31,216 research outputs found
Quantum Computing with Globally Controlled Exchange-type Interactions
If the interaction between qubits in a quantum computer has a non-diagonal
form (e.g. the Heisenberg interaction), then one must be able to "switch it
off" in order to prevent uncontrolled propagation of states. Therefore, such QC
schemes typically demand local control of the interaction strength between each
pair of neighboring qubits. Here we demonstrate that this degree of control is
not necessary: it suffices to switch the interaction collectively - something
that can in principle be achieved by global fields rather than with local
manipulations. This observation may offer a significant simplification for
various solid state, optical lattice and NMR implementations.Comment: 3 pages inc. 3 figure
Quantum Computing in Arrays Coupled by 'Always On' Interactions
It has recently been shown that one can perform quantum computation in a
Heisenberg chain in which the interactions are 'always on', provided that one
can abruptly tune the Zeeman energies of the individual (pseudo-)spins. Here we
provide a more complete analysis of this scheme, including several
generalizations. We generalize the interaction to an anisotropic form
(incorporating the XY, or Forster, interaction as a limit), providing a proof
that a chain coupled in this fashion tends to an effective Ising chain in the
limit of far off-resonant spins. We derive the primitive two-qubit gate that
results from exploiting abrupt Zeeman tuning with such an interaction. We also
demonstrate, via numerical simulation, that the same basic scheme functions in
the case of smoothly shifted Zeeman energies. We conclude with some remarks
regarding generalisations to two- and three-dimensional arrays.Comment: 16 pages (preprint format) inc. 3 figure
High threshold distributed quantum computing with three-qubit nodes
In the distributed quantum computing paradigm, well-controlled few-qubit
`nodes' are networked together by connections which are relatively noisy and
failure prone. A practical scheme must offer high tolerance to errors while
requiring only simple (i.e. few-qubit) nodes. Here we show that relatively
modest, three-qubit nodes can support advanced purification techniques and so
offer robust scalability: the infidelity in the entanglement channel may be
permitted to approach 10% if the infidelity in local operations is of order
0.1%. Our tolerance of network noise is therefore a order of magnitude beyond
prior schemes, and our architecture remains robust even in the presence of
considerable decoherence rates (memory errors). We compare the performance with
that of schemes involving nodes of lower and higher complexity. Ion traps, and
NV- centres in diamond, are two highly relevant emerging technologies.Comment: 5 figures, 12 pages in single column format. Revision has more
detailed comparison with prior scheme
Multi-Qubit Gates in Arrays Coupled by 'Always On' Interactions
Recently there has been interest in the idea of quantum computing without
control of the physical interactions between component qubits. This is highly
appealing since the 'switching' of such interactions is a principal difficulty
in creating real devices. It has been established that one can employ 'always
on' interactions in a one-dimensional Heisenberg chain, provided that one can
tune the Zeeman energies of the individual (pseudo-)spins. It is important to
generalize this scheme to higher dimensional networks, since a real device
would probably be of that kind. Such generalisations have been proposed, but
only at the severe cost that the efficiency of qubit storage must *fall*. Here
we propose the use of multi-qubit gates within such higher-dimensional arrays,
finding a novel three-qubit gate that can in fact increase the efficiency
beyond the linear model. Thus we are able to propose higher dimensional
networks that can constitute a better embodiment of the 'always on' concept - a
substantial step toward bringing this novel concept to full fruition.Comment: 20 pages in preprint format, inc. 3 figures. This version has fixed
typos and printer-friendly figures, and is to appear in NJ
Entangling spins by measuring charge: a parity-gate toolbox
The parity gate emerged recently as a promising resource for performing
universal quantum computation with fermions using only linear interactions.
Here we analyse the parity gate (P-gate) from a theoretical point of view in
the context of quantum networks. We present several schemes for entanglement
generation with P-gates and show that native networks simplify considerably the
resources required for producing multi-qubit entanglement, like n-GHZ states.
