Abstract
Projective measurements with high quantum efficiency are often assumed to be required for efficient circuit-based quantum computing. We argue that this is not the case and show that the fact that they are not required was actually known previously but was 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 considering 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.
Highlights
The work of DiVincenzo [1] states explicit requirements for scalable circuit based quantum computing
There exists an assumption that the measurement criteria requires strong projective measurements with near unit quantum efficiency to achieve the efficiency possible in quantum computing [3]
This may seem reasonable given that proposed quantum algorithms which are efficient compared to the best known classical algorithms are presented with measurements in the basis of the eigenstates of Hermitian operators
Summary
The work of DiVincenzo [1] states explicit requirements for scalable circuit based quantum computing. There exists an assumption that the measurement criteria requires strong projective measurements with near unit quantum efficiency to achieve the efficiency possible in quantum computing [3]. We hope to demonstrate in theory that when building a demonstration quantum computer based on the circuit model, strong projective measurement for read-out in the computational basis is not absolutely necessary. This is an important consideration when constructing small to medium scale quantum computers as it allows for an extra degree of freedom which can assist in the the design of algorithms matched to the strengths of the particular architecture used.
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