Probabilistic imaginary-time evolution in the XXZ-Heisenberg chain

Kurzfassung

In quantum computation, it is an essential task to prepare the ground state of the target system. So far, the variational quantum eigensolver algorithm has been mainly used for this task. Recently, it has been shown that the imaginary time evolution can also be achieved on quantum computers by introducing a single auxiliary site [1]. This probabilistic imaginary time evolution (PITE) algorithm allows us to determine the ground state in a manner analogous to well-known numerical methods of tensor-network algorithms on classical computers, such as the time-evolving block decimation technique. We apply this algorithm to the XXZ-Heisenberg chain in order to study its accuracy, the depth of circuits depending on imaginary-time steps and, in particular, the difference between gapless and gapped systems. More precisely, we demonstrate that the computation up to L=16 sites can be easily achieved on QASM simulators, showing a good accuracy compared to exact data. The obtained ground states provide us a valuable opportunity to perform further real-time evolutions to simulate time-dependent correlation functions, which gives us dynamic spectral functions.