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arXiv:quant-ph/0502042 · Physical Review A

Demonstration of quantum error correction using linear optics

T. B. Pittman, B. C. Jacobs, J. D. Franson

Published May 31, 2005• 82 citations
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Abstract

We describe a laboratory demonstration of a quantum error correction procedure that can correct intrinsic measurement errors in linear-optics quantum gates. The procedure involves a two-qubit encoding and fast feed-forward-controlled single-qubit operations. In our demonstration the qubits were represented by the polarization states of two single-photons from a parametric down-conversion source, and the real-time feed-forward control was implemented using an electro-optic device triggered by the output of single-photon detectors.

DOI
10.1103/physreva.71.052332

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One of the main requirements in linear optics quantum computing is the ability to perform single-qubit operations that are controlled by classical information fed forward from the output of single-photon detectors. These operations correspond to predetermined combinations of phase corrections and bit flips that are applied to the postselected output modes of nondeterministic quantum logic devices. Corrections of this kind are required in order to obtain the correct logical output for certain detection events, and their use can increase the overall success probability of the devices. In this paper, we report on the experimental demonstration of the use of this type of feed-forward system to increase the probability of success of a simple nondeterministic quantum logic operation from approximately 14\frac{1}{4}41​ to 12.\frac{1}{2}.21​. This logic operation involves the use of one target qubit and one ancilla qubit which, in this experiment, are derived from a parametric down-conversion photon pair. Classical information describing the detection of the ancilla photon is fed forward in real time and used to alter the quantum state of the output photon. A fiber-optic delay line is used to store the output photon until a polarization-dependent phase shift can be applied using a high-speed Pockels cell.
Probabilistic quantum logic operations can be performed using linear optical elements and post-selection based on the results of measurements on ancilla photons. We review the results of a number of recent experiments in this area, including the demonstration of several quantum logic gates, the use of feed-forward control, a new source of single photons, and a quantum memory device for single photons. A high-fidelity approach in which the logic gates always produce an output will also be discussed.
Two qubit gates for photons are generally thought to require exotic materials with huge optical nonlinearities. We show here that, if we accept two qubit gates that only work conditionally, single photon sources, passive linear optics and particle detectors are sufficient for implementing reliable quantum algorithms. The conditional nature of the gates requires feed-forward from the detectors to the optical elements. Without feed forward, non-deterministic quantum computation is possible. We discuss one proposed single photon source based on the surface acoustic wave guiding of single electrons.