Simulating Time Evolution of Entanglement Entropy on Quantum Computers via Algebraic Compression

Quantum computers are well suited to simulate the time evolution of a many-body system under both static and time-dependent Hamiltonians. The standard approach to producing time evolution circuits is with the Trotter product formula; however, for long simulation times this method produces deep circuits which have significant noise, limiting the applicability on today's quantum hardware. Thus, to obtain meaningful results, we need to minimize the noise by minimizing the depth of the circuit. This can be achieved for certain classes of Hamiltonians, as their time evolution can be algebraically compressed to a fixed depth circuit [1,2]. Here, we demonstrate the use of this compression algorithm by studying the time evolution of several fermionic models on IBM quantum computers. By using a controlled SWAP structure [3] and applying error mitigation techniques we are able to obtain the time-dependent Rényi entropy on quantum hardware, bringing us closer to understanding the behavior of entanglement entropy under time evolution.

[1] E. Kökcü et al., Phys. Rev. A 105, 032420 (2021)

[2] D. Camps et al., SIAM Journal on Matrix Analysis and Applications 2022 43:3, 1084-1108

[3] S. Johri et al., Phys. Rev. B 96, 195136 (2017)