22,463 research outputs found
Quantum Computing with Continuous-Variable Clusters
Continuous-variable cluster states offer a potentially promising method of
implementing a quantum computer. This paper extends and further refines
theoretical foundations and protocols for experimental implementation. We give
a cluster-state implementation of the cubic phase gate through photon
detection, which, together with homodyne detection, facilitates universal
quantum computation. In addition, we characterize the offline squeezed
resources required to generate an arbitrary graph state through passive linear
optics. Most significantly, we prove that there are universal states for which
the offline squeezing per mode does not increase with the size of the cluster.
Simple representations of continuous-variable graph states are introduced to
analyze graph state transformations under measurement and the existence of
universal continuous-variable resource states.Comment: 17 pages, 5 figure
All degree six local unitary invariants of k qudits
We give explicit index-free formulae for all the degree six (and also degree
four and two) algebraically independent local unitary invariant polynomials for
finite dimensional k-partite pure and mixed quantum states. We carry out this
by the use of graph-technical methods, which provides illustrations for this
abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom
Quantum automata, braid group and link polynomials
The spin--network quantum simulator model, which essentially encodes the
(quantum deformed) SU(2) Racah--Wigner tensor algebra, is particularly suitable
to address problems arising in low dimensional topology and group theory. In
this combinatorial framework we implement families of finite--states and
discrete--time quantum automata capable of accepting the language generated by
the braid group, and whose transition amplitudes are colored Jones polynomials.
The automaton calculation of the polynomial of (the plat closure of) a link L
on 2N strands at any fixed root of unity is shown to be bounded from above by a
linear function of the number of crossings of the link, on the one hand, and
polynomially bounded in terms of the braid index 2N, on the other. The growth
rate of the time complexity function in terms of the integer k appearing in the
root of unity q can be estimated to be (polynomially) bounded by resorting to
the field theoretical background given by the Chern-Simons theory.Comment: Latex, 36 pages, 11 figure
Limitations of quantum computing with Gaussian cluster states
We discuss the potential and limitations of Gaussian cluster states for
measurement-based quantum computing. Using a framework of Gaussian projected
entangled pair states (GPEPS), we show that no matter what Gaussian local
measurements are performed on systems distributed on a general graph, transport
and processing of quantum information is not possible beyond a certain
influence region, except for exponentially suppressed corrections. We also
demonstrate that even under arbitrary non-Gaussian local measurements, slabs of
Gaussian cluster states of a finite width cannot carry logical quantum
information, even if sophisticated encodings of qubits in continuous-variable
(CV) systems are allowed for. This is proven by suitably contracting tensor
networks representing infinite-dimensional quantum systems. The result can be
seen as sharpening the requirements for quantum error correction and fault
tolerance for Gaussian cluster states, and points towards the necessity of
non-Gaussian resource states for measurement-based quantum computing. The
results can equally be viewed as referring to Gaussian quantum repeater
networks.Comment: 13 pages, 7 figures, details of main argument extende
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