20,575 research outputs found
Generalised quantum weakest preconditions
Generalisation of the quantum weakest precondition result of D'Hondt and
Panangaden is presented. In particular the most general notion of quantum
predicate as positive operator valued measure (POVM) is introduced. The
previously known quantum weakest precondition result has been extended to cover
the case of POVM playing the role of a quantum predicate. Additionally, our
result is valid in infinite dimension case and also holds for a quantum
programs defined as a positive but not necessary completely positive
transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten
High-Level Methods for Quantum Computation and Information
A research programme is set out for developing the use of high-level methods
for quantum computation and information, based on the categorical formulation
of quantum mechanics introduced by the author and Bob Coecke.Comment: 5 page
QPCF: higher order languages and quantum circuits
qPCF is a paradigmatic quantum programming language that ex- tends PCF with
quantum circuits and a quantum co-processor. Quantum circuits are treated as
classical data that can be duplicated and manipulated in flexible ways by means
of a dependent type system. The co-processor is essentially a standard QRAM
device, albeit we avoid to store permanently quantum states in between two
co-processor's calls. Despite its quantum features, qPCF retains the classic
programming approach of PCF. We introduce qPCF syntax, typing rules, and its
operational semantics. We prove fundamental properties of the system, such as
Preservation and Progress Theorems. Moreover, we provide some higher-order
examples of circuit encoding
POVMs and Naimark's theorem without sums
We provide a definition of POVM in terms of abstract tensor structure only.
It is justified in two distinct manners. i. At this abstract level we are still
able to prove Naimark's theorem, hence establishing a bijective correspondence
between abstract POVMs and abstract projective measurements on an extended
system, and this proof is moreover purely graphical. ii. Our definition
coincides with the usual one for the particular case of the Hilbert space
tensor product. We also point to a very useful normal form result for the
classical object structure introduced in quant-ph/0608035
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