Southwest Quantum Information and Technology

Tenth Annual Meeting, February 14-17, 2008
University of New Mexico, Santa Fe, New Mexico

Full Program | Thursday Tutorials | Friday | Saturday | Sunday

SESSION 9: Quantum Error Correction
Session Chair: Dave Bacon
15:45-16:15	Mark Wilde, University of Southern California
	Quantum Convolutional Coding with Entanglement Assistance
	Abstract. We have recently developed quantum convolutional coding techniques for both entanglement distillation and quantum error correction. These techniques assume that the two parties participating in the communication protocols possess prior shared entanglement. Using these methods, we can import arbitrary classical binary or quaternary convolutional codes for use in quantum coding, with no requirement that these codes be self-orthogonal. Moreover, high-performance classical convolutional codes lead to high-performance quantum convolutional codes. We explicitly show how a convolutional entanglement distillation protocol operates, and how to encode and decode a stream of quantum information in an entanglement-assisted quantum convolutional code.
16:15-16:45	Ognyan Oreshkov, University of Southern California
	Fault-tolerant holonomic computation on quantum error-correcting codes
	Abstract. Holonomic quantum computation is a method of computation that uses non-abelian generalizations of the Berry phase. Due to its geometric nature, this approach is robust against various types of errors in the control parameters driving the evolution. In this study, we propose a scheme for fault-tolerant holonomic computation on stabilizer codes, which combines the virtues of error correction with those of the geometric approach. The scheme implements single-qubit operations on different qubits in the code by adiabatically varying Hamiltonians that are elements of the stabilizer, or in the case of subsystem codes---operators that act on the noisy subsystem. Two-qubit operations between qubits from different blocks require Hamiltonians whose weights are higher by one. Thus for certain codes, like the 9-qubit Shor code or its subsystem versions, it is possible to realize universal fault-tolerant computation using Hamiltonians of weight two and three, which is the optimal Hamiltonian weight for holonomic computation on a system of qubits. We also study the regime in which the adiabaticity condition becomes compatible with the fault-tolerance condition for fast gates on the time scale of the noise. Both conditions can be satisfied for a sufficiently large Hamiltonian strength, or equivalently, for a sufficiently low noise rate. This requires only a constant overhead of resources compared to those needed for fault-tolerant dynamical computation.
16:45-17:15	Matthew Elliott, University of New Mexico
	A graphical description of stabilizer states
	Abstract. Stabilizer states are ubiquitous elements of quantum information theory, as a consequence of both their power and of their relative simplicity. The purpose of this talk is to augment the stabilizer formalism by introducing a graphical representation of stabilizer states. We furthermore demonstrate how Clifford operations, Pauli measurements, and stabilizer codes can be interpreted graphically using this approach.