Capturing Non-Markovian Dynamics on Near-Term Quantum Computers

Abstract

With the rapid progress in quantum hardware, there has been an increased interest in new quantum algorithms to describe complex many-body systems searching for the still-elusive goal of 'useful quantum advantage'. Surprisingly, quantum algorithms for the treatment of open quantum systems (OQSs) have remained underexplored, in part due to the inherent challenges of mapping non-unitary evolution into the framework of unitary gates. Evolving an open system unitarily necessitates dilation into a new effective system to incorporate critical environmental degrees of freedom. In this context, we present and validate a new quantum algorithm to treat non-Markovian dynamics in OQSs built on the Ensemble of Lindblad's Trajectories approach, invoking the Sz.-Nagy dilation theorem. Here we demonstrate our algorithm on the Jaynes-Cummings model in the strong coupling and detuned regimes, relevant in quantum optics and driven quantum systems studies. This algorithm, a key step towards generalized modeling of non-Markovian dynamics on a noisy-quantum device, captures a broad class of dynamics and opens up a new direction in OQS problems.

A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex

“…Quantum computation offers an avenue to reduce the exponential complexity of the exact wavefunction on a classical computer to polynomial scaling on a quantum computer. One major advantage shared by our previous [6,7] and the generalized quantum algorithms lies in the potential to extend the exponential advantage in stationary-state preparation to time-dependent phenomena. While the previous and the generalized algorithms do not fully realize this possibility with the current imple- FIG.…”

“…The quantum algorithm was successfully applied to the amplitude damping quantum channel and implemented on the IBM Q quantum simulator and devices [6]. Although the quantum algorithm was designed with generality in mind -indeed it was successfully adapted to simulate another dynamical model (the Jaynes-Cummings model) in a related work [7] -there are two issues that must be solved before it can be applied to more complex dynamical processes. Firstly, the Kraus operators in the amplitude damping model have an explicit dependence on time, which allows each time step to be simulated independently.…”

Fitting quantum noise models to tomography data

“…Non-Markovianity can also be quantified by considering the change in the distinguishability of pairs of input states [26]. The observation of non-monotonic behaviour of channel capacity [27], the geometrical variation of the volume of the set of physical states [28], ensembles of Lindblad's trajectories [29] and deep-neural-network learning [30] are among the many alternative strategies to quantify dynamics with memory effects.…”