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arXiv:quant-ph/0211038 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum computations with optical waveguide modes

Jian Fu

Published Aug 5, 2003• 15 citations
arXivHTMLPDF

Abstract

A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed universal set of gates has the potential of being more compact and easily realized than other optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer configurations having semiconductor optical amplifiers with very high refractive nonlinearity in its arms.

DOI
10.1117/12.498150

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A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed universal set of gates has the potential of being more compact and easily realized than other optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer configurations having semiconductor optical amplifiers with very high refractive nonlinearity in its arms.
A fully optical method to perform quantum computation with transverse modes of the optical field propagating in waveguide is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed C-NOT gate has the potential of being more compact and easily realized than some optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer having semiconductor optical amplifiers with very large refractive nonlinearity in its arms.
A fully optical method to perform quantum computation with transverse modes of the optical field propagating in waveguide is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed C-NOT gate has the potential of being more compact and easily realized than some optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer having semiconductor optical amplifiers with very large refractive nonlinearitv in its arms.
Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, π/8\pi/8π/8 gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.
Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, π/8\pi/8π/8 gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.
Transverse modes of optical fields are proposed to be used as qubits for the implementation of quantum Hadamard gate. Mach-Zehnder Interferometer (MZI), phase shifter, y-junction beam splitters and other optical devices are utilized to realize a quantum Hadamard gate. The possibility of this encoding scheme was designed, simulated and verified through rigorous numerical analyses using the Beam propagation method. The proposed gate has the potential of being more compact and easily realizable than some other optical implementation proposals since it is based on planar light wave circuit technology and can be constructed very easily by using a Mach-Zehnder Interferometer. The Results proved that the design is able to perform the required Hadamard transformation and the conclusion was reached that the model was a successful implementation of a quantum Hadamard gate.