge; one does not know the solutions of the continuous time master equation for developing quantum gate operators. We give a theoretical framework for digital quantum simulation of ENAQT by introducing new quantum evolution operators. We develop the dynamical equation for the operators and prove that it is an analytical solution of the master equation. As an example, using the dynamical equations, we simulate the FMO complex in the digital setting, reproducing theoretical and experimental evidence of the dynamics. The framework gives an optimal method for quantum circuit implementation, giving a log reduction in complexity over known methods. The generic framework can be extrapolated to study other open quantum systems.
The way in which energy is transported through an interacting system governs fundamental properties in nature such as thermal and electric conductivity or phase changes. Remarkably, environmental noise can enhance the transport, an effect known as environment-assisted quantum transport (ENAQT). In this Letter, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions, and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We find that in the regime where ENAQT is most effective, the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by non-Markovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport efficiency. Our approach represents a controlled and scalable way to investigate quantum transport in many-body networks under static disorder and dynamic noise.
Abstract Nontrivial quantum effects in biological systems are of high interest among physicists over the past decade. They allow for information and energy to be exchanged with near-unity efficiency despite hindered by the warm, wet, and noisy environment. Several models suggests that the efficient quantum energy transport is due to the interplay between dephasing dynamics and unitary evolution of the disordered biological systems i.e in photosynthetic complex. However, the proposed models have not yet included the driving force depicting the external perturbation used in the experiment such as laser in 2D spectroscopy involved in the detection of the exciton transfer or an artificial quantum transport experiments. Here, we resolve this issue by subjecting the dephasing assisted transport model by Plenio and Huelga [New J. Phys. 10, 11 (2012)] to a driving force. We analyze dynamical evolution of the driven system and show that further efficiency enhancement achieved by driving the transport site. We also discuss some experimental realizations of the quantum transport system.
Noise is commonly regarded as an adverse effect disrupting communication and coherent transport processes or limiting their efficiency. However, as has been shown for example for small light-harvesting protein complexes decoherence processes can play a significant role in facilitating transport processes, a phenomenon termed environment-assisted quantum transport (ENAQT). We here study numerically and analytically how dephasing noise improves the efficiency of spin excitation transport in a two dimensional lattice with small homogeneous losses. In particular we investigate the efficiency and time of excitation transfer from a random initial site to a specific target site and show that for system sizes below a characteristic scale it can be substantially enhanced by adding small dephasing noise. We derive approximate analytic expressions for the efficiency which become rather accurate in the two limits of small (coherent regime) and large noise (Zeno regime) and give a very good overall estimate. These analytic expressions provide a quantitative description of ENAQT in spatially extended systems and allow to derive conditions for its existence.
Digital quantum computers have the potential to study the dynamics of many-body quantum systems. Nonequilibrium open quantum systems are, however, less straightforward to be implemented. Here we explore the feasibility of studying steady-state transport in strongly interacting many-body quantum systems on a digital quantum computer. To do so, we consider a collisional model representation of the nonequilibrium open dynamics for a boundary-driven XXZXXZXXZ spin chain. More specifically, we investigate how the depth of the quantum circuit is affected by how close we want the steady state to be to the one expected from the underlying master equation. We study the simulation of a boundary-driven spin chain in regimes of weak and strong interactions, which would lead in large systems to diffusive and ballistic dynamics, considering also possible errors in the implementation of the protocol. Last, we analyze the effectiveness of digital simulation via the collisional model of current rectification when the XXZXXZXXZ spin chains are subject to nonuniform magnetic fields and show that, although the circuit depths required to reach steady states are still prohibitive for today's hardware, few collisions are enough to suggest a strong rectifying power.