Efficient Simulation of Quantum Thermalization Dynamics

Dominik Hahn, Ryan Sweke, Abhinav Deshpande +1 more

The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, algorithms for preparing thermal states—crucial for probing equilibrium behavior—became available only recently with breakthrough algorithms based on the simulation of well-designed dissipative processes, a quantum-analog to Markov chain Monte Carlo algorithms. We show a way to implement these algorithms avoiding expensive block encoding and relying only on dense local circuits, akin to Hamiltonian simulation. Specifically, our method leverages spatial truncation and Trotterization of exact quasilocal dissipative processes. We rigorously prove that the approximations we use have little effect on rapid mixing at high temperatures and allow convergence to the thermal state with small bounded error. Moreover, we accompany our analytical results with numerical simulations that show that this method, unlike previously thought, is within the reach of current generation of quantum hardware. These results provide the first provably efficient quantum thermalization protocol implementable on near-term quantum devices, offering a concrete path toward practical simulation of equilibrium quantum phenomena.

Kurt A. Jacobs, Maxim Olshanii, Vanja Dunjko

Maxim F. Gelin, Raffaele Borrelli

Abstract We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.

Osamu Fukushima

Chi-Fang Chen, Michael J. Kastoryano, Fernando G. S. L. Brandão +1 more

Abstract Quantum computers promise to tackle quantum simulation problems that are classically intractable 1 . Although a lot of quantum algorithms 2–4 have been developed for simulating quantum dynamics, a general-purpose method for simulating low-temperature quantum phenomena remains unknown. In classical settings, the analogous task of sampling from thermal distributions has been largely addressed by Markov Chain Monte Carlo (MCMC) methods 5,6 . Here we propose an efficient quantum algorithm for thermal simulation that—akin to MCMC methods—exhibits detailed balance, respects locality and serves as a toy model for thermalization in open quantum systems. The enduring impact of MCMC methods suggests that our new construction may play an equally important part in quantum computing and applications in the physical sciences and beyond.

Felix M. Izrailev