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arXiv:quant-ph/0204142 · Physical Review A

Demonstration of feed-forward control for linear optics quantum computation

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

Published Nov 14, 2002• 64 citations

Abstract

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 $\frac{1}{4}$ to $\frac{1}{2}.$ 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.

DOI: 10.1103/physreva.66.052305

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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

\frac{1}{4}

to

\frac{1}{2}.

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.

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.

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.

Summary form only given. Knill, Laflamme, and Milburn (2001) showed that probabilistic quantum logic devices could be implemented using only linear optical elements, additional ancilla photons, and post-selection based on the output of single-photon detectors. These devices produce the desired result with certainty when a specific output from the detectors is obtained, but that will only occur for some fraction of the events. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT gate and a quantum parity check. In each of these devices, two polarization-encoded qubits in the form of two single photons from a parametric down-conversion source are incident on a polarizing beam splitter.

We have successfully used fast electronic feed-forward to increase the probability of success of a linear optical implementation of a programmable phase gate from 25

%

to its theoretical limit of 50

%

. The feed-forward applies a conditional unitary operation, which changes the incorrect output states of the data qubit to the correct ones. The gate itself rotates an arbitrary quantum state of the data qubit around the

z

axis of the Bloch sphere with the angle of rotation being fully determined by the state of the program qubit. The gate implementation is based on fiber optics components. Qubits are encoded into spatial modes of single photons. The signal from the feed-forward detector is led directly to a phase modulator using only a passive voltage divider. We have verified the increase of the probability of success and characterized the gate operation by means of quantum process tomography. We have demonstrated that the use of feed-forward affects neither the process fidelity nor the output-state fidelities.

Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (nondestructive) CNOT that succeeds with a probability of 1/4.