Considerations for the extension of coherent optical processors into the quantum computing regime

Abstract

Previously we have examined the similarities of the quantum Fourier transform to the classical coherent optical implementation of the Fourier transform (R. Young et al, Proc SPIE Vol 87480,. In this paper, we further consider how superposition states can be generated on coherent optical wave fronts, potentially allowing coherent optical processing hardware architectures to be extended into the quantum computing regime. In particular, we propose placing the pixels of a Spatial Light Modulator (SLM) individually in a binary superposition state and illuminating them with a coherent wave front from a conventional (but low intensity) laser source in order to make a so-called 'interaction free' measurement. In this way, the quantum object, i.e. the individual pixels of the SLM in their superposition states, and the illuminating wavefront would become entangled. We show that if this were possible, it would allow the extension of coherent processing architectures into the quantum computing regime and we give an example of such a processor configured to recover one of a known set of images encrypted using the well-known coherent optical processing technique of employing a random Fourier plane phase encryption mask which classically requires knowledge of the corresponding phase conjugate key to decrypt the image. A quantum optical computer would allow interrogation of all possible phase masks in parallel and so immediate decryption.

A simplification of the Shor quantum factorization algorithm employing a quantum Hadamard transform

“…However, since they comprise the overall wavefunction they will not be directly accessible to measurement. Rather the probability of detection, by a single measurement, will be given by |Ψ| 2 . If the input wavefunction is periodic, e.g.…”

“…Previously we have compared the central importance of the Fourier transform in classical coherent optical processing systems and in algorithms proposed for implementation in quantum computers noting the similarities, and fundamental differences, between the classical and quantum Fourier transform 1,2 . In this paper, we consider in more detail the Shor quantum factorization algorithm from a signal processing viewpoint, emphasizing the importance of the quantum Fourier transform (QFT) in its operation.…”