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Electronics and Communications in Japan (Part III Fundamental Electronic Science)

A simple quantum computer: Experimental realization of quantum computation algorithms with linear optics

Shigeki Takeuchi

Published May 23, 2001• 5 citations

Abstract

Abstract In efforts toward the realization of quantum computers, there have been many proposals to implement controlled NOT gates between quantum bits (qubits). However, the number of quanta in the experimentally realized system has been at most two. Because it is difficult to cope with both the realization of the conditional interaction (e.g., huge nonlinear interaction) between the quanta, and the maintenance of quantum coherence for a sufficient time, the realization of quantum logic gates using several quanta may be difficult in the near future. In this paper, a new method which implements a quantum algorithm using linear optics and single photons is described. This method does not need any huge nonlinearity. Hence, it is practical with today's technology and will be one of the useful physical test beds for the quantum algorithms. The optical implementation of the Deutsch–Jozsa algorithm with a 4‐bit input is proposed, and the mechanism is explained. As one instance of the recent progress of our project, an experiment of single‐photon interference using parametric fluorescence with highly stabilized interferometer system is reported. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 52–60, 2001

DOI: 10.1002/ecjc.1049

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Abstract In efforts toward the realization of quantum computers, there have been many proposals to implement controlled NOT gates between quantum bits (qubits). However, the number of quanta in the experimentally realized system has been at most two. Because it is difficult to cope with both the realization of the conditional interaction (e.g., huge nonlinear interaction) between the quanta, and the maintenance of quantum coherence for a sufficient time, the realization of quantum logic gates using several quanta may be difficult in the near future. In this paper, a new method which implements a quantum algorithm using linear optics and single photons is described. This method does not need any huge nonlinearity. Hence, it is practical with today's technology and will be one of the useful physical test beds for the quantum algorithms. The optical implementation of the Deutsch–Jozsa algorithm with a 4‐bit input is proposed, and the mechanism is explained. As one instance of the recent progress of our project, an experiment of single‐photon interference using parametric fluorescence with highly stabilized interferometer system is reported. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 52–60, 2001

A quantum computation algorithm is demonstrated using single photons and linear optics. Quantum registers are realized by modes and polarization of photons, and the unitary transformations for them are implemented with linear optics. For each quantum computation, the answer to the Deutsch Jozsa problem for any 4 bit digit is given by a single-photon detection signal with a small error rate. The origin of the error is also studied and categorized according to the sources: systematic errors of quantum gates, phase relaxation, amplitude dumping, and misreadout. It is suspected that a demonstration of 11 qubits using linear optics anda single photon with less than a 20 % error rate is achievable by the technique used in the experiment. As a further objective, an idea to construct controlled-NOT gate using quantum phase gate (QPG) given by Chuang et. al., is introduced and experiments on the QPGs are also reviewed.

Summary form only given. Quantum computers are expected to increase the efficiency of solving problems such as factoring large integers. However an experimental implementation of even relatively simple quantum information processing with a few to a dozen qubits presents an enormous technological challenge. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing due to the ease with which photon interference can be observed. However these early proposals required huge single photon optical nonlinearities. Unfortunately currently available optical nonlinearities are too weak and too noisy to be useful. Recently however we have discovered that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photodetectors. Our methods exploit feed forward from photo-detectors and are robust against errors from photon loss and detector inefficiency. In this tutorial I will outline this scheme, highlighting the technical challenges required to implement it. The tutorial will be relatively self contained with a brief introduction to quantum optics and quantum computation.

One of the earliest proposals for implementing quantum computation was based on encoding each qubit in two optical modes, each containing exactly one photon. However, it is extremely difficult to unitarily couple two optical modes containing few photons. In 2001, Knill, Laflamme, and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation using only passive linear optics, photodetectors, and single photon sources. This efficient linear optical quantum computing (LOQC) is distinct from other linear optical schemes that are not efficiently scalable. The technological requirements for even the simplest gates in the KLM proposal initially seemed out of reach. However, Ralph, White, Munro and Milburn soon showed that, in principle, demonstrations of key gates and techniques could be achieved with current technology. The objective of the research undertaken in this project was to produce, in three years, a prototype two-qubit gate for photons using the KLM linear optics quantum computation approach, and to develop a blue-print for a multiple qubit device that might be implemented over a longer time scale. A non-deterministic two-qubit gate was demonstrated that operates with high fidelity. A number of key tasks were demonstrated using this gate, and several theoretical investigations of short, medium, and longer term issues for the LOQC approach were successfully completed.

One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally very difficult. We therefore employ linear optics with projective measurements to generate these non-linearities. The downside is that the measurement-induced nonlinearities achieved with linear optics are less versatile and the success rate can be quite low. This project is mainly the result of a literature study but also a theoretical work on the physics behind quantum optical multiports which is essential for realizing two-photon gates. By applying different postcorrection techniques we increase the probability of success in a modifed non-linear sign shift gate which is foundational for the two photon controlled-NOT gate. We prove that it's not possible to correct the states by only using a single beam splitter. We show that it might be possible to increase the probability of success using a more complex setup with at least two error-correcting beam splitters.

Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear interaction between the two photons, and the efficiency of this nonlinear interaction is typically very tiny in bulk materials. However, we recently have shown that this barrier can be circumvented with effective nonlinearities produced by projective measurements, and with this work linear-optical quantum computing becomes a new possibility of scalable quantum computation. We review several issues concerning its principles and requirements.