This thesis is devoted to the study of coherent storage of quantum information as well as its potential applications.Quantum memories are crucial to harnessing the potential of quantum physics for information processing tasks.They are required for almost all quantum computation proposals.However, despite the large arsenal of theoretical techniques and proposals dedicated to their implementation, the realization of long-lived quantum memories remains an elusive task.Encoding information in quantum states associated to many-body topological phases of matter and protecting them by means of a static Hamiltonian is one of the leading proposals to achieve quantum memories.While many genuine and well publicized virtues have been demonstrated for this approach, equally real limitations were widely disregarded.In the first two projects of this thesis, we study limitations of passive Hamiltonian protection of quantum information under two different noise models.Chapter 2 deals with arbitrary passive Hamiltonian protection for a many body system under the effect of local depolarizing noise.It is shown that for both constant and time dependent Hamiltonians, the optimal enhancement over the natural single-particle memory time is logarithmic in the number of particles composing the system.The main argument involves a monotonic increase of entropy against which a Hamiltonian can provide little protection.Chapter 3 considers the recoverability of quantum information when it is encoded in a many-body state and evolved under a Hamiltonian composed of known geometrically local interactions and a weak yet unknown Hamiltonian perturbation.We obtain some generic criteria which must be fulfilled by the encoding of information.For specific proposals of protecting Hamiltonian and encodings such as Kitaev's toric code and a subsystem code proposed by Bacon, we additionally provide example perturbations capable of destroying the memory which imply upper bounds for the provable memory times.vi
This thesis is devoted to the study of coherent storage of quantum information as well as its potential applications.Quantum memories are crucial to harnessing the potential of quantum physics for information processing tasks.They are required for almost all quantum computation proposals.However, despite the large arsenal of theoretical techniques and proposals dedicated to their implementation, the realization of long-lived quantum memories remains an elusive task.Encoding information in quantum states associated to many-body topological phases of matter and protecting them by means of a static Hamiltonian is one of the leading proposals to achieve quantum memories.While many genuine and well publicized virtues have been demonstrated for this approach, equally real limitations were widely disregarded.In the first two projects of this thesis, we study limitations of passive Hamiltonian protection of quantum information under two different noise models.Chapter 2 deals with arbitrary passive Hamiltonian protection for a many body system under the effect of local depolarizing noise.It is shown that for both constant and time dependent Hamiltonians, the optimal enhancement over the natural single-particle memory time is logarithmic in the number of particles composing the system.The main argument involves a monotonic increase of entropy against which a Hamiltonian can provide little protection.Chapter 3 considers the recoverability of quantum information when it is encoded in a many-body state and evolved under a Hamiltonian composed of known geometrically local interactions and a weak yet unknown Hamiltonian perturbation.We obtain some generic criteria which must be fulfilled by the encoding of information.For specific proposals of protecting Hamiltonian and encodings such as Kitaev's toric code and a subsystem code proposed by Bacon, we additionally provide example perturbations capable of destroying the memory which imply upper bounds for the provable memory times.vi
The results of this thesis concern the real-world realization of quantum computers, specifically how to build their "hard drives" or quantum memories. These are many-body quantum systems, and their building blocks are qubits, the same way bits are the building blocks of classical computers. Quantum memories need to be robust against thermal noise, noise that would otherwise destroy the encoded information, similar to how strong magnetic field corrupts data classically stored in magnetic many-body systems (e.g., in hard drives). In this work I focus on a subset of many-body models, called quantum doubles, which, in addition to storing the information, could be used to perform the steps of the quantum computation, i.e., work as a "quantum processor". In the first part of my thesis, I investigate how long a subset of quantum doubles (qudit surface codes) can retain the quantum information stored in them, referred to as their memory time. I prove an upper bound for this memory time, restricting the maximum possible performance of qudit surface codes. Then, I analyze the structure of quantum doubles, and find two interesting properties. First, that the high-level description of doubles, utilizing only their quasi-particles to describe their states, disregards key components of their microscopic properties. In short, quasi-particles (anyons) of quantum doubles are not in a one-to-one correspondence with the energy eigenstates of their Hamiltonian. Second, by investigating phase transitions of a simple quantum double, D(S3), I map its phase diagram, and interpret the physical processes the theory undergoes through terms borrowed from the Landau theory of phase transitions.
Building a working quantum computer that is able to perform useful calculations remains a challenge. With this thesis, we are trying to contribute a small piece to this puzzle by addressing three of the many fundamental questions one encounters along the way of reaching that goal. These questions are: (i) What is an easy way to create highly entangled states as a resource for quantum computation? (ii) What can we do to efficiently quantify states of noisy entanglement in systems coupled to the outside world? (iii) How can we protect and store fragile quantum states for arbitrary long times? \n \nThe first two questions are the subject of part one of this thesis, `Entanglement Measures & Highly Entangled States'. We devise a particular proposal for generating entanglement within a solid-state setup, starting first with the tripartite case and continuing with a generalization to four and more qubits. The main idea there is to realize systems with highly entangled ground states in order for entanglement to be created by merely cooling to low enough temperatures. We have addressed the issue of quantifying entanglement in these systems by numerically calculating mixed-state entanglement measures and maximizing the latter as a function of the external magnetic field strength. The research along these lines has led to the development of the numerical library 'libCreme'. \n \nThe second part of the thesis, 'Self-Correcting Quantum Memories', addresses the question how to reliably store quantum states long enough to perform useful calculations. Every computer, be it classical or quantum, needs the information it processes to be protected from corruption caused by faulty gates and perturbations from interactions with its environment. However, quantum states are much more susceptible to these adverse effects than classical states, making the manipulation and storage of quantum information a challenging task. Promising candidates for such 'quantum memories' are systems exhibiting topological order, because they are robust against local perturbations, and information encoded in their ground state can only be manipulated in a non-local fashion. We extend the so-called toric code by repulsive long-range interactions between anyons and show that this makes the code stable against thermal fluctuations. Furthermore, we investigate incoherent effects of quenched disorder in the toric code and similar systems.
