Quantum algorithms for quantum dynamics: A performance study on the spin-boson model

Abstract

Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial limitations of available noisy and near-term quantum hardware. On the other hand, variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. However, despite the recent development of variational quantum algorithms for quantum dynamics, a detailed assessment of their efficiency and scalability is yet to be presented. In this talk, I will present results that aim to fill this gap. For this purpose, we applied a VQA based on McLachlan’s principle to simulate the dynamics of a spin-boson model subject to varying levels of realistic hardware noise as well as in different physical regimes. We observe a good performance of the variational approach used in combination with a general, physically motivated wavefunction ansatz. Furthermore, in addition to the algorithm’s accuracy, I will talk about its scaling behavior as a function of system size in comparison to the conventional first-order Trotter-evolution, and present scaling predictions for the simulation of a classically intractable system. I will conclude by showing that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage for the solution of time-dependent problems.