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

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.

A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy

“…For example, it is possible to employ a stochastic propagation of the state vector exploiting the repetition of the quantum circuit due to sampling, as demonstrated in the context of the simulation of exciton transport with digital QCs. 51 Indeed, this method has already proven effective in designing resource-efficient algorithms for classical computers. 52,53 Alternatively, other quantum algorithms to simulate open system dynamics of excitonic systems have been proposed 54,55 including an explicit representation of the environment through the use of a collision model 51 or by inserting vibrational degrees of freedom 56 to follow the wavepacket dynamics in the excited state.…”

“…51 Indeed, this method has already proven effective in designing resource-efficient algorithms for classical computers. 52,53 Alternatively, other quantum algorithms to simulate open system dynamics of excitonic systems have been proposed 54,55 including an explicit representation of the environment through the use of a collision model 51 or by inserting vibrational degrees of freedom 56 to follow the wavepacket dynamics in the excited state. 19,57 For multidimensional spectra, scanning of delay times represents a particularly demanding computational task in both classical and quantum simulations.…”

“…The software used for the simulations is freely available in an online repository. 40 Once the quantum circuit version of the Feynman diagrams is established, we discuss the emergence of a quantum advantage when the dimension of the Hilbert space grows to include the vibrational degrees of freedom.…”

“…For example, it is possible to employ a stochastic propagation of the state vector exploiting the repetition of the quantum circuit due to sampling, as demonstrated in the context of the simulation of exciton transport with digital QCs . Indeed, this method has already proven effective in designing resource-efficient algorithms for classical computers. , Alternatively, other quantum algorithms to simulate open system dynamics of excitonic systems have been proposed , including an explicit representation of the environment through the use of a collision model or by inserting vibrational degrees of freedom to follow the wavepacket dynamics in the excited state. , For multidimensional spectra, scanning of delay times represents a particularly demanding computational task in both classical and quantum simulations. To reduce the computational burden, strategies already implemented in experiments, such as compressed sensing techniques, − may aid in effectively reducing the number of sampled points.…”

Environment-Assisted Modulation of Heat Flux in a Bio-Inspired System Based on Collision Model

“…Chisholm et al, using a stochastic collision model, studied the transport phenomena in a quantum network model of the Fenna-Matthews-Olson (FMO) complex, and investigated the Markovian and non-Markovian effects [ 53 ]. FMO complex is a pigment-protein complex found in green sulfur bacteria and is responsible for funneling the exciton energy collected by the chlorosome antenna to the reaction center.Gallina et al have simulated the dephasing assisted transport of a four-site network based on a collision model using the IBM Qiskit QASM simulator [ 54 ].…”