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arXiv:quant-ph/0202160 · Physical Review Letters

High-Fidelity Quantum Logic Operations Using Linear Optical Elements

J. D. Franson, Michelle M. Donegan, Michael J. Fitch, B. C. Jacobs, T. B. Pittman

Published Sep 4, 2002• 132 citations
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Abstract

Knill, Laflamme, and Milburn [Nature (London) 409, 46 ((2001))]] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1/n, where n is the number of ancilla. Here we present an alternative approach in which the logic devices always produce an output with an intrinsic error rate that scales as 1/n(2), which may have several advantages in quantum computing applications.

DOI
10.1103/physrevlett.89.137901

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Knill, Laflamme, and Milburn [Nature (London) 409, 46 ((2001))]] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1/n, where n is the number of ancilla. Here we present an alternative approach in which the logic devices always produce an output with an intrinsic error rate that scales as 1/n(2), which may have several advantages in quantum computing applications.
Knill, Laflamme, and Milburn [1] have shown that probabilistic quantum logic operations can be implemented using linear optical elements, such as beam splitters and phase shifters, additional photons (ancilla) and post-selection based on the results of measurements on the ancilla. This may seem somewhat surprising, since logic operations are inherently nonlinear. Here the nonlinearity is produced by the quantum measurement process used in the post-selection. Nonlinearities of this kind are inherently quantum-mechanical and have no classical analogy.
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.
Ever since Knill, Laflamme and Milburn [Nature (London) 409, 46 (2001)] showed that nondeterministic quantum logic operations could be performed with linear optical elements, additional photons (ancilla) and projective measurements, the idea of linear-optics quantum computation has attracted considerable interest. Our group has recently demonstrated several devices of this kind. We give an overview of recent experimental results, including the quantum parity check, the destructive controlled-NOT, and a cyclical quantum memory. The need for high-efficiency detection of single photons, and for detectors capable of distinguishing photon number will be discussed. Some experimental improvements towards meeting that need will be presented.
Quantum logic operations can be performed using linear optical elements, additional photons (ancilla photons), and postselection based on measurements made on the ancilla. Here we describe a method for generating the required entangled state of nnn ancilla photons using elementary logic gates and postselection. This approach is capable of generating the ancilla states required for either the original proposal by Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001)] or those required for the more general high-fidelity approach [J. D. Franson, M. M. Donegan, M. J. Fitch, B. C. Jacobs, and T. B. Pittman, Phys. Rev. Lett. 89, 137901 (2002)]. We also show that the entangled ancilla photons could be generated using a series of quantum wells coupled with tunnel junctions.
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.
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.