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.
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.
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 on discretized photon wavefront 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.
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This article develops coherent and comprehensive methodologies and mathematical models to describe Fourier optical signal processing in full quantum terms for any input quantum state of light. We begin this article by introducing a spatially 2-D quantum state of a photon, associated with its wavefront and expressible as a 2-D creation operator. Then, by breaking down the Fourier optical processing apparatus into its key components, we strive to acquire the quantum unitary transformation or the input/output quantum relation of the 2-D creation operators. Subsequently, we take advantage of the above results to develop and obtain the quantum analogous of a few essential Fourier optical apparatuses, such as quantum convolution via a 4f-processing system and a quantum 4f-processing system with periodic pupils. Moreover, due to the importance and widespread use of optical pulse shaping in various optical communications and optical sciences fields, we also present an analogous system in full quantum terms, namely quantum pulse shaping with an 8f-processing system. Finally, we apply our results to two extreme examples of the quantum state of light. One is based on a coherent (Glauber) state and the other on a single-photon number (Fock) state for each of the above optical systems. We believe the schemes and mathematical models developed in this article can impact many areas of quantum optical signal processing, quantum holography, quantum communications, quantum radars and multiple-input/multiple-output antennas, and many more applications in quantum imaging, quantum computations, and quantum machine learning algorithms.
We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.
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, 874806-1, -11). 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.
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.
Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.