7,985 research outputs found
Systematic Analysis of Majorization in Quantum Algorithms
Motivated by the need to uncover some underlying mathematical structure of
optimal quantum computation, we carry out a systematic analysis of a wide
variety of quantum algorithms from the majorization theory point of view. We
conclude that step-by-step majorization is found in the known instances of fast
and efficient algorithms, namely in the quantum Fourier transform, in Grover's
algorithm, in the hidden affine function problem, in searching by quantum
adiabatic evolution and in deterministic quantum walks in continuous time
solving a classically hard problem. On the other hand, the optimal quantum
algorithm for parity determination, which does not provide any computational
speed-up, does not show step-by-step majorization. Lack of both speed-up and
step-by-step majorization is also a feature of the adiabatic quantum algorithm
solving the 2-SAT ``ring of agrees'' problem. Furthermore, the quantum
algorithm for the hidden affine function problem does not make use of any
entanglement while it does obey majorization. All the above results give
support to a step-by-step Majorization Principle necessary for optimal quantum
computation.Comment: 15 pages, 14 figures, final versio
Stability of dynamical distribution networks with arbitrary flow constraints and unknown in/outflows
A basic model of a dynamical distribution network is considered, modeled as a
directed graph with storage variables corresponding to every vertex and flow
inputs corresponding to every edge, subject to unknown but constant inflows and
outflows. We analyze the dynamics of the system in closed-loop with a
distributed proportional-integral controller structure, where the flow inputs
are constrained to take value in closed intervals. Results from our previous
work are extended to general flow constraint intervals, and conditions for
asymptotic load balancing are derived that rely on the structure of the graph
and its flow constraints.Comment: published in proceeding of 52nd IEEE Conference on Decision and
Control (CDC 2013). arXiv admin note: text overlap with arXiv:1403.5198,
arXiv:1403.520
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