A variational method for quantum simulation of time evolution*

The simulation of quantum systems is one of the most promising applications of quantum computing. Typically, simulation of time evolution is achieved by decomposing the time evolution operator into a series of quantum gates through a process known as "Trotterization" [1], where the accuracy of the simulation can always be improved by adding more gates to the Trotter sequence. However, in the era of noisy, intermediate-scale quantum (NISQ) computing, applying many gates in sequence leads to compound errors that quickly make the simulation unreliable. Thus, it would be desirable to find a way to increase the accuracy of a given quantum simulation without increasing the number of gates.

It has been shown that Trotterization is not necessarily the optimal decomposition of a given unitary operator [2]. Here we present an alternative variational method for finding gate sequences that approximate unitary evolution and evaluate the effectiveness of this method for simulating the Heisenberg model.

[1] H. F. Trotter, Proc. Am. Math. Soc. 10, 545–551 (1959)
[2] B. D. M. Jones et al. arXiv:1904.01336 (2019)