Unravelling open quantum systems on a NISQ Computer

It is well-know that the simulation of the stochastic Schrödinger equations unravelling the typical master equations describing the dynamics of open quantum systems is a very useful computational tool. Here, we show how such unravellings can be simulated on a NISQ computer. The quantum algorithm maintains the cost of initial state preparation constant via quantum forking. Quantum forking creates an entangled state in which a single copy of a quantum state is encoded and evolves under independent quantum processes in each subspace, thereby allowing parallel unravelling from one wave function. A protocol for implementing a generic non-Hermitian evolution using quantum circuit elements is described. The algorithm is applied to the simulation of Markovian master equations describing quantum neural networks.