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arXiv:quant-ph/0504215 · Quantum Information and Computation

Universal quantum computation with shutter logic

Juan Carlos García-Escartín, Pedro Chamorro‐Posada

Published Sep 1, 2006• 0 citations
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Abstract

We show that universal quantum logic can be achieved using only linear optics and a quantum shutter device. With these elements, we design a quantum memory for any number of qubits and a CNOT gate which are the basis of a universal quantum computer. An interaction-free model for a quantum shutter is given.
DOI
10.26421/qic6.6-3

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In order for quantum communications systems to become widely used, it will probably be necessary to develop quantum repeaters that can extend the range of quantum key distribution systems and correct for errors in the transmission of quantum information. Quantum logic gates based on linear optical techniques appear to be a promising approach for the development of quantum repeaters, and they may have applications in quantum computing as well. Here we describe the basic principles of logic gates based on linear optics, along with the results from several experimental demonstrations of devices of this kind. A prototype source of single photons and a quantum memory device for photons are also discussed. These devices can be combined with a four-qubit encoding to implement a quantum repeater.
In order for quantum communications systems to become widely used, it will probably be necessary to develop quantum repeaters that can extend the range of quantum key distribution systems and correct for errors in the transmission of quantum information. Quantum logic gates based on linear optical techniques appear to be a promising approach for the development of quantum repeaters, and they may have applications in quantum computing as well. Here we describe the basic principles of logic gates based on linear optics, along with the results from several experimental demonstrations of devices of this kind. A prototype source of single photons and a quantum memory device for photons are also discussed. These devices can be combined with a four-qubit encoding to implement a quantum repeater. 2 I.
The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.
The first section of the work investigates light modes as a means of implementing optical qubits and qudits. The modes considered are polarization mode, path mode, transverse spatial mode, frequency mode, temporal bin-mode and temporal mode. Subsequently, mathematical model of linear optical elements like beam splitters (BS) and phase shifters are deduced and their capability of representing any single qubit optical gate is exposed. Finally Knill, Laflamme and Milburn (KLM) method of using linear optical elements to promote nonlinear operations based on nonlinear (nondeterministic) sign-flip gate (NS) is explained, and designs of two qubits conditional sign flip gate (c-z1/16) and CNOT gate, both based on KLM method, are demonstrated. So, universal set of quantum gates based on linear optics is possible.
The design for an all optical XOR gate is proposed. The basic idea is to split the input beams and let them cancel or strengthen each other selectively or flip the encoded information based on their polarization properties. The information is encoded in terms of polarization of the beam. Polarization of a light beam is well understood hence the design should be feasible to implement. The truth table of the optical circuit is worked out and compared with the expected truth table. Then it is demonstrated that the design complies with the linear behavior of the XOR function. In the next section, based on a similar idea, the design of an all optical CNOT gate is proposed. The truth table for the gate is verified. Then, it is discussed how this approach can be used for Linear Optics Quantum Computation (LOQC). It is shown that with a Hadamard gate and a rotation gate, the CNOT gate makes up a universal set of quantum gates based on linear optics. This novel approach requires no additional power supply, extra input beam or ancilla photon to operate. It also doesn't require the expensive and complex single photon source and detector. Only narrowband laser sources are required to operate these gates.