Southwest Quantum Information and Technology

Thirteenth Annual Meeting, February 17-20, 2011
Boulder, Colorado

Full Program | Thursday | Friday | Saturday | Sunday | All Sessions

SESSION 10b: Breakout B -- Quantum Error Correction and Algorithms
Session Chair:
4:00pm-4:30pm	Mark Byrd, Southern Illinois University
	Pseudo-unitary freedom in the operator-sum representation, positive maps, and quantum error correction
	Abstract. A dynamical map is a map which takes one density operator to another. Such a map can be written in an operator-sum representation (OSR) using a spectral decomposition. The method of the construction applies to more general maps which need not be completely positive. The OSR is not unique; there is a freedom to choose a different set of operators in the OSR, yet still obtain the same map. Here we show that, whereas the freedom for completely positive maps is unitary, the freedom for maps which are not necessarily completely positive is pseudo-unitary. Those that are genuinely different must therefore differ by the number and type of spectral decomposition. Moreover, our theorem enables us to prove a necessary and sufficient condition for error correcting codes which can correct errors due to maps which are not completely positive.
4:30pm-5:00pm	Jim Harrington, HRL Laboratories
	Addressable multi-qubit logic via permutations
	Abstract. An important issue when encoding multiple logical qubits into a single code block is identifying how to separately address the different logical qubits. Previous schemes have generally required unpacking of the logical qubits into empty code blocks before computing on them, thus giving up much of the space advantage of these codes. We solve the addressability problem by instead taking advantage of the permutation automorphism structure of the 15-qubit Hamming code, and we present schemes for implementing targeted logical gates with a space efficiency of one-third or two-fifths. This is joint work with Ben Reichardt. Sponsored by United States Department of Defense.
5:00pm-5:30pm	Ching-Yi Lai, University of Southern California
	Entanglement-Assisted Quantum Error-Correcting Codes when the Ebits of Receiver are not Perfect
	Abstract. The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability of quantum codes. We provide two different schemes to cope with this problem. We first show that any (nondegenerate) standard stabilizer codes can be transformed into EAQEC codes that can correct both errors on the qubits of sender and receiver. These EAQEC codes are equivalent to standard stabilizer codes, and hence the decoding techniques of standard stabilizer codes can be applied. Several EAQEC codes of this type are found to be optimal. In the second scheme, the receiver uses a standard stabilizer code to protect the ebits. The decoding procedure has two stages: decode the ebits of the receiver and then decode the information protected by the EAQEC code. To achieve high channel capacity, the second scheme is preferable, with a good EAQEC code that is not equivalent to any standard stabilizer code, at the cost of more resources at the receiver. Several optimal EAQEC codes not equivalent to any standard stabilizer code are found by the encoding optimization algorithm.
5:30pm-6:00pm	Asif Shakeel, University of California at San Diego
	An Improved Query for the Hidden Subgroup Problem
	Abstract. An equal superposition query with \|0> in the response register is used in the "standard method" of single-query algorithms for the Hidden Subgroup Problem (HSP). Here we introduce a different query, the character query, a generalization of the well-known phase kickback trick. This query maximizes the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We then apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.