Joseph Cunningham

We propose a general framework for analysing the performance of quantum algorithms that consist of performing discrete operations controlled by a Poisson process. This extends our previous work [1]. In particular, we are interested in emulating certain features of adiabatic quantum computation without having to simulate time-dependent Hamiltonian evolution, since this typically causes a significant discretisation cost. We can also Poissonise the discretisation processes themselves. In this way we are able to show that discretisation in the context of adiabatic quantum computing is less costly than the general bounds on the Trotterisation error would imply. In this way we are able to reproduce key results from [2]. The resulting error bounds share many key features with the error bounds in adiabatic quantum computation. And many results are directly applicable. As applications, we show how our framework yields six distinct approaches to both the Grover search problem and the quantum linear systems problem that almost all achieve optimal asymptotic complexity.