We consider the problem of switching off unwanted interactions in a given
multi-partite Hamiltonian. This is known to be an important primitive in
quantum information processing and several schemes have been presented in the
literature to achieve this task. A method to construct decoupling schemes for
quantum systems of pairwise interacting qubits was introduced by M.
Stollsteimer and G. Mahler and is based on orthogonal arrays. Another approach
based on triples of Hadamard matrices that are closed under pointwise
multiplication was proposed by D. Leung. In this paper, we show that both
methods lead to the same class of decoupling schemes. Moreover, we establish a
characterization of orthogonal arrays by showing that they are equivalent to
decoupling schemes which allow a refinement into equidistant time-slots.
Furthermore, we show that decoupling schemes for networks of higher-dimensional
quantum systems with t-local Hamiltonians can be constructed from classical
error-correcting codes.Comment: 26 pages, latex, 1 figure in tex

Roetteler, Martin

Wocjan, Pawel

English

arXiv

Decoupling schemes are used in quantum information processing to selectively switch off unwanted interactions in a multipartite Hamiltonian. A decoupling scheme consists of a sequence of local unitary operations which are applied to the system's qudits and alternate with the natural time evolution of the Hamiltonian. Several constructions of decoupling schemes have been given in the literature. Here we focus on two such schemes. The first is based on certain triples of submatrices of Hadamard matrices that are closed under pointwise multiplication (see Leung, “Simulation and reversal of n-qubit Hamiltonians using Hadamard matrices,” J. Mod. Opt., vol. 49, pp. 1199–1217, 2002), the second uses orthogonal arrays (see Stollsteimer and Mahler, “Suppression of arbitrary internal couplings in a quantum register,” Phys. Rev. A., vol. 64, p. 052301, 2001). We show that both methods lead to the same class of decoupling schemes. We extend the first method to 2-local qudit Hamiltonians, where d ≥ 2. Furthermore, we extend the second method to t-local qudit Hamiltonians, where t ≥ 2 and d ≥ 2, by using orthogonal arrays of strength t. We also establish a characterization of orthogonal arrays of strength t by showing that they are equivalent to decoupling schemes for t-local Hamiltonians which have the property that they can be refined to have time-slots of equal length. The methods used to derive efficient decoupling schemes are based on classical error-correcting codes

Rötteler, Martin

Caltech Authors - Main

Equivalence of Decoupling Schemes and Orthogonal Arrays

M. Rotteler

P. Wocjan

Crossref

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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.4592

Equivalence of Decoupling Schemes and Orthogonal Arrays

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