[eng] This thesis lies at the intersection of three burgeoning fields: quantum computation, neural networks and bosonic systems. These disciplines have recently attracted significant attention due to their potential to revolutionize information processing. Quantum computation promises to solve problems that are intractable for classical computers, while neural networks have achieved remarkable success in a variety of applications, ranging from image recognition to natural language processing. Finally, bosonic systems offer unique advantages for quantum information processing thanks to their versatility and resilience against certain errors. Motivated by the challenges of preserving quantum information in the Noisy Intermediate-Scale Quantum (NISQ) era and by the potential of continuous-variable platforms, this thesis explores noise-biased bosonic encodings that exploit high-order nonlinearities. Two distinct memory architectures are studied in detail, distinguished by the nature of the nonlinearities: a squeezed cat code stabilized by competing driving and dissipation processes of different orders, and a chiral cat code that uses intrinsic Hamiltonian nonlinearities of superconducting circuits. The former, owing to the squeezed nature of the code states, provides additional protection against bit-flip errors without compromising the decoherence time. The latter, through competing high-order Hamiltonian nonlinearities, generates two quasi-orthogonal manifolds endowed in a chiral flow in phase space, which allow to construct an error-correcting mechanism for bit-flip errors. Both schemes demonstrate how engineered nonlinearities can be harnessed as practical tools for realizing fault-tolerant quantum memories in continuous-variable platforms. In complement to the study of robust quantum memories, this thesis presents a general theoretical framework for quantum associative memories (QAMs) within open quantum systems. This attractor-based neural network algorithm can store and retrieve patterns from partial or noisy inputs. The study addresses the broadest possible scenarios, encompassing both quantum and classical patterns, orthogonal and non-orthogonal memories, stationary and metastable operational regimes, and measurement-based outputs. Several physical mechanisms for implementing QAMs are proposed and analysed, with a focus on the importance of symmetries and dissipation in QAM functioning. We identify strong symmetries that allow for multiple steady states, as well as metastable regimes that enable the rapid retrieval of patterns. This general framework provides the context for an original proposal of a QAM in a bosonic system featuring high-order nonlinearities, which allow patterns to be encoded in presence of strong symmetries or metastable regimes. This specific model exposes all the ingredients developed in the general framework, demonstrate their potential to increase storage capacity beyond that of classical associative memories and introduce the possibility to store genuine quantum states as patterns.
This paper develops a comprehensive theoretical framework for designing quantum memory systems with enhanced resilience to thermal decoherence through engineered lattice geometries and protective structures. We formulate a unified mathematical description connecting material properties, geometric configurations, and quantum information retention capabilities, establishing design principles for long-lived quantum states. The theory begins with a detailed analysis of decoherence mechanisms in structured quantum materials, deriving analytical expressions for coherence time as functions of lattice topology, defect engineering, and environmental coupling strength. We prove theoretical bounds on achievable memory lifetimes under various physical constraints and identify optimal geometric configurations that maximize information retention. The framework incorporates both passive protection mechanisms-arising from intrinsic material properties and geometric shielding-and active stabilization strategies involving periodic error detection and correction. We establish scaling laws that predict how memory performance varies with system size, temperature, and structural parameters, providing design guidelines for practical implementations. Our analysis reveals fundamental trade-offs between memory density, access time, and coherence preservation, offering a theoretical roadmap for next-generation quantum memory architectures. This work bridges quantum information theory, condensed matter physics, and materials science to advance understanding of thermally resilient quantum storage.
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.
Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information. In this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations. Next, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local quantum processing due to the topological properties of the quantum error correcting codes upon which they are built. I show that each protocol's fault-dependence behavior exhibits an order-disorder phase transition when mapped onto an associated statistical-mechanical model. I review the critical error rates of these protocols found by numerical study of the associated models, and I present new analytic bounds for them using a self-avoiding random walk argument. Moreover, I discuss fault-tolerant procedures for encoding, error-correction, computing, and decoding quantum information using these protocols, and calculate the accuracy threshold of fault-tolerant quantum memory for protocols using them. I end by presenting a new class of quantum algorithms that solve combinatorial optimization problems solely by measurement. I compute the running times of these algorithms by establishing an explicit dynamical model for the measurement process. This model, the digitized version of von Neumann's measurement model, is recognized as Kitaev's phase estimation algorithm. I show that the running times of these algorithms are closely related to the running times of adiabatic quantum algorithms. Finally, I present a two-measurement algorithm that achieves a quadratic speedup for Grover's unstructured search problem.