2,869 research outputs found
New Examples of Kochen-Specker Type Configurations on Three Qubits
A new example of a saturated Kochen-Specker (KS) type configuration of 64
rays in 8-dimensional space (the Hilbert space of a triple of qubits) is
constructed. It is proven that this configuration has a tropical dimension 6
and that it contains a critical subconfiguration of 36 rays. A natural
multicolored generalisation of the Kochen-Specker theory is given based on a
concept of an entropy of a saturated configuration of rays.Comment: 24 page
Efficient Hamiltonian programming in qubit arrays with nearest-neighbour couplings
We consider the problem of selectively controlling couplings in a practical
quantum processor with always-on interactions that are diagonal in the
computational basis, using sequences of local NOT gates. This methodology is
well-known in NMR implementations, but previous approaches do not scale
efficiently for the general fully-connected Hamiltonian, where the complexity
of finding time-optimal solutions makes them only practical up to a few tens of
qubits. Given the rapid growth in the number of qubits in cutting-edge quantum
processors, it is of interest to investigate the applicability of this control
scheme to much larger scale systems with realistic restrictions on
connectivity. Here we present an efficient scheme to find near time-optimal
solutions that can be applied to engineered qubit arrays with local
connectivity for any number of qubits, indicating the potential for practical
quantum computing in such systems.Comment: 5 pages, 5 figures. Shortened and clarified from previous versio
Direct evaluation of pure graph state entanglement
We address the question of quantifying entanglement in pure graph states.
Evaluation of multipartite entanglement measures is extremely hard for most
pure quantum states. In this paper we demonstrate how solving one problem in
graph theory, namely the identification of maximum independent set, allows us
to evaluate three multipartite entanglement measures for pure graph states. We
construct the minimal linear decomposition into product states for a large
group of pure graph states, allowing us to evaluate the Schmidt measure.
Furthermore we show that computation of distance-like measures such as relative
entropy of entanglement and geometric measure becomes tractable for these
states by explicit construction of closest separable and closest product states
respectively. We show how these separable states can be described using
stabiliser formalism as well as PEPs-like construction. Finally we discuss the
way in which introducing noise to the system can optimally destroy
entanglement.Comment: 23 pages, 9 figure
Tube algebras, excitations statistics and compactification in gauge models of topological phases
We consider lattice Hamiltonian realizations of (+1)-dimensional
Dijkgraaf-Witten theory. In (2+1)d, it is well-known that the Hamiltonian
yields point-like excitations classified by irreducible representations of the
twisted quantum double. This can be confirmed using a tube algebra approach. In
this paper, we propose a generalization of this strategy that is valid in any
dimensions. We then apply the tube algebra approach to derive the algebraic
structure of loop-like excitations in (3+1)d, namely the twisted quantum
triple. The irreducible representations of the twisted quantum triple algebra
correspond to the simple loop-like excitations of the model. Similarly to its
(2+1)d counterpart, the twisted quantum triple comes equipped with a compatible
comultiplication map and an -matrix that encode the fusion and the braiding
statistics of the loop-like excitations, respectively. Moreover, we explain
using the language of loop-groupoids how a model defined on a manifold that is
-times compactified can be expressed in terms of another model in -lower
dimensions. This can in turn be used to recast higher-dimensional tube algebras
in terms of lower dimensional analogues.Comment: 71 page
Efficient Refocussing of One Spin and Two Spin Interactions for NMR Quantum Computation
The use of spin echoes to refocus one spin interactions (chemical shifts) and
two spin interactions (spin-spin couplings) plays a central role in both
conventional NMR experiments and NMR quantum computation. Here we describe
schemes for efficient refocussing of such interactions in both fully and
partially coupled spin systems.Comment: 4 pages, RevTeX, including 4 LaTeX figure
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