Recompilation-enhanced simulation of electron–phonon dynamics on IBM quantum computers

Abstract

Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems as dictated by the number of Trotter steps and bosonic energy levels necessary for the convergence of dynamics. We then apply these findings to perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation. Our results represent a significant step in utilising near term quantum computers for simulation of quantum dynamics and highlight the novelty of approximate circuit recompilation as a tool for reducing noise.

Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians

“…At first glance it would seem reasonable to find the evolution operator by directly applying the standard techniques of DQS to (15). However, to do so efficiently, it would be convenient to leverage the structure and the symmetries of the linear operator  in (16). These are not obvious from the expression of .…”

“…First the time evolution operator of a given Hamiltonian is expressed as a series of unitary quantum gates through the Jordan-Wigner isomorphism [9]. Second, the time evolution operator is used to propagate an initial state [3,5], typically by shifting locally the wave function forward in time over discrete and sufficiently small time slices [3][4][5] as long as the interval Δt is small enough [16]. Through the Trotter-Suzuki formula [17][18][19], that takes into account the non-commutativity of the H i ʼs, the accuracy of U(t) can then be improved but at the cost of increasing the circuit depth.…”

Digital Quantum Simulation of the Spin-Boson Model under Markovian Open-System Dynamics

“…Existing quantum computers are based on unitary quantum circuits. Consequently, there has been a plethora of research on closed quantum systems [ 3 , 4 , 5 , 6 ]. Amongst the spin models, an important class is the spin-boson problem, where one or more spins are coupled to several bosonic degrees of freedom.…”

“…They include approaches based on imaginary time evolution [ 23 , 24 ], stochastic Schrödinger Equation [ 25 ], variational quantum eigensolvers to reach steady states [ 26 , 27 ], and the quantum-assisted simulator without a classical-quantum feedback loop [ 28 ]. Mapping bosonic problems to quantum circuits has been laid out in [ 29 , 30 , 31 ], while a recent implementation of spin-boson models can be found in [ 6 ].…”

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 . 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.…”