Contact:
Marcus Greferath
School of Math. Sciences
University College Dublin
Belfield, Dublin 4, Ireland
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Joachim Rosenthal
Institut of Mathematics
University of Zurich
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Phone:
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ITW 2010 Dublin
IEEE Information Theory Workshop
Dublin, August 30 - September 3, 2010

Quantum information processing

Thu 02 Sep, 14.45-17.35, Room 1

Invited session
Organizer: Jean-Pierre Tillich

Graeme Smith Quantum Channel Capacities

Abstract: A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each of these settings there is a capacity that quantifies a channel's potential for communication. In this short review, I summarize what is known about the various capacities of a quantum channel, including a discussion of the relevant additivity questions. I also give some indication of potentially interesting directions for future research. Thu 02 Sep, 14.45-15.10, Room 1

Sergey Bravyi Stabilizer subsystem codes with spatially local generators

Abstract: We derive new tradeoffs for reliable quantum information storage in a 2D local architecture based on subsystem quantum codes. Our results apply to stabilizer subsystem codes, that is, stabilizer codes in which part of the logical qubits does not encode any information. A stabilizer subsystem code can be specified by its gauge group -- a subgroup of the Pauli group that includes the stabilizers and the logical operators on the unused logical qubits. We assume that the physical qubits are arranged on a two-dimensional grid and the gauge group has spatially local generators such that each generator acts only on a few qubits located close to each other. Our main result is an upper bound kd = O(n), where k is the number of encoded qubits, d is the minimal distance, and n is the number of physical qubits. In the special case when both gauge group and the stabilizer group have spatially local generators, we derive a stronger bound kd2 = O(n) which is tight up to a constant factor. Thu 02 Sep, 15.10-15.35, Room 1

Nicolas Delfosse and Gilles Zémor Quantum erasure-correcting codes and percolation on regular tilings of the hyperbolic plane

Abstract: We are interested in percolation for a family of self-dual tilings of the hyperbolic plane. We achieve an upper bound on the critical probability for these tilings by taking appropriate finite quotients and associating them with a family of quantum CSS codes. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel. Thu 02 Sep, 15.35-16.00, Room 1

Markus Grassl and Martin Rötteler On Encoders for Quantum Convolutional Codes

Abstract: We consider the problem of computing an encoding circuit for a quantum convolutional code given by a polynomial stabilizer matrix S(D) = (X(D) | Z(D)). We present an algorithm that is very similar to a polynomial-time algorithm for computing the Smith form of a polynomial matrix. This is a step towards the conjecture that any quantum convolutional code has an encoder with polynomially bounded depth. Thu 02 Sep, 16.20-16.45, Room 1

Guillaume Duclos-Cianci and David Poulin A renormalization group decoding algorithm for topological quantum codes

Abstract: Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we present a decoding algorithm for topological codes that is faster than previously known algorithms and applies to a wider class of topological codes. Our algorithm makes use of two methods inspired from statistical physics: renormalization groups and mean-field approximations. First, the topological code is approximated by a concatenated block code that can be efficiently decoded. To improve this approximation, additional consistency conditions are imposed between the blocks, and are solved by a belief propagation algorithm. Thu 02 Sep, 16.45-17.10, Room 1

Pradeep Sarvepalli Topological Color Codes over Higher Alphabet

Abstract: Color codes are a class of topological codes that have come into prominence in the recent years. Like the surface codes the codespace defined by them can be associated to the degenerate ground state of a local Hamiltonian. In addition they can be designed to have an extended set of transversal encoded gates (compared to surface codes) increasing their appeal for fault tolerant quantum computation. In this paper we generalize the color codes to arbitrary prime power alphabet. We show that in the 2D case there exist color codes for which the nonbinary Clifford group can be implemented transversally. Thu 02 Sep, 17.10-17.35, Room 1

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