45,819 research outputs found
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
We consider quantum computations comprising only commuting gates, known as
IQP computations, and provide compelling evidence that the task of sampling
their output probability distributions is unlikely to be achievable by any
efficient classical means. More specifically we introduce the class post-IQP of
languages decided with bounded error by uniform families of IQP circuits with
post-selection, and prove first that post-IQP equals the classical class PP.
Using this result we show that if the output distributions of uniform IQP
circuit families could be classically efficiently sampled, even up to 41%
multiplicative error in the probabilities, then the infinite tower of classical
complexity classes known as the polynomial hierarchy, would collapse to its
third level. We mention some further results on the classical simulation
properties of IQP circuit families, in particular showing that if the output
distribution results from measurements on only O(log n) lines then it may in
fact be classically efficiently sampled.Comment: 13 page
Global Quantum Discord in Multipartite Systems
We propose a global measure for quantum correlations in multipartite systems,
which is obtained by suitably recasting the quantum discord in terms of
relative entropy and local von Neumann measurements. The measure is symmetric
with respect to subsystem exchange and is shown to be non-negative for an
arbitrary state. As an illustration, we consider tripartite correlations in the
Werner-GHZ state and multipartite correlations at quantum criticality. In
particular, in contrast with the pairwise quantum discord, we show that the
global quantum discord is able to characterize the infinite-order quantum phase
transition in the Ashkin-Teller spin chain.Comment: v3: 7 pages, 6 figures. Published versio
Transition from Icosahedral to Decahedral Structure in a Coexisting Solid-Liquid Nickel Cluster
We have used molecular dynamics simulations to construct a microcanonical
caloric curve for a 1415-atom Ni icosahedron. Prior to melting the Ni cluster
exhibits static solid-liquid phase coexistence. Initially a partial icosahedral
structure coexists with a non-wetting melt. However at energies very close to
the melting point the icosahedral structure is replaced by a truncated
decahedral structure which is almost fully wet by the melt. This structure
remains until the cluster fully melts. The transition appears to be driven by a
preference for the melt to wet the decahedral structure.Comment: 7 pages, 6 figure
Quantum computation via translation-invariant operations on a chain of qubits
A scheme of universal quantum computation on a chain of qubits is described
that does not require local control. All the required operations, an Ising-type
interaction and spatially uniform simultaneous one-qubit gates, are
translation-invariant.Comment: Comment after Eq. (2) inserted, journal versio
Why Nature has made a choice of one time and three space coordinates?
We propose a possible answer to one of the most exciting open questions in
physics and cosmology, that is the question why we seem to experience four-
dimensional space-time with three ordinary and one time dimensions. We have
known for more than 70 years that (elementary) particles have spin degrees of
freedom, we also know that besides spin they also have charge degrees of
freedom, both degrees of freedom in addition to the position and momentum
degrees of freedom. We may call these ''internal degrees of freedom '' the
''internal space'' and we can think of all the different particles, like quarks
and leptons, as being different internal states of the same particle. The
question then naturally arises: Is the choice of the Minkowski metric and the
four-dimensional space-time influenced by the ''internal space''?
Making assumptions (such as particles being in first approximation massless)
about the equations of motion, we argue for restrictions on the number of space
and time dimensions. (Actually the Standard model predicts and experiments
confirm that elementary particles are massless until interactions switch on
masses.)
Accepting our explanation of the space-time signature and the number of
dimensions would be a point supporting (further) the importance of the
''internal space''.Comment: 13 pages, LaTe
Information erasure without an energy cost
Landauer argued that the process of erasing the information stored in a
memory device incurs an energy cost in the form of a minimum amount of
mechanical work. We find, however, that this energy cost can be reduced to zero
by paying a cost in angular momentum or any other conserved quantity. Erasing
the memory of Maxwell's demon in this way implies that work can be extracted
from a single thermal reservoir at a cost of angular momentum and an increase
in total entropy. The implications of this for the second law of thermodynamics
are assessed.Comment: 8 pages with 1 figure. Final published versio
Entanglement versus mixedness for coupled qubits under a phase damping channel
Quantification of entanglement against mixing is given for a system of
coupled qubits under a phase damping channel. A family of pure initial joint
states is defined, ranging from pure separable states to maximally entangled
state. An ordering of entanglement measures is given for well defined initial
state amount of entanglement.Comment: 9 pages, 2 figures. Replaced with final published versio
Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates
We investigate the disorder-induced localization transition in Bose-Einstein
condensates for the Anderson and Aubry-Andre models in the non-interacting
limit using exact diagonalization. We show that, in addition to the standard
superfluid fraction, other tools such as the entanglement and fidelity can
provide clear signatures of the transition. Interestingly, the fidelity
exhibits good sensitivity even for small lattices. Effects of the system size
on these quantities are analyzed in detail, including the determination of a
finite-size-scaling law for the critical disorder strength in the case of the
Anderson model.Comment: 15 pages, 7 figure
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