Sparse Probabilistic Synthesis of Quantum Operations

Abstract

Successful implementations of quantum technologies require protocols and algorithms that use as few quantum resources as possible. However, many important quantum operations, such as continuous rotation gates in quantum computing or broadband pulses in NMR or MRI applications, can only be implemented approximately using finite quantum resources. This work develops an approach that enables -- at the cost of a modestly increased measurement repetition rate -- exact implementations on average. One proceeds by first building a library of a large number of different approximations to the desired gate operation; by randomly selecting these operations according to a pre-optimised probability distribution, one can on average implement the desired operation with a rigorously controllable approximation error. The approach relies on sophisticated tools from convex optimisation to efficiently find optimal probability distributions. A diverse spectrum of applications are demonstrated as (a) exactly synthesising rotations in fault-tolerant quantum computers using only low T-count circuits and (b) synthesising broadband and band-selective pulses of superior performance in quantum optimal control with (c) further applications in NMR or MRI. The approach is very general and a broad spectrum of practical applications in quantum technologies are explicitly demonstrated.