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Implementation of the Quantum Fourier Transform in Quantum Optical Processors Using Linear Optics with Imperfect Circuits

Mohammad Bayat, Mehran Gholipour Shahraki, Mehdi Mirzaee

Published Aug 26, 2026• 0 citations
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Abstract

Abstract This paper investigates the implementation of the Quantum Fourier Transform (QFT) using linear optical devices and the Cooley-Tukey algorithm, with a focus on the impact of device imperfections and phase errors due to optical path differences. It examines real-world defects in optical gate circuits, systematically analyzing these imperfections for systems with two, three, and general γ-qubit states, providing a comprehensive formula for the γ-qubit case.

DOI
10.21203/rs.3.rs-10522134/v1

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Abstract This paper investigates the implementation of the Quantum Fourier Transform (QFT) using linear optical devices and the Cooley-Tukey algorithm, with a focus on the impact of device imperfections and phase errors due to optical path differences. It examines real-world defects in optical gate circuits, systematically analyzing these imperfections for systems with two, three, and general γ-qubit states, providing a comprehensive formula for the γ-qubit case.
Using the quantum fast Fourier transform in linear optics the input mode annihilation operators {â0,â1,...,âs−1} are transformed into output mode annihilation operators {b̂0,b̂1,...,b̂s−1}. We show how to implement experimentally such transformations based on the Cooley-Tukey algorithm, by the use of beam splitters and phase shifters in a linear optical system. Optical systems implementing 1,2, and 3 qubits discrete Fourier transform (DFT) are described, and a general method for implementing the n-qubit DFT is analyzed. These transformations are used on various input radiation states by which phase estimation and order finding can be computed.
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 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.
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.