Combined Error Correction Techniques for Quantum Computing Architectures

Abstract

Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This uses a decoherence-free subspace and an efficient set of dynamical decoupling operations. It also addresses the problems of controllability in solid state quantum dot devices.

Contribution to Proceedings of the 2002 Physics of Quantum Electronics Conference", to be published in J. Mod. Optics. This paper provides a summary and review of quant-ph/0205156 and quant-ph/0112054, and some new results

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• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Universal Leakage Elimination
• Distance Bounds on Quantum Dynamics
• Overview of Quantum Error Prevention and Leakage Elimination
• Soft-Pulse Dynamical Decoupling with Markovian Decoherence
• Quantum Error Correction in the Zeno Regime
• Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems
• Entanglement-Preserving Limit Cycles from Sequential Quantum Measurements and Feedback
• Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling
• A Unified Picture of Decoherence Control
• Layer-Wise Security Framework and Analysis for the Quantum Internet
• Decoherence Rates in Large Scale Quantum Computers and Macroscopic Systems
• Quantum Computers and Decoherence: Exorcising the Demon from the Machine