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Conference on Lasers and Electro-Optics

Coherent-feedback formulation of continuous quantum error correction protocols

Joseph Kerckhoff, Hendra I. Nurdin, Dmitri S. Pavlichin, Hideo Mabuchi

Published Jan 1, 2010• 0 citations
Publisher

Abstract

We propose an approach to continuous-time quantum error correction based on the coherent feedback of optical probes that naturally utilizes photonic device physics to implement a stationary and ’on-chip’ protected quantum memory.
DOI
10.1364/cleo.2010.jthf5

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Quantum mechanical applications range from quantum computers to quantum key distribution to teleportation. In these applications, quantum error correction is extremely important for protecting quantum states against decoherence. Here I present two main results regarding quantum error correction protocols. The first main topic I address is the development of continuous-time quantum error correction protocols via combination with techniques from quantum control. These protocols rely on weak measurement and Hamiltonian feedback instead of the projective measurements and unitary gates usually assumed by canonical quantum error correction. I show that a subclass of these protocols can be understood as a quantum feedback protocol, and analytically analyze the general case using the stabilizer formalism; I show that in this case perfect feedback can perfectly protect a stabilizer subspace. I also show through numerical simulations that another subclass of these protocols does better than canonical quantum error correction when the time between corrections is limited. The second main topic is development of improved overhead results for fault-tolerant computation. In particular, through analysis of topological quantum error correcting codes, it will be shown that the required blowup in depth of a noisy circuit performing a fault-tolerant computation can be reduced to a factor of O(log log L), an improvement over previous results. Showing this requires investigation into a local method of performing fault-tolerant correction on a topological code of arbitrary dimension.
It was shown by Ahn, Wiseman, and Milburn [Phys. Rev. A 67, 052310 (2003)] that feedback control could be used as a quantum error correction process for errors induced by weak continuous measurement, given one perfectly measured error channel per qubit. Here we point out that this method can be easily extended to an arbitrary number of error channels per qubit. We show that the feedback protocols generated by our method encode $n\ensuremath{-}2$ logical qubits in nnn physical qubits, thus requiring just one more physical qubit than in the previous case.