Efficient quantum computing with weak measurements

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.

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Cited by in corpus (6)

• Characterizations and Quantifications of Macroscopic Quantumness and Its Implementations using Optical Fields
• Nonlocal Measurements via Quantum Erasure
• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• Overcoming experimental limitations in a non-linear two-qubit gate through postselection
• Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation