164,706 research outputs found
Polynomial time quantum computation with advice
Advice is supplementary information that enhances the computational power of
an underlying computation. This paper focuses on advice that is given in the
form of a pure quantum state and examines the influence of such advice on the
behaviors of an underlying polynomial-time quantum computation with
bounded-error probability.Comment: 9 page
Quantum Discord and Quantum Computing - An Appraisal
We discuss models of computing that are beyond classical. The primary
motivation is to unearth the cause of nonclassical advantages in computation.
Completeness results from computational complexity theory lead to the
identification of very disparate problems, and offer a kaleidoscopic view into
the realm of quantum enhancements in computation. Emphasis is placed on the
`power of one qubit' model, and the boundary between quantum and classical
correlations as delineated by quantum discord. A recent result by Eastin on the
role of this boundary in the efficient classical simulation of quantum
computation is discussed. Perceived drawbacks in the interpretation of quantum
discord as a relevant certificate of quantum enhancements are addressed.Comment: To be published in the Special Issue of the International Journal of
Quantum Information on "Quantum Correlations: entanglement and beyond." 11
pages, 4 figure
Computation in generalised probabilistic theories
From the existence of an efficient quantum algorithm for factoring, it is
likely that quantum computation is intrinsically more powerful than classical
computation. At present, the best upper bound known for the power of quantum
computation is that BQP is in AWPP. This work investigates limits on
computational power that are imposed by physical principles. To this end, we
define a circuit-based model of computation in a class of operationally-defined
theories more general than quantum theory, and ask: what is the minimal set of
physical assumptions under which the above inclusion still holds? We show that
given only an assumption of tomographic locality (roughly, that multipartite
states can be characterised by local measurements), efficient computations are
contained in AWPP. This inclusion still holds even without assuming a basic
notion of causality (where the notion is, roughly, that probabilities for
outcomes cannot depend on future measurement choices). Following Aaronson, we
extend the computational model by allowing post-selection on measurement
outcomes. Aaronson showed that the corresponding quantum complexity class is
equal to PP. Given only the assumption of tomographic locality, the inclusion
in PP still holds for post-selected computation in general theories. Thus in a
world with post-selection, quantum theory is optimal for computation in the
space of all general theories. We then consider if relativised complexity
results can be obtained for general theories. It is not clear how to define a
sensible notion of an oracle in the general framework that reduces to the
standard notion in the quantum case. Nevertheless, it is possible to define
computation relative to a `classical oracle'. Then, we show there exists a
classical oracle relative to which efficient computation in any theory
satisfying the causality assumption and tomographic locality does not include
NP.Comment: 14+9 pages. Comments welcom
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