Efficient quantum computing with weak measurements

TL;DR

This paper demonstrates that efficient quantum computing can be achieved using weak measurements instead of high-efficiency projective measurements, challenging common assumptions and exploring the trade-offs involved.

Contribution

It shows how to perform quantum algorithms with non-local weak measurements efficiently and discusses the exponential overhead when using only local weak measurements.

Findings

Efficient quantum algorithms can be implemented with non-local weak measurements.

Local weak measurements require exponential overhead for the same tasks.

High quantum efficiency projective measurements are not strictly necessary for efficiency.

Abstract

Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not deeply explored. We examine this issue by giving an example of how to perform the quantum ordering finding algorithm efficiently using non-local weak measurements given that the measurements used are of bounded weakness and some fixed but arbitrary probability of success less than unity is required. We also show that it is possible to perform the same computation with only local weak measurements but this must necessarily introduce an exponential overhead.