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arXiv:quant-ph/0108001

Franson-type experiment realizes two-qubit quantum logic gate

Kaoru Sanaka, Karin Kawahara, Takahiro Kuga

Published Aug 1, 2001• 1 citation
arXivHTMLPDF

Abstract

Quantum computers promise great improvements in solving problems such as factoring large integers, simulating quantum systems, and database searching. Using a photon as a quantum bit (qubit) is one of the most promising ways to realize a universal quantum computer because the coherent superposition state of a photon is very robust against various sources of decoherence. However, it is too difficult to realize two-qubit (photon) gates because it requires huge nonlinearity between photons. Here we show the realization of a controlled-NOT (CNOT) gate, the most important and elemental two-qubit gate for quantum computation, by extending our previous research. The heart of our experiment is the conditional measurement of two-photon coincidences in the Franson-type experiment[7]. The photon counting measurement plays the same role as the nonlinearity required for the two-qubit gate, and our system reproduces the truth table of the CNOT gate. Furthermore, we create an entangled state from the superposition state by our gate, which is clear evidence that our gate works as a quantum logic gate. Our results make it possible to manipulate the quantum state of photons including entanglement and represent significant progress in the operation of various algorithms in quantum computation.

DOI
10.48550/arxiv.quant-ph/0108001

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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

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Quantum computers promise great improvements in solving problems such as factoring large integers, simulating quantum systems, and database searching. Using a photon as a quantum bit (qubit) is one of the most promising ways to realize a universal quantum computer because the coherent superposition state of a photon is very robust against various sources of decoherence. However, it is too difficult to realize two-qubit (photon) gates because it requires huge nonlinearity between photons. Here we show the realization of a controlled-NOT (CNOT) gate, the most important and elemental two-qubit gate for quantum computation, by extending our previous research. The heart of our experiment is the conditional measurement of two-photon coincidences in the Franson-type experiment[7]. The photon counting measurement plays the same role as the nonlinearity required for the two-qubit gate, and our system reproduces the truth table of the CNOT gate. Furthermore, we create an entangled state from the superposition state by our gate, which is clear evidence that our gate works as a quantum logic gate. Our results make it possible to manipulate the quantum state of photons including entanglement and represent significant progress in the operation of various algorithms in quantum computation.
Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum information processing. However, photons, one of the best candidates for qubits, suffer from a lack of strong nonlinear coupling, which is required for quantum logic operations. Here we show how this drawback can be overcome by reporting a proof-of-principle experimental demonstration of a nondestructive controlled-NOT (CNOT) gate for two independent photons using only linear optical elements in conjunction with single-photon sources and conditional dynamics. Moreover, we exploit the CNOT gate to discriminate all four Bell states in a teleportation experiment.
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.
Generating strong interactions between single quanta of light and matter is central to quantum information science, and a key component of quantum computers and long-distance quantum networks. In quantum information processing, these interactions are required to create elementary logic operations (quantum gates) between stationary matter quantum bits (qubits) and photonic qubits that can be transmitted over long distances. Efficient quantum gates between photonic and matter qubits are a crucial enabler for a broad range of applications that include robust quantum networks, nondestructive quantum measurements, and strong photon-photon interactions. So far these qubit-photon gates have been achieved using single atoms and at microwave frequencies in circuit QED systems. Their implementation with solidstate quantum emitters, however, has remained a difficult challenge. We demonstrate that the qubit state of a photon can be controlled by a single solid-state qubit composed of a quantum dot (QD) strongly coupled to an optical nanocavity. We show that the QD acts as a coherently controllable qubit system that conditionally flips the polarization of a photon reflected from the cavity mode on picosecond timescales. This operation implements a controlled NOT (cNOT) logic gate between the QD and the incident photon, which is a universal quantum operation that can serve as a general light-matter interface for remote entanglements and quantum computations. Our results represent an important step towards an all solid-state implementation of quantum networks and quantum computers, and provide a versatile approach for controlling and probing interactions between a photon and a single quantum emitter on ultra-fast timescales.
Optical qubits uniquely combine information transfer in optical fibres with a good processing capability and are therefore attractive tools for quantum technologies. A large challenge, however, is to overcome the low efficiency of two-qubit logic gates. The experimentally achieved efficiency in an optical controlled NOT (CNOT) gate reached approximately 11% in 2003 and has seen no increase since. Here we report on a new platform that was designed to surpass this long-standing record. The new scheme avoids inherently probabilistic protocols and, instead, combines aspects of two established quantum nonlinear systems: atom-cavity systems and Rydberg electromagnetically induced transparency (EIT). We demonstrate a CNOT gate between two optical photons with an efficiency of 41.7(4)% at a postselected process fidelity of 79(2)%. Moreover, we extended the scheme to a CNOT gate with multiple target qubits and produce entangled states of presently up to 5 photons. All these achievements are promising and have the potential to advance optical quantum information processing in which almost all advanced protocols would profit from high-efficiency logic gates.
In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390-393], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multiparticle entangled states, Bell-state measurements, and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods, we demonstrate the smallest nontrivial module in such a scheme--a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates, and the other uses four-photon hyperentanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step toward the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.
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