7,389 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
QuASeR -- Quantum Accelerated De Novo DNA Sequence Reconstruction
In this article, we present QuASeR, a reference-free DNA sequence
reconstruction implementation via de novo assembly on both gate-based and
quantum annealing platforms. Each one of the four steps of the implementation
(TSP, QUBO, Hamiltonians and QAOA) is explained with simple proof-of-concept
examples to target both the genomics research community and quantum application
developers in a self-contained manner. The details of the implementation are
discussed for the various layers of the quantum full-stack accelerator design.
We also highlight the limitations of current classical simulation and available
quantum hardware systems. The implementation is open-source and can be found on
https://github.com/prince-ph0en1x/QuASeR.Comment: 24 page
Parallel eigensolvers in plane-wave Density Functional Theory
We consider the problem of parallelizing electronic structure computations in
plane-wave Density Functional Theory. Because of the limited scalability of
Fourier transforms, parallelism has to be found at the eigensolver level. We
show how a recently proposed algorithm based on Chebyshev polynomials can scale
into the tens of thousands of processors, outperforming block conjugate
gradient algorithms for large computations
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