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Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays

Wocjan, Pawel (2006) Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays. Physical Review A, 73 (6). Art. No. 062317. ISSN 1050-2947. doi:10.1103/PhysRevA.73.062317.

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The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to effect sequences of instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To overcome the shortcomings of bang-bang control, Viola and Knill proposed a method called "Eulerian decoupling" that allows the use of bounded-strength controls for decoupling. However, their method was not directly designed to take advantage of the local structure of internal couplings and couplings to an environment that typically occur in multipartite quantum systems. In this paper we define a combinatorial structure called Eulerian orthogonal array. It merges the desirable properties of orthogonal arrays and Eulerian cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show that this structure gives rise to decoupling schemes with bounded-strength control Hamiltonians that can be used to remove both internal couplings and couplings to an environment of a multipartite quantum system. Furthermore, we show how to construct Eulerian orthogonal arrays having good parameters in order to obtain efficient decoupling schemes.

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Additional Information:©2006 The American Physical Society (Received 6 March 2006; published 13 June 2006) The author would like to thank Anja Groch and Markus Grassl for helpful discussions. This work has been supported by the National Science Foundation under Grant No. EIA-0086038 through the Institute for Quantum Information at the California Institute of Technology and the BMBF Project No. 01/BB01B.
Subject Keywords:quantum theory; Hadamard matrices; graph theory; information theory
Issue or Number:6
Record Number:CaltechAUTHORS:WOCpra06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5218
Deposited By: Archive Administrator
Deposited On:05 Oct 2006
Last Modified:08 Nov 2021 20:23

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