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Quantum Generative Modelling (QGM) relies on preparing quantum states and generating samples from these states as hidden - or known - probability distributions. As distributions from some classes of quantum states (circuits) are inherently hard to sample classically, QGM represents an excellent testbed for quantum supremacy experiments. Furthermore, generative tasks are increasingly relevant for industrial machine learning applications, and thus QGM is a strong candidate for demonstrating a practical quantum advantage. However, this requires that quantum circuits are trained to represent industrially relevant distributions, and the corresponding training stage has an extensive training cost for current quantum hardware in practice. In this work, we propose protocols for classical training of QGMs based on circuits of the specific type that admit an efficient gradient computation, while remaining hard to sample. In particular, we consider Instantaneous Quantum Polynomial (IQP) circuits and their extensions. Showing their classical simulability in terms of the time complexity, sparsity and anti-concentration properties, we develop a classically tractable way of simulating their output probability distributions, allowing classical training to a target probability distribution. The corresponding quantum sampling from IQPs can be performed efficiently, unlike when using classical sampling. We numerically demonstrate the end-to-end training of IQP circuits using probability distributions for up to 30 qubits on a regular desktop computer. When applied to industrially relevant distributions this combination of classical training with quantum sampling represents an avenue for reaching advantage in the NISQ era.

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy, prove its lower bounds, and investigate its relation to quantum fidelity. In the classical case, minimizing cross entropy is equivalent to maximizing likelihood. In the quantum case, when the quantum cross entropy is constructed from quantum data undisturbed by quantum measurements, this relation holds. Classical cross entropy is equal to negative log-likelihood. When we obtain quantum cross entropy through empirical density matrix based on measurement outcomes, the quantum cross entropy is lower-bounded by negative log-likelihood. These two different scenarios illustrate the information loss when making quantum measurements. We conclude that to achieve the goal of full quantum machine learning, it is crucial to utilize the deferred measurement principle.

Static information flow control (IFC) systems provide the ability to restrict data flows within a program, enabling vulnerable functionality or confidential data to be statically isolated from unsecured data or program logic. Despite the wide applicability of IFC as a mechanism for guaranteeing confidentiality and integrity -- the fundamental properties on which computer security relies -- existing IFC systems have seen little use, requiring users to reason about complicated mechanisms such as lattices of security labels and dual notions of confidentiality and integrity within these lattices. We propose a system that diverges significantly from previous work on information flow control, opting to reason directly about the data that programmers already work with. In doing so, we naturally and seamlessly combine the clasically separate notions of confidentiality and integrity into one unified framework, further simplifying reasoning. We motivate and showcase our work through two case studies on TLS private key management: one for Rocket, a popular Rust web framework, and another for Conduit, a server implementation for the Matrix messaging service written in Rust.

The Galois inner product is a generalization of the Euclidean inner product and Hermitian inner product. The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these years. In this paper, we study Galois hulls of linear codes. Firstly, the symmetry of the dimensions of Galois hulls is found. Some new necessary and sufficient conditions for linear codes being Galois self-orthogonal codes, Galois self-dual codes and Galois linear complementary dual codes are characterized. Then, based on these properties, we develop the previous theory and propose explicit methods to construct Galois self-orthogonal codes of lengths $n+2i$ ($i\geq 0$) and $n+2i+1$ ($i\geq 1$) from Galois self-orthogonal codes of length $n$. As applications, linear codes of lengths $n+2i$ and $n+2i+1$ with Galois hulls of arbitrary dimensions are derived immediately. After this, two new classes of Hermitian self-orthogonal MDS codes are also constructed. Finally, applying all the results to the constructions of entanglement-assisted quantum error-correcting codes (EAQECCs), many new EAQECCs and MDS EAQECCs with rates greater than or equal to $\frac{1}{2}$ and positive net rates can be obtained.

Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world applications. Existing verification algorithms on ReLU neural networks (NNs) based on classical branch and bound (BaB) techniques cannot be trivially applied to PN verification. In this work, we devise a new bounding method, equipped with BaB for global convergence guarantees, called Verification of Polynomial Networks or VPN for short. One key insight is that we obtain much tighter bounds than the interval bound propagation (IBP) and DeepT-Fast [Bonaert et al., 2021] baselines. This enables sound and complete PN verification with empirical validation on MNIST, CIFAR10 and STL10 datasets. We believe our method has its own interest to NN verification. The source code is publicly available at //github.com/megaelius/PNVerification.