Other applications include a Bell-state analyser and teleportation. We also
show that cluster state fusion can be performed deterministically with parity
measurements. We then extend this analysis to hybrid quantum networks
containing spin and mode qubits. Starting from an easy-to-prepare resource
(spin-mode entanglement of single electrons) we show how to produce a spin
n-GHZ state with linear elements (beam-splitters and local spin-flips) and
charge-parity detectors; this state can be used as a resource in a spin quantum
computer or as a precursor for constructing cluster states. Finally, we
construct a novel spin CZ-gate by using the mode degrees of freedom as
ancillae.Comment: updated to the published versio
Leray's fundamental work on the Navier-Stokes equations: a modern review of "Sur le mouvement d'un liquide visqueux emplissant l'espace"
This article offers a modern perspective which exposes the many contributions
of Leray in his celebrated work on the Navier--Stokes equations from 1934.
Although the importance of his work is widely acknowledged, the precise
contents of his paper are perhaps less well known. The purpose of this article
is to fill this gap. We follow Leray's results in detail: we prove local
existence of strong solutions starting from divergence-free initial data that
is either smooth, or belongs to , (with ),
as well as lower bounds on the norms ,
() as approaches a putative blow-up time. We show global
existence of a weak solution and weak-strong uniqueness. We present Leray's
characterisation of the set of singular times for the weak solution, from which
we deduce that its upper box-counting dimension is at most .
Throughout the text we provide additional details and clarifications for the
modern reader and we expand on all ideas left implicit in the original work,
some of which we have not found in the literature. We use some modern
mathematical tools to bypass some technical details in Leray's work, and thus
expose the elegance of his approach.Comment: 81 pages. All comments are welcom
Using a Goal-Driven Approach in the Investigation of a Questioned Contract
Part 3: FORENSIC TECHNIQUESInternational audienceThis paper presents a systematic process for describing digital forensic investigations. It focuses on forensic goals and anti-forensic obstacles and their operationalization in terms of human and software actions. The paper also demonstrates how the process can be used to capture the various forensic and anti-forensic aspects of a real-world case involving document forgery
Optical Quantum Computation with Perpetually Coupled Spins
The possibility of using strongly and continuously interacting spins for
quantum computation has recently been discussed. Here we present a simple
optical scheme that achieves this goal while avoiding the drawbacks of earlier
proposals. We employ a third state, accessed by a classical laser field, to
create an effective barrier to information transfer. The mechanism proves to be
highly efficient both for continuous and pulsed laser modes; moreover it is
very robust, tolerating high decay rates for the excited states. The approach
is applicable to a broad range of systems, in particular dense structures such
as solid state self-assembled (e.g., molecular) devices. Importantly, there are
existing structures upon which `first step' experiments could be immediately
performed.Comment: 5 pages including 3 figures. Updated to published versio
Efficient growth of complex graph states via imperfect path erasure
Given a suitably large and well connected (complex) graph state, any quantum
algorithm can be implemented purely through local measurements on the
individual qubits. Measurements can also be used to create the graph state:
Path erasure techniques allow one to entangle multiple qubits by determining
only global properties of the qubits. Here, this powerful approach is extended
by demonstrating that even imperfect path erasure can produce the required
graph states with high efficiency. By characterizing the degree of error in
each path erasure attempt, one can subsume the resulting imperfect entanglement
into an extended graph state formalism. The subsequent growth of the improper
graph state can be guided, through a series of strategic decisions, in such a
way as to bound the growth of the error and eventually yield a high-fidelity
graph state. As an implementation of these techniques, we develop an analytic
model for atom (or atom-like) qubits in mismatched cavities, under the
double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71,
060310 (2005)]. Compared to straightforward postselection techniques our
protocol offers a dramatic improvement in growing complex high-fidelity graph
states.Comment: 15 pages, 10 figures (which print to better quality than when viewed
as an on screen pdf
Schemes for Parallel Quantum Computation Without Local Control of Qubits
Typical quantum computing schemes require transformations (gates) to be
targeted at specific elements (qubits). In many physical systems, direct
targeting is difficult to achieve; an alternative is to encode local gates into
globally applied transformations. Here we demonstrate the minimum physical
requirements for such an approach: a one-dimensional array composed of two
alternating 'types' of two-state system. Each system need be sensitive only to
the net state of its nearest neighbors, i.e. the number in state 1 minus the
number in state 2. Additionally, we show that all such arrays can perform quite
general parallel operations. A broad range of physical systems and interactions
are suitable: we highlight two potential implementations.Comment: 12 pages + 3 figures. Several small corrections mad
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