This thesis is an exploration of the power of photonic resources, as viewed from several different but related perspectives. They range from quantum computation, precision parameter estimation to the thermodynamics of relativistic quantum systems, as applied to cosmology in particular. In chapter 1, we propose a new quantum computational model, called the `power of one qumode', that relies mainly on a single-mode photonic squeezed state. In particular, we show the amount of squeezing can quantitatively relate the resource requirements of factoring to the problem of finding the trace of large unitary matrices, a result with consequences for understanding how powerful quantum computation really is. Furthermore, we can connect squeezing to other known resources like precision, energy, qudit dimensionality and qubit number, which is a useful stepping stone to finding the resources that enable quantum computation. In chapter 2, we exploit the quantum mechanical properties of photonic states for use in precision parameter estimation of general linear optical processes, which is useful for a diverse number of applications, from characterising an unknown process in a photonic quantum computer to biological imaging. We introduce a formalism that quantifies this improvement in precision. We also provide conditions under which one can easily check for photonic states that are optimal to use in this context, which is a potentially important result for future experimental efforts. In chapter 3, we explore the connection between two-mode squeezed states, commonly used in quantum optics, and relativistic quantum processes, in particular in cosmology. Using this connection, we apply recently developed tools from the thermodynamics of quantum systems perturbed far from equilibrium to address an old question of entropy production in cosmology from a surprising new angle.
This thesis is an exploration of the power of photonic resources, as viewed from several different but related perspectives. They range from quantum computation, precision parameter estimation to the thermodynamics of relativistic quantum systems, as applied to cosmology in particular. In chapter 1, we propose a new quantum computational model, called the `power of one qumode', that relies mainly on a single-mode photonic squeezed state. In particular, we show the amount of squeezing can quantitatively relate the resource requirements of factoring to the problem of finding the trace of large unitary matrices, a result with consequences for understanding how powerful quantum computation really is. Furthermore, we can connect squeezing to other known resources like precision, energy, qudit dimensionality and qubit number, which is a useful stepping stone to finding the resources that enable quantum computation. In chapter 2, we exploit the quantum mechanical properties of photonic states for use in precision parameter estimation of general linear optical processes, which is useful for a diverse number of applications, from characterising an unknown process in a photonic quantum computer to biological imaging. We introduce a formalism that quantifies this improvement in precision. We also provide conditions under which one can easily check for photonic states that are optimal to use in this context, which is a potentially important result for future experimental efforts. In chapter 3, we explore the connection between two-mode squeezed states, commonly used in quantum optics, and relativistic quantum processes, in particular in cosmology. Using this connection, we apply recently developed tools from the thermodynamics of quantum systems perturbed far from equilibrium to address an old question of entropy production in cosmology from a surprising new angle.
This thesis is an exploration of the power of photonic resources, as viewed from several different but related perspectives. They range from quantum computation, precision parameter estimation to the thermodynamics of relativistic quantum systems, as applied to cosmology in particular. The use of photonic states allows us to address several important questions about the resources required in quantum mechanical processes. In chapter 1, we propose a new quantum computational model, called the `power of one qumode', that relies mainly on a single-mode photonic squeezed state. In particular, we show the amount of squeezing can quantitatively relate the resource requirements of factoring to the problem of finding the trace of large unitary matrices, a result with consequences for understanding how powerful quantum computation really is. Furthermore, we can connect squeezing to other known resources like precision, energy, qudit dimensionality and qubit number, which is a useful stepping stone to finding the resources that enable quantum computation. In chapter 2, we exploit the quantum mechanical properties of photonic states for use in precision parameter estimation of general linear optical processes, which is useful for a diverse number of applications, from characterising an unknown process in a photonic quantum computer to biological imaging. We introduce a formalism that quantifies this improvement in precision. We also provide conditions under which one can easily check for photonic states that are optimal to use in this context, which is a potentially important result for future experimental efforts. In chapter 3, we explore the connection between two-mode squeezed states, commonly used in quantum optics, and relativistic quantum processes, in particular in cosmology. Using this connection, we apply recently developed tools from the thermodynamics of quantum systems perturbed far from equilibrium to address an old question of entropy production in cosmology from a surprising new angle.
