Simulation of exponential decay on simple quantum circuits: a case study : Wigner centennial issue

One of potential applications of quantum processors should be a simulation of dynamics of quantum systems. In this paper we analyse whether it is possible to simulate a paradigmatic model of an exponential decay of a two-level system using a programmable quantum gate array. That is, we would like to simulate the decay of a two-level system in such a way that the parameters of the decay itself are encoded in the state of the ancilla that serves as a program for the programmable gate array. We show that it is impossible to simulate the exponential decay precisely with the finite-dimensional programmable gate array. On the other hand, we present a very simple model of a Markovian decay process that can be efficiently simulated on a simple programmable gate array. We compare this Markovian process with the exponential decay.