A gedanken model of an analog optical computer for general purpose Fourier transform tasks is built and studied assuming entangled or non-entangled photons appearing at the input. The performance of the entangled and non-entangled operation modes, regarding information content, power consumption, acquisition time, wavelength and bandwidth limitations are analyzed as function of qubit repetition rate and number of qubits in the entangled state, respectively, based on fundamental physical laws. The total number of input photons is assumed the same for the two operation modes. It is sown that the entangled mode outperforms the non-entangled one, but only above a certain number of qubits in the entangled state. It is argued that, for practical applications to general purpose computing, several limitations should be imposed regarding qubit repetition rate and number of qubits in the entangled state. In addition, it is pointed out that the conclusions that we present are equally valid for general purpose optical quantum computing and for quantum information processing, too.
A gedanken model of an analog optical computer for general purpose Fourier transform tasks is built and studied assuming entangled or non-entangled photons appearing at the input. The performance of the entangled and non-entangled operation modes, regarding information content, power consumption, acquisition time, wavelength and bandwidth limitations are analyzed as function of qubit repetition rate and number of qubits in the entangled state, respectively, based on fundamental physical laws. The total number of input photons is assumed the same for the two operation modes. It is sown that the entangled mode outperforms the non-entangled one, but only above a certain number of qubits in the entangled state. It is argued that, for practical applications to general purpose computing, several limitations should be imposed regarding qubit repetition rate and number of qubits in the entangled state. In addition, it is pointed out that the conclusions that we present are equally valid for general purpose optical quantum computing and for quantum information processing, too.
A model of parallel optical computer for Fourier transform tasks is built. The computer operates in both quantum and classical modes. The quantum computer (QC) works with entangled photons and the input gates are n-qubit sensitive, while the classical computer (CC) operates without entanglement. The information capacity (I) for both CC and QC is given as a function of number of qubits and Np (number of photons per input pixel). It is shown that the information capacity significantly increases for the quantum computer compared to the classical one as the number of qubits is increased, assuming that Np is constant for both the QC and CC, i.e. same amount of energy input is assumed for the computers. However, it is also pointed out that the complexity of the QC significantly increases, too. To quantify this, we introduce a new physical quantity called physical complexity (noted as Q). We define the physical complexity (Q) of a computer as ∑i,klog2nkai where k runs over all the gates/elements in the computer; nai is the number of distinguishable states what a gate can set for ai. For QC ai is defined as the ith coefficient of the wave function. For CC it is the ith independent component of the Fourier transform of the energy flow what a particular gate is able to control. By using this definition we show that, for both the quantum and classical computers built in this work, I ≤ Q, in other words the information capacity is less or equal than the physical complexity. Intuitively we suggest that this is a general law that is valid for every computer irrespectively of type, quantum or classic, and architecture.
We present a novel and simple theoretical model of computation that captures what we believe are the most important characteristics of an optical Fourier transform processor. We use this abstract model to reason about the computational properties of the physical systems it describes. We define a grammar for our model's instruction language, and use it to write algorithms for well-known filtering and correlation techniques. We also suggest suitable computational complexity measures that could be used to analyze any coherent optical information processing technique, described with the language, for efficiency. Our choice of instruction language allows us to argue that algorithms describable with this model should have optical implementations that do not require a digital electronic computer to act as a master unit. Through simulation of a well known model of computation from computer theory we investigate the general-purpose capabilities of analog optical processors.
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.
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.
We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position–momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.
In recent years, quantum information has rapidly evolved as a field with transformative potential in science and technology. It provides secure encryption for communication, accurate emulation of practical physical systems, streamlined and accelerated machine learning models, and advanced computational powers that outperform classical supercomputers in solving complex problems. These advancements are all reliant on the superposition and entanglement properties of qubits. While various candidates such as trapped ions or superconducting qubits have been proposed to realize quantum technologies, photons have demonstrated a prominent advantage due to their robustness against decoherence and noise, high clock cycle rate, fast and easy measurement, and room temperature working environment. In addition, photonic integrated chip (PIC) technology has developed rapidly since the beginning of the 21st century. The number of devices integrated on a single chip has increased rapidly, and its complexity has also increased. Quantum computing combined with integrated photonics is expected to solve bottleneck problems in practical situations. In this thesis, based on the silicon-on-insulator (SOI) platform, an optical computing chip and a large-scale quantum computing chip with various practical applications are specifically studied. In the first part of the thesis, a novel integrated diffractive optical network is studied, and a scheme is designed to realize parallel Fourier transform, convolution operations, and application-specific optical computing. Due to the utilization of on-chip compact diffractive cells (slab waveguides), the footprint and power consumption of the proposed architecture is reduced from quadratic scaling in the input data dimensions required for Mach-Zehnder interferometer (MZI)-based optical neural network (ONN) architectures to linear scaling for the improved deep neural networks. A 10-fold reduction in both footprint and energy consumption and equal high accuracy with previous MZI-based ONNs was experimentally achieved for computations performed on the Modified National Institute of Standards and Technology (MNIST) and Fashion-MNIST datasets. This reduction in the resource scaling from quadratic to linear has a profound impact on the realization of large-scale silicon-photonics computing circuits with current fabrication technologies. A quantum photonic microprocessor based on Gaussian Boson sampling (GBS) that offers dynamic programmability to solve various graph-related NP-complete problems is then demonstrated. The system with optical, electrical, and thermal packaging implements a GBS with 16 modes of single-mode squeezed vacuum states, a universal programmable 16-mode interferometer, and a single photon readout on all outputs with high accuracy, generality, and controllability. The developed system is applied to demonstrate applications in solving NP-complete problems, manifesting the ability of photonic quantum computing to realize practical applications for conventionally intractable computations. The GBS-based quantum photonic microprocessor is applied to solve task assignment, Boolean satisfiability, graph clique, max cut, and vertex cover. These demonstrations suggest an excellent benchmarking platform, paving the way toward large-scale combinatorial optimization. Finally, this thesis explores the application possibility of large-scale PICs in molecular simulation. A new algorithm utilizing states with zero displacements (vacuum-squeezed states) coupling to a linear network is proposed to calculate molecular vibronic spectra. With a large-scale PIC, molecular vibronic spectra are accurately simulated for formic acid and thymine with high reconstructed fidelity (>91%) and for naphthalene, phenanthrene, and benzene under the non-Condon regime. Our experimental demonstration will open pathways toward conducting large-scale molecular quantum simulations, a task surpassing classical computers’ capabilities.