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Optics and Spectroscopy

Quantum information processing with fiber optics: Quantum Fourier transform of 1024 qubits

Akihisa Tomita

Published Aug 1, 2005• 1 citation
Publisher

Abstract

Among a number of candidates, photons have advantages for implementing qubits: very weak coupling to the environment, the existing single photon measurement technique, and so on. Moreover, commercially available fiber-optic devices enable us to construct quantum circuits that consist of one-qubit operations (including classically controlled gates). Fiber optics resolves the mode matching problems in conventional optics and provides mechanically stable optical circuits. A quantum Fourier transform (QFT) followed by measurement was demonstrated with a simple circuit based on fiber optics. The circuit was shown to be robust against imperfections in the rotation gate. The error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation for 100 qubits. The error probability can be further reduced to achieve successful QFT of 1024 qubits by taking the majority of the accumulated results. As is well known, QFT is a key function in quantum computations such as the final part of Shor’s factorization algorithm. The present QFT circuit, in combination with controlled unitary gates, would make possible practical quantum computers. Possible schemes of realizing quantum computers in this line are explored.

DOI
10.1134/1.2034605

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Among a number of candidates, photons have advantages for implementing qubits: very weak coupling to the environment, the existing single photon measurement technique, and so on. Moreover, commercially available fiber-optic devices enable us to construct quantum circuits that consist of one-qubit operations (including classically controlled gates). Fiber optics resolves the mode matching problems in conventional optics and provides mechanically stable optical circuits. A quantum Fourier transform (QFT) followed by measurement was demonstrated with a simple circuit based on fiber optics. The circuit was shown to be robust against imperfections in the rotation gate. The error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation for 100 qubits. The error probability can be further reduced to achieve successful QFT of 1024 qubits by taking the majority of the accumulated results. As is well known, QFT is a key function in quantum computations such as the final part of Shor’s factorization algorithm. The present QFT circuit, in combination with controlled unitary gates, would make possible practical quantum computers. Possible schemes of realizing quantum computers in this line are explored.
Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation on 100 qubits. The error probability can be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted in a successful QFT demonstration on 1024 qubits. 1
Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation on 100 qubits. The error probability can be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted in a successful QFT demonstration on 1024 qubits.
Quantum Fourier transform (QFT) is an important subroutine in quantum computation. A QFT followed by measurement (MQFT) which appears in the final part of the phase estimation algorithm was demonstrated on a simple circuit based on fiber-optics. The MQFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit but could be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted in a successful MQFT of 1024 qubits. The present results not only demonstrate the potential of fiber optics but provide an important clue for quantum computer design.
This survey presents a comprehensive analysis of the quantum Fourier transform (QFT), a fundamental tool in quantum computing, in comparison to its classical counterpart, the fast Fourier transform (FFT). The study begins with an introduction to the classical Fourier transform, which is widely used in different disciplines such as signal and image processing. The article introduces the QFT as a quantum version of the Fourier transform, detailing how it leverages quantum parallelism and superposition to reduce the time complexity of the operation, and highlighting its crucial role in quantum algorithms like Shor’s algorithm for integer factorization. The analysis also addresses the mathematical foundations of the QFT, its implementation in quantum circuits, and the key advantages and challenges associated with its use, such as measurement precision and quantum decoherence. Finally, it concludes with an exploration of the current and potential applications of QFT in quantum computing.
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the implementation. We focus here on an interesting decomposition of the QFT as a product of the non-selective Hadamard transformation followed by multiqubit gates corresponding to square- and higher-roots of controlled-NOT gates. This decomposition requires only O(n) operations and is thus linear in the number of qubits n. The schemes were implemented on a two-qubit NMR quantum information processor and the resultant density matrices reconstructed using standard quantum state tomography techniques. Their experimental fidelities have been measured and compared.
The light's image is the primary source of information carrier in nature. Indeed, a single photon's image possesses a vast information capacity that can be harnessed for quantum information processing. Our scheme for implementing quantum information processing via universal multiport processors employs a class of quantum Fourier optical systems composed of spatial phase modulators and 4f-processors with phase-only pupils having a characteristic periodicity that reduces the number of optical resources quadratically as compared to other conventional path encoding techniques. In particular, this paper employs quantum Fourier optics to implement some key quantum logical gates that can be instrumental in optical quantum computations. For instance, we demonstrate the principle by implementing the single-qubit Hadamard and the two-qubit controlled-NOT gates via simulation and optimization techniques. Due to various advantages of the proposed scheme, including the large information capacity of the photon wavefront, a quadratically reduced number of optical resources compared with other conventional path encoding techniques, and dynamic programmability, the proposed scheme has the potential to be an essential contribution to linear optical quantum computing and optical quantum signal processing.