[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.
[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.
Abstract Associative memory (AM) refers to the ability to relate a memory with an input and targets the restoration of corrupted patterns. It has been intensively studied in classical physical systems, as in neural networks where an attractor dynamics settles on stable solutions. Several extensions to the quantum domain have been recently reported, displaying different features. In this work, we develop a comprehensive framework for a quantum AM (QAM) based on open quantum system dynamics, which allows us to compare existing models, identify the theoretical prerequisites for performing AM tasks, and extend it in different forms. The map that achieves an exponential increase in the number of stored patterns with respect to classical systems is derived. We establish the crucial role of symmetries and dissipation in the operation of QAM. Our theoretical analysis demonstrates the feasibility of addressing both quantum and classical patterns, orthogonal and non-orthogonal memories, stationary and metastable operating regimes, and measurement-based outputs. Finally, this opens up new avenues for practical applications in quantum computing and machine learning, such as quantum error correction or quantum memories.
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error correction. We investigate superconducting microwave implementations of continuous-variable quantum computing, including the deterministic generation of cubic phase states, and introduce the dissipatively stabilized squeezed cat qubit, a noise-biased bosonic encoding with enhanced error suppression and faster gates. The performance of rotation-symmetric and GKP codes is analyzed under realistic noise and measurement models, revealing key trade-offs in measurement-based schemes. To integrate bosonic codes into larger architectures, we develop decoding methods that exploit analog syndrome information, enabling quasi-single-shot decoding in concatenated systems. On the discrete-variable side, we introduce localized statistics decoding, a highly parallelizable decoder for quantum LDPC codes, and propose quantum radial codes, a new family of single-shot LDPC codes with low overhead and strong circuit-level performance. Finally, we present fault complexes, a homological framework for analyzing faults in dynamic quantum error correction protocols. Extending the role of homology in static CSS codes, fault complexes provide a general language for the design and analysis of fault-tolerant schemes.
Nowadays, the research field of Machine Learning (ML) is undergoing a rapid expansion. In addition, in the last decades, within the research area of quantum computation, several quantum protocols and algorithms have shown the ability to outperform their classical counterparts. In the light of these twofold advances, a frontier field investigating the potentiality of quantum implementations of ML architectures arose. Among the latter, many efforts are concentrated on Artificial Neural Networks (ANNs), which represent a highly successful ML architecture. This thesis focuses on characterizing and understanding the role of quantum effects on the behavior of an instance of ANN, the so-called Hopfield Neural Network (HNN). The HNN is an example of an associative memory model and it permits the recognition, or retrieval, of patterns, such as letters of an alphabet. Formally, it can be described in terms of a classical spin network with an all-to-all interaction, ruled by a stochastic dynamics. Its relatively intuitive behavior, and its physical description make the HNN being a good candidate for a theoretical investigation of its possible quantum generalizations. In the first part of our work we deal with the implementation of fully connected Ising models, such as the HNN one, in terms of quantum systems. To this end, we refer to the cases where the theory of Open Quantum System (OQS) is exploited for engineering steady states of out-of-equilibrium dynamics. This paradigm allows us to build a dissipative - yet quantum - dynamics which encodes in its stationary state the thermal state of the original (classical) problem. Such a construction gives us the chance to address the question as to whether the quantum description could lead to a speed-up in reaching the shared stationary state with respect to the classical counterpart. We show that a suitable choice of the parameters allows the system to switch between a classical regime and a quantum one, the latter being characterized by an accelerated approach towards the long-time limit state. In the second part of our work we focus on practically relevant implementations of quantum systems that can show analogies with the HNN model. To this end, we consider spin-boson models as described by the Dicke Hamiltonian. Indeed, at strong spin-boson interaction couplings, and when the latter are additionally characterized by disorder, the equilibrium Dicke model is able to reproduce the retrieval mechanism typical of HNNs. When dissipation is included, the theoretical description becomes more challenging. We analyze the open, disordered Dicke model by employing some perturbative techniques in order to deal with the out-of-equilibrium dynamics at strong coupling. As a result, we are able to highlight similarities and differences between the quantum model and HNNs.
Quantum computing promises exponential advantages for simulating quantum systems and solving certain computational problems beyond the reach of classical computers, but the fragility of qubits and the resulting errors present a major challenge for scalable implementations. One promising approach is to engineer qubits whose physical noise processes are intrinsically biased, enabling more efficient quantum error correction. This dissertation investigates quantum computing with superconducting Kerr-cat qubits, a bosonic qubit architecture in which qubit states are encoded in coherent states of a nonlinear oscillator stabilized by a two-photon drive. This stabilization creates an effective double-well pseudo-potential that strongly suppresses bit-flip errors while enabling universal quantum control, leading to a noise-biased qubit. A superconducting device architecture based on SNAIL nonlinear oscillators is developed to realize Kerr-cat qubits with tunable parameters and high coherence, integrating readout resonators, dedicated filters, and microwave control lines for measurement and manipulation. Universal single-qubit gates are implemented using engineered single-photon and two-photon drives to deform the pseudo-potential, and a cat-quadrature readout method is employed to achieve high-fidelity quantum nondemolition measurement. The performance of the qubits is systematically characterized through lifetime measurements and benchmarking protocols, including quantum process tomography, gate set tomography, and dihedral randomized benchmarking, revealing a strongly biased noise structure with high performance. These results establish an experimental framework for the design, control, and characterization of Kerr-cat qubits and demonstrate their potential as hardware-efficient building blocks for scalable fault-tolerant quantum computing.
To solve problems of practical importance1,2, quantum computers probably need to incorporate quantum error correction, in which a logical qubit is redundantly encoded in many noisy physical qubits3–5. The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches6–18. Here, using a superconducting quantum circuit19, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance d = 5 (ref. 10). A stabilizing circuit passively protects cat qubits against bit flips20–24. The repetition code, using ancilla transmons for syndrome measurement, corrects cat qubit phase flips. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below the threshold. The logical bit-flip error is suppressed with increasing cat qubit mean photon number, enabled by our realization of a cat-transmon noise-biased CX gate. The minimum measured logical error per cycle is on average 1.75(2)% for the distance-3 code sections, and 1.65(3)% for the distance-5 code. Despite the increased number of fault locations of the distance-5 code, the high degree of noise bias preserved during error correction enables comparable performance. These results, where the intrinsic error suppression of the bosonic encodings enables us to use a hardware-efficient outer error-correcting code, indicate that concatenated bosonic codes can be a compelling model for reaching fault-tolerant quantum computation. Bosonic qubits can be engineered to feature intrinsic protection against certain kinds of errors, which makes quantum error correction across many bosonic qubits possible with less overhead.
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.