Physics – Quantum Physics
Scientific paper
2007-04-10
Journal of the ACM, Volume 54, Issue 2 (April 2007)
Physics
Quantum Physics
46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new version also include formalization of several other measuremen
Scientific paper
Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer stands out as fundamental. We develop a rigorous mathematical model underlying the one-way quantum computer and present a concrete syntax and operational semantics for programs, which we call patterns, and an algebra of these patterns derived from a denotational semantics. More importantly, we present a calculus for reasoning locally and compositionally about these patterns. We present a rewrite theory and prove a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements and expressiveness theorems. Furthermore we formalize several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. This allows us to transfer all the theory we develop for the one-way model to these models. This shows that the framework we have developed has a general impact on measurement-based computation and is not just particular to the one-way quantum computer.
Danos Vincent
Kashefi Elham
Panangaden Prakash
No associations
LandOfFree
The Measurement Calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Measurement Calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Measurement Calculus will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-207780