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)