Quantum cloud computing is a promising paradigm for efficiently provisioning quantum resources (i.e., qubits) to users. In quantum cloud computing, quantum cloud providers provision quantum resources in reservation and on-demand plans for users. Literally, the cost of quantum resources in the reservation plan is expected to be cheaper than the cost of quantum resources in the on-demand plan. However, quantum resources in the reservation plan have to be reserved in advance without information about the requirement of quantum circuits beforehand, and consequently, the resources are insufficient, i.e., under-reservation. Hence, quantum resources in the on-demand plan can be used to compensate for the unsatisfied quantum resources required. To end this, we propose a quantum resource allocation for the quantum cloud computing system in which quantum resources and the minimum waiting time of quantum circuits are jointly optimized. Particularly, the objective is to minimize the total costs of quantum circuits under uncertainties regarding qubit requirement and minimum waiting time of quantum circuits. In experiments, practical circuits of quantum Fourier transform are applied to evaluate the proposed qubit resource allocation. The results illustrate that the proposed qubit resource allocation can achieve the optimal total costs.

Minimum distance estimation methodology based on empirical distribution function has been popular due to its desirable properties including robustness. Even though the statistical literature is awash with the research on the minimum distance estimation, the most of it is confined to the theoretical findings: only few statisticians conducted research on the application of the method to real world problems. Through this paper, we extend the domain of application of this methodology to various applied fields by providing a solution to a rather challenging and complicated computational problem. The problem this paper tackles is an image segmentation which has been used in various fields. We propose a novel method based on the classical minimum distance estimation theory to solve the image segmentation problem. The performance of the proposed method is then further elevated by integrating it with the "segmenting-together" strategy.

We present CartoonX (Cartoon Explanation), a novel model-agnostic explanation method tailored towards image classifiers and based on the rate-distortion explanation (RDE) framework. Natural images are roughly piece-wise smooth signals -- also called cartoon-like images -- and tend to be sparse in the wavelet domain. CartoonX is the first explanation method to exploit this by requiring its explanations to be sparse in the wavelet domain, thus extracting the relevant piece-wise smooth part of an image instead of relevant pixel-sparse regions. We demonstrate that CartoonX can reveal novel valuable explanatory information, particularly for misclassifications. Moreover, we show that CartoonX achieves a lower distortion with fewer coefficients than other state-of-the-art methods.

The use of quantum computation for wireless network applications is emerging as a promising paradigm to bridge the performance gap between in-practice and optimal wireless algorithms. While today's quantum technology offers limited number of qubits and low fidelity gates, application-based quantum solutions help us to understand and improve the performance of such technology even further. This paper introduces QGateD-Polar, a novel Quantum Gate-based Maximum-Likelihood Decoder design for Polar error correction codes, which are becoming widespread in today's 5G and tomorrow's NextG wireless networks. QGateD-Polar uses quantum gates to dictate the time evolution of Polar code decoding -- from the received wireless soft data to the final decoded solution -- by leveraging quantum phenomena such as superposition, entanglement, and interference, making it amenable to quantum gate-based computers. Our early results show that QGateD-Polar achieves the Maximum Likelihood performance in ideal quantum simulations, demonstrating how performance varies with noise.

The field of quantum machine learning (QML) explores how quantum computers can be used to more efficiently solve machine learning problems. As an application of hybrid quantum-classical algorithms, it promises a potential quantum advantages in the near term. In this thesis, we use the ZXW-calculus to diagrammatically analyse two key problems that QML applications face. First, we discuss algorithms to compute gradients on quantum hardware that are needed to perform gradient-based optimisation for QML. Concretely, we give new diagrammatic proofs of the common 2- and 4-term parameter shift rules used in the literature. Additionally, we derive a novel, generalised parameter shift rule with 2n terms that is applicable to gates that can be represented with n parametrised spiders in the ZXW-calculus. Furthermore, to the best of our knowledge, we give the first proof of a conjecture by Anselmetti et al. by proving a no-go theorem ruling out more efficient alternatives to the 4-term shift rule. Secondly, we analyse the gradient landscape of quantum ans\"atze for barren plateaus using both empirical and analytical techniques. Concretely, we develop a tool that automatically calculates the variance of gradients and use it to detect likely barren plateaus in commonly used quantum ans\"atze. Furthermore, we formally prove the existence or absence of barren plateaus for a selection of ans\"atze using diagrammatic techniques from the ZXW-calculus.