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Vol.19
No.1&12,
February 1, 2019
Research Articles:
Toward an optimal quantum
algorithm for polynomial factorization over finite fields
(pp0001-0013)
Javad Dolizkani
We present a randomized quantum
algorithm for polynomial factorization over finite fields. For
polynomials of degree $n$
over a finite field $\F_q$,
the average-case complexity of our algorithm is an expected
$O(n^{1 + o(1)} \log^{2 + o(1)}q)$
bit operations. Only for a negligible subset of polynomials of degree
$n$
our algorithm has a higher complexity of
$O(n^{4/3 + o(1)} \log^{2 + o(1)}q)$
bit operations. This breaks the classical
$3/2$-exponent
barrier for polynomial factorization over finite fields
\cite{guo2016alg}.
Teleportation via the
entangled derivative of coherent state
(pp0014-0022)
Anas Othman
Recently, David Yevick and I
published an article [Othman, A.
\&
Yevick, D. Int J Theor
Phys {\bf
57}, 2293 (2018)] about constructing a superposition of two nearly
identical coherent states (near coherent state). We showed that this
state becomes a superposition of a derivative state and a coherent
state. Here, we use the definition of the derivative state to create the
entangled derivative of coherent state (EDCS).
We show that this state can be used to teleport qubits encoded in the
near coherent states. The decoherence of EDCS is also studied. In
addition, we propose an experimental scheme to produce the EDCS
and to perform teleportation.
Periodicity for the Fourier
quantum walk on regular graphs
(pp0023-0034)
Kei
Saito
Quantum walks determined by the
coin operator on graphs have been intensively studied. The typical
examples of coin operator are the Grover and Fourier matrices. The
periodicity of the Grover walk is well investigated. However, the
corresponding result on the Fourier walk is not known. In this paper, we
present a necessary condition for the Fourier walk on regular graphs to
have the finite period. As an application of our result, we show that
the Fourier walks do not have any finite period for some classes of
regular graphs such as complete graphs, cycle graphs with
selfloops,
and
hypercubes.
Grover-based Ashenhurst-Curtis
decomposition using quantum language quipper
(pp0035-0066)
Yiwei Li, Edison Tsai, Marek Perkowski, and Xiaoyu Song
Functional decomposition plays a key role in several areas
such as system design, digital circuits, database systems, and Machine
Learning. This paper presents a novel quantum computing approach
based on Grover’s search algorithm for a generalized Ashenhurst-Curtis
decomposition. The method models the decomposition problem as a search
problem and constructs the oracle circuit based on the set-theoretic
partition algebra. A hybrid quantum-based algorithm takes advantage of
the quadratic speedup achieved by Grover’s search algorithm with quantum
oracles for finding the minimum-cost decomposition. The method is
implemented and simulated in the quantum programming language Quipper.
This work constitutes the first attempt to apply quantum computing to
functional decomposition.
Quantum complementarity and
operator structures
(pp0067-0083)
David
W. Kribs, Jeremy Livick, Mike I. Nelson, Rajesh Perira,
and Mizanur Rahaman
We establish operator structure
identities for quantum channels and their error-correcting and private
codes, emphasizing the
complementarity relationship
between the two perspectives. Relevant structures include correctable
and private operator algebras, and operator spaces such as
multiplicative domains and
nullspaces
of quantum channels and their complementary maps. For the case of
privatizing to quantum states, we also derive dimension inequalities on
the associated operator algebras that further quantify the trade-off
between correction and privacy.
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