The technologies utilizing quantum states of light have been in the spotlight for the last two decades. In this regard, quantum metrology, quantum imaging, quantum-optical communication are some of the important applications that exploit fascinating quantum properties like quantum superposition, quantum correlations, and nonclassical photon statistics. However, the state-of-art technologies operating at the single-photon level are not robust enough to truly realize a reliable quantum-photonic technology. In Chapter 1, I present a historical account of photon-based technologies. Furthermore, I discuss recent efforts and encouraging developments in the field of quantum-photonic technologies, and major challenges for the experimental realization of reliable quantum technologies utilizing photons, setting up a stage for unveiling our smart methodologies to cope with them. Similarly, in Chapter 2, I review the fundamental concepts such as states of light, spatial modes of light, and machine learning. In Chapter 3 of this dissertation, I present a theoretical work on a nonlinear quantum metrology scheme, showing a sub-shot-noise limited phase estimation using the displaced-squeezed light and on/off detection. Furthermore, I discuss a camera-based squeezed-light detection technique that can be a smart and time-efficient alternative to conventional balanced-homodyne detection. In Chapter 4, I discuss our efforts to incorporate artificial intelligence in a quest to improve the efficiency of discriminating thermal light sources from coherent light sources. The conventional identification technique requires a large number of measurements. We utilize artificial neural networks to dramatically reduce the number of measurements required to distinguish thermal light and coherent light. In Chapter 5, I present a communication protocol that utilizes the spatial modes of light. Despite being valuable resources for a wide variety of quantum technologies, spatial modes of light are extremely vulnerable to random phase fluctuations. The conventional techniques to cope with these challenges are relatively inefficient. We utilize convolutional neural networks to perform the spatial mode correction of single photons, resulting in a near-unity fidelity of correction. I wrap up my dissertation in Chapter 6 by summarizing the historical context of quantum technologies, challenging problems facing state-of-art quantum technologies, and the importance of our efforts to introduce artificial intelligence in photonic technologies.
Since its inception, quantum information processing (QIP) has been branched into many new directions. As well as well-known applications such as teleportation and metrology, researchers are beginning to investigate interdisciplinary areas such as quantum machine learning. One of the interesting areas is where quantum information science meets stochastic modelling, from the field of complexity science. Recently, it has been shown theoretically that, for simulating classical systems, quantumassisted models and simulators are more efficient in terms of memory storage they require to do simulations, compared with classical computers. That is, for most systems, classical simulators demand an excessive amount of memory storage, while quantum simulators can do the same simulation with less memory. The main focus of this thesis is on experimental realisation of quantum simulators that are capable of simulating stochastic processes with a reduced amount of memory. To implement the (nearly) exact simulation of stochastic processes using quantum simulators, it is essential to have low-noise state preparation, robust unitary operations, and high-precision read-out. These requirements, and the flexibility and precision of photonic quantum optics, make photonics the ideal system for developing the science of this new quantum advantage and for making strides towards its technological realisation. In the context of stochastic simulation, I have experimentally studied three key problems that serve as stepping stones in advancing this new field. In the first experiment, an error-tolerant quantum simulator was designed, and realised to simulate a 1D Ising spin chain, using internal states that store less information than the corresponding classical approach. Furthermore, an interesting and fundamental phenomenon named the ambiguity of simplicity is witnessed. This is the inconsistency that we observe in the order of relative complexity of two systems when we change the simulators from classical to quantum. In the second experiment, a quantum simulator was built that can simulate classical processes for more than one step of the simulation at a time, storing the information from multiple steps coherently. In the third experiment, a new type of quantum memory advantage, which is based on the dimensionality of the memory register, rather than on information entropy measure, is demonstrated. This advantage is realisable in a single simulator, in contrast to previous works. Realising the dimensionality memory advantage in practical applications does not rely on running multiple simulators in parallel.In the field of optical QIP, realising an ideal single-photon source has been a longstanding challenge. In another part of my PhD, I have worked on a source that aims to tackle some of the existing issues in this context. We built a source of high-quality entangled photons with a high heralding efficiency, which has the potential to be used in multi-photon experiments. This source was also essential to demonstrate a fundamental task in quantum non-locality, one-way steering, which was performed conclusively for the first time.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated
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.
Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class of problems where quantum computers possess an advantage is phase estimation, which includes applications like factoring. We introduce a computational model based on a single squeezed state resource that can perform phase estimation, which we call the power of one qumode. This model is inspired by an interesting computational model known as deterministic quantum computing with one quantum bit (DQC1). Using the power of one qumode, we identify that the amount of squeezing is sufficient to quantify the resource requirements of different computational problems based on phase estimation. In particular, we can use the amount of squeezing to quantitatively relate the resource requirements of DQC1 and factoring. Furthermore, we can connect the squeezing to other known resources like precision, energy, qudit dimensionality, and qubit number. We show the circumstances under which they can likewise be considered good resources.