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.
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.
This thesis is divided into five parts, each with an accompanying publication. In Chapter 1, I motivate the broad scientific pursuit that underlies this thesis: the quest to build universal, fault-tolerant technology that operates on the principles of quantum mechanics and quantum information theory. I motivate the use of single photons as the quantum particles of choice for this task, and I describe the open challenges facing the field of researchers embarking on this quest. This motivation pervades each subsequent chapter of this thesis, which focus in turn on overcoming four distinct technological and scientific hurdles related to these open challenges. The first of these open challenges is to demonstrate experimentally a useful single-photon source. This source of single photons ought to release just one photon at a time, in an on-demand fashion, with high-rate, low-latency, and high quantum-state purity and indistinguishability, in a single spatial mode, at the right wavelengths for a given application, and ought to satisfy certain practical constraints on size, weight, power, and sensitivity to environmental noise and perturbation. This is a long list of performance metrics, some of which are orthogonal, some not, and non-trivial tradeoffs often exist between metrics. While in this thesis we do not present a solution to this general open problem, we modestly expand scientific knowledge of one of the fundamental mechanisms behind single-photon generation. In particular, we present a new formalism for describing the quantum properties of spontaneous Stokes scattering in the Raman interaction, and we probe its effects on the quantum state purity of resulting Stokes photons both experimentally and theoretically. This is the focus of Chapter 2. Another open challenge to universal, fault-tolerant photonic quantum processing is the experimental demonstration of a useful photonic quantum memory—a device that is capable of storing and releasing single photons in a quantum-information-conserving manner, and which possesses sufficiently high performance across, again, a large set of non-orthogonal metrics. On this challenge, we have made several substantial contributions. Chapter 3 describes a novel approach to optimizing the efficiency of photonic quantum memories in atomic ensembles possessing a three-level Lambda-type energy level structure, in an experimentally friendly fashion. Chapter 4 discusses the practical side of implementing robust quantum memory in these atomic systems, where we carefully consider the theoretical sensitivity of these systems to experimental noise and perturbation. These two Chapters lead up to the experimental work described in Chapter 5, where we experimentally demonstrate a state-of-the-art and best-in-class photonic quantum memory in neutral barium vapor that possesses simultaneously high efficiency, broad bandwidth, and low noise. Our experimental demonstration features >95% storage efficiency, at roughly 3 orders of magnitude larger bandwidth (higher speed) than the previous state of the art, as well as record-low noise for Lambda-type atomic memories. The noise is so low, and the bandwidth so large, that we are able to perform a novel characterization experiment to extract the temporal amplitude and phase of the photons retrieved from our memory, based on spectral interferometry with a known reference. This is the most demanding possible characterization of one of these memories, and has direct implications for using this type of memory in quantum processing tasks that require temporally indistinguishable photons. In Chapter 6 I do the requisite summing up of the thesis, and discuss ongoing and future work on the memory project. In the various and sundry appendices I include information that will chiefly be useful for my successors in the lab, but may be of passing interest to other readers.
Stochastic processes underlie a vast range of natural and social phenomena.Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g., traffic congestion, are effectively probabilistic because we cannot track all relevant variables.To simulate a stochastic system's future behavior, information about its past must be stored, and thus memory is a key resource.Quantum information processing promises a memory advantage for stochastic simulation.Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the required information in fewer dimensions than any classical simulator, thereby achieving a quantum advantage in minimal memory requirements using an individual simulator.This advantage is in contrast to recent proof-of-concept experiments, where the memory saving would only become accessible in the limit of a large number of parallel simulations.In those examples, the minimal memory registers of individual quantum simulators had the same dimensionality as their classical counterparts.Our photonic experiment thus establishes the potential of new, practical resource savings in the simulation of complex systems.
The photon is a quantum system that is by nature robust against noise, and fast travelling, providing an ideal information carrier for quantum information science. The field of quantum information science has generated a great deal of interest for both researchers and the public due to the advantages it can have over classical technologies in areas including communication, computing and cryptography. In this thesis, I explore several different ways that photons can be used to realize quantum information advantages and enable quantum technologies, information tasks and fundamental studies of physics. A strong emphasis is placed on their practical implementation in optical experiments, where the challenges of noise, loss and device imperfections must be considered and combated. I utilize spontaneous parametric downconversion-based sources of high-quality single photons, and their polarization, path, and temporal degrees of freedom for encoding quantum information. In my first experimental project, I demonstrate the first violation of noncontextuality with time-polarization intraparticle entangled states encoded in a single photon by implementing a powerful interference-based measurement technique for photonic states. I perform a test of noncontextuality, acquiring a parameter |SCHSH| = 2.744 ± 0.006, which violates the classical bound of 2 by over 110 standard deviations, rigorously certifying both entanglement and contextuality of the system. We propose a new approach for preparing and measuring high-dimensional time-bin states, that overcomes many of the limitations of previous techniques, and demonstrate it for time-bin qubits and qutrits. In the next experimental project, I investigate the topic of universal cloning in quantum steering-with cloning and steering being two fundamental aspects of quantum physics deeply involved in the security of quantum protocols. I report the first experimental demonstration of cloned quantum steering, showing a simultaneous violation in a steering test by two clones made from one part of an entangled pair of photons. This provides a conclusive result on the question of whether the cloning of quantum steering is possible. We also present theoretical results that clarify our understanding of cloned steering for qubits: we find a no-go theorem where quantum steering can only be copied by a qubit universal cloning machine for 2 and 3 clones, and a monogamy relation where for N clones, steering is only possible if a minimum of N + 1 measurements are performed on each clone. I discuss the field of random number generation, and study how quantum physics allows for certifiably unpredictable random sequences, without needing complete trust in all of the physical devices, offering high levels of security over classical approaches. I report the first discrete-variable detection-loophole-free implementation of one-sided device-independent randomness expansion of certified random bits, based on the quantum steering task. These results illustrate an approach to secure randomness with greater tolerance to noise and loss compared to Bell test-based protocols. The final experimental project looks at quantum autoencoders, which are a quantum machine learning tool that we investigate for the purpose of denoising quantum states. I model and simulate a denoising quantum autoencoder which compresses ququarts into a qubit space and reconstructs noise-reduced ququart states. I construct an experimental apparatus that implements this device, and demonstrate quantum state tomography of ququart states, and the training of the autoencoder.
Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 ± 0.02.
Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes - where the future behaviour depends on events that happened far in the past - must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling.
Abstract Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 ± 0.02.