14,306 research outputs found
Alternation in Quantum Programming: From Superposition of Data to Superposition of Programs
We extract a novel quantum programming paradigm - superposition of programs -
from the design idea of a popular class of quantum algorithms, namely quantum
walk-based algorithms. The generality of this paradigm is guaranteed by the
universality of quantum walks as a computational model. A new quantum
programming language QGCL is then proposed to support the paradigm of
superposition of programs. This language can be seen as a quantum extension of
Dijkstra's GCL (Guarded Command Language). Surprisingly, alternation in GCL
splits into two different notions in the quantum setting: classical alternation
(of quantum programs) and quantum alternation, with the latter being introduced
in QGCL for the first time. Quantum alternation is the key program construct
for realizing the paradigm of superposition of programs.
The denotational semantics of QGCL are defined by introducing a new
mathematical tool called the guarded composition of operator-valued functions.
Then the weakest precondition semantics of QGCL can straightforwardly derived.
Another very useful program construct in realizing the quantum programming
paradigm of superposition of programs, called quantum choice, can be easily
defined in terms of quantum alternation. The relation between quantum choices
and probabilistic choices is clarified through defining the notion of local
variables. We derive a family of algebraic laws for QGCL programs that can be
used in program verification, transformations and compilation. The expressive
power of QGCL is illustrated by several examples where various variants and
generalizations of quantum walks are conveniently expressed using quantum
alternation and quantum choice. We believe that quantum programming with
quantum alternation and choice will play an important role in further
exploiting the power of quantum computing.Comment: arXiv admin note: substantial text overlap with arXiv:1209.437
Quantum Alternation: Prospects and Problems
We propose a notion of quantum control in a quantum programming language
which permits the superposition of finitely many quantum operations without
performing a measurement. This notion takes the form of a conditional construct
similar to the IF statement in classical programming languages. We show that
adding such a quantum IF statement to the QPL programming language simplifies
the presentation of several quantum algorithms. This motivates the possibility
of extending the denotational semantics of QPL to include this form of quantum
alternation. We give a denotational semantics for this extension of QPL based
on Kraus decompositions rather than on superoperators. Finally, we clarify the
relation between quantum alternation and recursion, and discuss the possibility
of lifting the semantics defined by Kraus operators to the superoperator
semantics defined by Selinger.Comment: In Proceedings QPL 2015, arXiv:1511.0118
The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3
A possibility of the uniform antiferromagnetic order is pointed out in an
S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg
quantum spin chain compound: (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3. The system
possesses the bond alternation of strong random bonds that take +/- 2J and weak
uniform AF bonds of -J. In the pure concentration limits, the model reduces to
the AF-AF alternation chain at x=0 and to the F-AF alternation chain at x=1.
The nonequilibrium relaxation of large-scale quantum Monte Carlo simulations
exhibits critical behaviors of the uniform AF order in the intermediate
concentration region, which explains the experimental observation of the
magnetic phase transition. The present results suggest that the uniform AF
order may survive even in the presence of the randomly located ferromagnetic
bonds.Comment: 4 pages, 3 figure
Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?
The study of bond alternation in one-dimensional electronic systems has had a
long history. Theoretical work in the 1930s predicted the absence of bond
alternation in the limit of infinitely long conjugated polymers; a result later
contradicted by experimental investigations. When this issue was re-examined in
the 1950s it was shown in the adiabatic limit that bond alternation occurs for
any value of electron-phonon coupling. The question of whether this conclusion
remains valid for quantized nuclear degrees of freedom was first addressed in
the 1980s. Since then a series of numerical calculations on models with gapped,
dispersionless phonons have suggested that bond alternation is destroyed by
quantum fluctuations below a critical value of electron-phonon coupling. In
this work we study a more realistic model with gapless, dispersive phonons. By
solving this model with the DMRG method we show that bond alternation remains
robust for any value of electron-phonon coupling
Alternation in Quantum Programming: From Superposition of Data to Superposition of Programs
We extract a novel quantum programming paradigm - superposition of programs - from the design idea of a popular class of quantum algorithms, namely quantum walk-based algorithms. The generality of this paradigm is guaranteed by the universality of quantum walks as a computational model. A new quantum programming language QGCL is then proposed to support the paradigm of superposition of programs. This language can be seen as a quantum extension of Dijkstra's GCL (Guarded Command Language). Surprisingly, alternation in GCL splits into two different notions in the quantum setting: classical alternation (of quantum programs) and quantum alternation, with the latter being introduced in QGCL for the first time. Quantum alternation is the key program construct for realizing the paradigm of superposition of programs. The denotational semantics of QGCL are defined by introducing a new mathematical tool called the guarded composition of operator-valued functions. Then the weakest precondition semantics of QGCL can straightforwardly derived. Another very useful program construct in realizing the quantum programming paradigm of superposition of programs, called quantum choice, can be easily defined in terms of quantum alternation. The relation between quantum choices and probabilistic choices is clarified through defining the notion of local variables. We derive a family of algebraic laws for QGCL programs that can be used in program verification, transformations and compilation. The expressive power of QGCL is illustrated by several examples where various variants and generalizations of quantum walks are conveniently expressed using quantum alternation and quantum choice. We believe that quantum programming with quantum alternation and choice will play an important role in further exploiting the power of quantum computing
Phase diagram of ferrimagnetic ladders with bond-alternation
We study the phase diagram of a 2-leg bond-alternation spin-(1/2, 1) ladder
for two different configurations using a quantum renormalization group
approach. Although d-dimensional ferrimagnets show gapless behavior, we will
explicitly show that the effect of the spin mixing and the bond-alternation can
open the possibility for observing an energy gap. We show that the gapless
phases of such systems can be equivalent to the 1-dimensional half-integer
antiferroamgnets, besides the gapless ferrimagnetic phases. We therefore
propose a phase transition between these two gapless phases that can be seen in
the parameter space.Comment: 5 pages and 3 ps figures, accepted in Phys. Rev.
Low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond-alternation
We investigate the low-temperature properties of the spin-1 antiferromagnetic
Heisenberg chain with bond-alternation by the quantum Monte Carlo method (loop
algorithm). The strength of bond-alternation at the gapless point is estimated
as . We confirm numerically that the
low-temperature properties at the gapless point are consistent with field
theoretical predictions. The numerical results are compared with those of the
spin-1/2 antiferromagnetic Heisenberg chain and recent experimental results for
[\{Ni(333-tet)(-N)\}](ClO) (333-tet=tetraamine
-bis(3-aminopropyl)-1,3-propanediamine).Comment: 18 pages, RevTex, 9 figures, Submitted to Phys.Rev.
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