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arXiv:1111.3237 · Physical Review A

Increasing efficiency of a linear-optical quantum gate using electronic feed-forward

Martina Miková, Helena Fikerová, Ivo Straka, Michal Mičuda, Jaromı́r Fiurášek, Miroslav Ježek, Miloslav Dušek

Published Jan 4, 2012• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.85.012305

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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 zzz 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.
Nonlinear optical quantum gates can be created probabilistically using only single-photon sources, linear optical elements, and photon-number-resolving detectors. These gates are heralded but operate with probabilities much less than 1. There is currently a large gap between the performance of the known circuits and the established upper bounds on their success probabilities. One possibility for increasing the probability of success of such gates is feed-forward, where one attempts to correct certain failure events that occurred in the gate's operation. In this Brief Report we examine the role of feed-forward in improving the success probability. In particular, for the nonlinear sign-shift gate, we find that in a three-mode implementation with a single round of feed-forward the optimal average probability of success is approximately given by psuccess=0.272{p}_{\mathrm{success}}=0.272psuccess​=0.272. This value is only slightly larger than the general optimal success probability without feed-forward, psuccess=0.25{p}_{\mathrm{success}}=0.25psuccess​=0.25.
We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good performance of the gate for all values of the encoded phase shift. We also show that by using a different set of program states the device can operate as a programmable partial polarization filter.
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.
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.
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.