Sparse Probabilistic Synthesis of Quantum Operations

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 magnetic resonance imaging (MRI) applications, can only be implemented approximately using finite quantum resources. This work develops an approach that, on average—at the cost of a modestly increased measurement repetition rate—enables exact implementations. 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 preoptimized probability distribution, one can on average implement the desired operation with a rigorously controllable approximation error. The approach relies on sophisticated tools from convex optimization to efficiently find optimal probability distributions. A diverse spectrum of applications are demonstrated as (a) exactly synthesizing rotations in fault-tolerant quantum computers using only low <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>T</a:mi></a:math>-count circuits and (b) synthesizing 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. Published by the American Physical Society 2024