Commutation simulator for open quantum dynamics

Abstract

Recent progress in quantum simulation and algorithms has demonstrated a rapid expansion in capabilities. The search continues for new techniques and applications to exploit quantum advantage.Here we propose an innovative method to investigate directly the properties of a time-dependent density operator ρ(t). Using generalised quantum commutation simulators, we can directly compute the expectation value of the commutation relation and thus of the rate of change of ρ(t). The approach can be utilised as a quantum eigen-vector solver for the von Neumann equation and a decoherence investigator for the Lindblad equation, by using just the statistics of single-qubit measurements. A simple but important example is demonstrated in the single-qubit case and we discuss extension of the method for practical quantum simulation with many qubits, towards investigation of more realistic quantum systems.

Assisted quantum simulation of open quantum systems

“…The novel advantages of fault-tolerant quantum (FTQ) computers, a hardware platform to perform universal quantum algorithms (UQA), have been theoretically and experimentally demonstrated in simulation of many-body quantum systems, 1 , 2 , 3 , 4 prime factorization, 5 linear equation solving 6 and machine learning problems. 7 , 8 However, enough long coherent time induced by the deep quantum circuits could be a catastrophic obstacles to the execution of UQA.…”