49,398 research outputs found
Quantum Computational Complexity in the Presence of Closed Timelike Curves
Quantum computation with quantum data that can traverse closed timelike
curves represents a new physical model of computation. We argue that a model of
quantum computation in the presence of closed timelike curves can be formulated
which represents a valid quantification of resources given the ability to
construct compact regions of closed timelike curves. The notion of
self-consistent evolution for quantum computers whose components follow closed
timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197
(1991)], implies that the evolution of the chronology respecting components
which interact with the closed timelike curve components is nonlinear. We
demonstrate that this nonlinearity can be used to efficiently solve
computational problems which are generally thought to be intractable. In
particular we demonstrate that a quantum computer which has access to closed
timelike curve qubits can solve NP-complete problems with only a polynomial
number of quantum gates.Comment: 8 pages, 2 figures. Minor changes and typos fixed. Reference adde
Pairing in finite nuclei from low-momentum two- and three-nucleon interactions
The present contribution reviews recent advances made toward a microscopic
understanding of superfluidity in nuclei using many-body methods based on the
BCS ansatz and low-momentum inter-nucleon interactions, themselves based on
chiral effective field theory and renormalization group techniques.Comment: 15 pages, contribution to "50 years of nuclear BCS", edited by R.A.
Broglia and V. Zelevinsk
Reflections on the Role of Entanglement in the Explanation of Quantum Computational Speedup
Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is still a matter of debate. In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill \& Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play
Infinite-range transverse field Ising models and quantum computation
We present a brief review on information processing, computing and inference
via quantum fluctuation, and clarify the relationship between the probabilistic
information processing and theory of quantum spin glasses through the analysis
of the infinite-range model. We also argue several issues to be solved for the
future direction in the research field.Comment: 13 pages, 6 figures, using svjour.cls, to appear in EPJ-Special
Topic
Almost quantum correlations
There have been a number of attempts to derive the set of quantum non-local
correlations from reasonable physical principles. Here we introduce
, a set of multipartite supra-quantum correlations that has appeared
under different names in fields as diverse as graph theory, quantum gravity and
quantum information science. We argue that may correspond to the
set of correlations of a reasonable physical theory, in which case the research
program to reconstruct quantum theory from device-independent principles is met
with strong obstacles. In support of this conjecture, we prove that
is closed under classical operations and satisfies the physical principles of
Non-Trivial Communication Complexity, No Advantage for Nonlocal Computation,
Macroscopic Locality and Local Orthogonality. We also review numerical evidence
that almost quantum correlations satisfy Information Causality.Comment: 15+2 pages, 1 figur
A bird's eye view of quantum computers
Quantum computers are discussed in the general framework of computation, the
laws of physics and the foundations of quantum mechanics.Comment: 6 pages, 1 figur
Energy Spectrum and Exact Cover in an Extended Quantum Ising Model
We investigate an extended version of the quantum Ising model which includes
beyond-nearest neighbour interactions and an additional site-dependent
longitudinal magnetic field. Treating the interaction exactly and using
perturbation theory in the longitudinal field, we calculate the energy spectrum
and find that the presence of beyond-nearest-neighbour interactions enhances
the minimal gap between the ground state and the first excited state,
irrespective of the nature of decay of these interactions along the chain. The
longitudinal field adds a correction to this gap that is independent of the
number of qubits. We discuss the application of our model to implementing
specific instances of 3-satisfiability problems (Exact Cover) and make a
connection to a chain of flux qubits.Comment: 9 pages, 3 figures, published versio
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