201 research outputs found
An Introduction to Quantum Complexity Theory
We give a basic overview of computational complexity, query complexity, and
communication complexity, with quantum information incorporated into each of
these scenarios. The aim is to provide simple but clear definitions, and to
highlight the interplay between the three scenarios and currently-known quantum
algorithms.Comment: 28 pages, LaTeX, 11 figures within the text, to appear in "Collected
Papers on Quantum Computation and Quantum Information Theory", edited by C.
Macchiavello, G.M. Palma, and A. Zeilinger (World Scientific
Entanglement-Resistant Two-Prover Interactive Proof Systems and Non-Adaptive Private Information Retrieval Systems
We show that, for any language in NP, there is an entanglement-resistant
constant-bit two-prover interactive proof system with a constant completeness
vs. soundness gap. The previously proposed classical two-prover constant-bit
interactive proof systems are known not to be entanglement-resistant. This is
currently the strongest expressive power of any known constant-bit answer
multi-prover interactive proof system that achieves a constant gap. Our result
is based on an "oracularizing" property of certain private information
retrieval systems, which may be of independent interest.Comment: 8 page
GEOGRAPHIC INFORMATION SYSTEMS AND APPLIED ECONOMICS: AN INITIAL DISCUSSION OF POTENTIAL APPLICATIONS AND CONTRIBUTIONS
Geographic Information Systems (GIS) are becoming increasingly important to virtually all of the natural and social sciences. Applied economists will find that GIS can make valuable contributions to many of the problems with which they are concerned. Moreover, a great deal of the science behind GIS technology would benefit from the contributions of applied economists. This paper presents some initial suggestions for the ways in which GIS may be important to economics and the GIS related issues concerning which applied economists could provide useful insights.Research and Development/Tech Change/Emerging Technologies,
The cost of exactly simulating quantum entanglement with classical communication
We investigate the amount of communication that must augment classical local
hidden variable models in order to simulate the behaviour of entangled quantum
systems. We consider the scenario where a bipartite measurement is given from a
set of possibilities and the goal is to obtain exactly the same correlations
that arise when the actual quantum system is measured. We show that, in the
case of a single pair of qubits in a Bell state, a constant number of bits of
communication is always sufficient--regardless of the number of measurements
under consideration. We also show that, in the case of a system of n Bell
states, a constant times 2^n bits of communication are necessary.Comment: 9 pages, LaTeX, no figure
Gate-efficient discrete simulations of continuous-time quantum query algorithms
We show how to efficiently simulate continuous-time quantum query algorithms
that run in time T in a manner that preserves the query complexity (within a
polylogarithmic factor) while also incurring a small overhead cost in the total
number of gates between queries. By small overhead, we mean T within a factor
that is polylogarithmic in terms of T and a cost measure that reflects the cost
of computing the driving Hamiltonian. This permits any continuous-time quantum
algorithm based on an efficiently computable driving Hamiltonian to be
converted into a gate-efficient algorithm with similar running time.Comment: 28 pages, 2 figure
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