21,263 research outputs found
Quantum Discord and Quantum Computing - An Appraisal
We discuss models of computing that are beyond classical. The primary
motivation is to unearth the cause of nonclassical advantages in computation.
Completeness results from computational complexity theory lead to the
identification of very disparate problems, and offer a kaleidoscopic view into
the realm of quantum enhancements in computation. Emphasis is placed on the
`power of one qubit' model, and the boundary between quantum and classical
correlations as delineated by quantum discord. A recent result by Eastin on the
role of this boundary in the efficient classical simulation of quantum
computation is discussed. Perceived drawbacks in the interpretation of quantum
discord as a relevant certificate of quantum enhancements are addressed.Comment: To be published in the Special Issue of the International Journal of
Quantum Information on "Quantum Correlations: entanglement and beyond." 11
pages, 4 figure
Quantum Algorithms for Fermionic Quantum Field Theories
Extending previous work on scalar field theories, we develop a quantum
algorithm to compute relativistic scattering amplitudes in fermionic field
theories, exemplified by the massive Gross-Neveu model, a theory in two
spacetime dimensions with quartic interactions. The algorithm introduces new
techniques to meet the additional challenges posed by the characteristics of
fermionic fields, and its run time is polynomial in the desired precision and
the energy. Thus, it constitutes further progress towards an efficient quantum
algorithm for simulating the Standard Model of particle physics.Comment: 29 page
Quantum Algorithms for Quantum Field Theories
Quantum field theory reconciles quantum mechanics and special relativity, and
plays a central role in many areas of physics. We develop a quantum algorithm
to compute relativistic scattering probabilities in a massive quantum field
theory with quartic self-interactions (phi-fourth theory) in spacetime of four
and fewer dimensions. Its run time is polynomial in the number of particles,
their energy, and the desired precision, and applies at both weak and strong
coupling. In the strong-coupling and high-precision regimes, our quantum
algorithm achieves exponential speedup over the fastest known classical
algorithm.Comment: v2: appendix added (15 pages + 25-page appendix
Quantum Computation of Scattering in Scalar Quantum Field Theories
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling
Thermal correlators of anyons in two dimensions
The anyon fields have trivial -commutator for not integer.
For integer the commutators become temperature-dependent operator
valued distributions. The -point functions do not factorize as for quasifree
states.Comment: 14 pages, LaTeX (misprints corrected, a reference added
BQP-completeness of Scattering in Scalar Quantum Field Theory
Recent work has shown that quantum computers can compute scattering
probabilities in massive quantum field theories, with a run time that is
polynomial in the number of particles, their energy, and the desired precision.
Here we study a closely related quantum field-theoretical problem: estimating
the vacuum-to-vacuum transition amplitude, in the presence of
spacetime-dependent classical sources, for a massive scalar field theory in
(1+1) dimensions. We show that this problem is BQP-hard; in other words, its
solution enables one to solve any problem that is solvable in polynomial time
by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be
accurately estimated by any efficient classical algorithm, even if the field
theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding
decision problem can be solved by a quantum computer in a time scaling
polynomially with the number of bits needed to specify the classical source
fields, and this problem is therefore BQP-complete. Our construction can be
regarded as an idealized architecture for a universal quantum computer in a
laboratory system described by massive phi^4 theory coupled to classical
spacetime-dependent sources.Comment: 41 pages, 7 figures. Corrected typo in foote
Boundary and impurity effects on entanglement of Heisenberg chains
We study entanglement of a pair of qubits and the bipartite entanglement
between the pair and the rest within open-ended Heisenberg and XY models.
The open boundary condition leads to strong oscillations of entanglements with
a two-site period, and the two kinds of entanglements are 180 degree out of
phase with each other. The mean pairwise entanglement and ground-state energy
per site in the model are found to be proportional to each other. We
study the effects of a single bulk impurity on entanglement, and find that
there exists threshold values of the relative coupling strength between the
impurity and its nearest neighbours, after which the impurity becomes pairwise
entangled with its nearest neighbours.Comment: 6 pages and 6 figure
Upper limit to in scalar-tensor gravity theories
In a previous paper (Serna & Alimi 1996), we have pointed out the existence
of some particular scalar-tensor gravity theories able to relax the
nucleosynthesis constraint on the cosmic baryonic density. In this paper, we
present an exhaustive study of primordial nucleosynthesis in the framework of
such theories taking into account the currently adopted observational
constraints. We show that a wide class of them allows for a baryonic density
very close to that needed for the universe closure. This class of theories
converges soon enough towards General Relativity and, hence, is compatible with
all solar-system and binary pulsar gravitational tests. In other words, we show
that primordial nucleosynthesis does not always impose a very stringent bound
on the baryon contribution to the density parameter.Comment: uuencoded tar-file containing 16 pages, latex with 5 figures,
accepted for publication in Astrophysical Journal (Part 1
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