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Networked-Control Systems (NCSs), a type of cyber-physical systems, consist of tightly integrated computing, communication and control technologies. While being very flexible environments, they are vulnerable to computing and networking attacks. Recent NCSs hacking incidents had major impact. They call for more research on cyber-physical security. Fears about the use of quantum computing to break current cryptosystems make matters worse. While the quantum threat motivated the creation of new disciplines to handle the issue, such as post-quantum cryptography, other fields have overlooked the existence of quantum-enabled adversaries. This is the case of cyber-physical defense research, a distinct but complementary discipline to cyber-physical protection. Cyber-physical defense refers to the capability to detect and react in response to cyber-physical attacks. Concretely, it involves the integration of mechanisms to identify adverse events and prepare response plans, during and after incidents occur. In this paper, we make the assumption that the eventually available quantum computer will provide an advantage to adversaries against defenders, unless they also adopt this technology. We envision the necessity for a paradigm shift, where an increase of adversarial resources because of quantum supremacy does not translate into higher likelihood of disruptions. Consistently with current system design practices in other areas, such as the use of artificial intelligence for the reinforcement of attack detection tools, we outline a vision for next generation cyber-physical defense layers leveraging ideas from quantum computing and machine learning. Through an example, we show that defenders of NCSs can learn and improve their strategies to anticipate and recover from attacks.

Quantum computing systems rely on the principles of quantum mechanics to perform a multitude of computationally challenging tasks more efficiently than their classical counterparts. The architecture of software-intensive systems can empower architects who can leverage architecture-centric processes, practices, description languages, etc., to model, develop, and evolve quantum computing software (quantum software for short) at higher abstraction levels. We conducted a systematic literature review (SLR) to investigate (i) architectural process, (ii) modeling notations, (iii) architecture design patterns, (iv) tool support, and (iv) challenging factors for quantum software architecture. Results of the SLR indicate that quantum software represents a new genre of software-intensive systems; however, existing processes and notations can be tailored to derive the architecting activities and develop modeling languages for quantum software. Quantum bits (Qubits) mapped to Quantum gates (Qugates) can be represented as architectural components and connectors that implement quantum software. Tool-chains can incorporate reusable knowledge and human roles (e.g., quantum domain engineers, quantum code developers) to automate and customize the architectural process. Results of this SLR can facilitate researchers and practitioners to develop new hypotheses to be tested, derive reference architectures, and leverage architecture-centric principles and practices to engineer emerging and next generations of quantum software.

Secure software leasing (SSL) is a quantum cryptographic primitive that enables users to execute software only during the software is leased. It prevents users from executing leased software after they return the leased software to its owner. SSL can make software distribution more flexible and controllable. Although SSL is an attractive cryptographic primitive, the existing SSL scheme is based on public key quantum money, which is not instantiated with standard cryptographic assumptions so far. Moreover, the existing SSL scheme only supports a subclass of evasive functions. In this work, we present SSL schemes based on the learning with errors assumption (LWE). Specifically, our contributions consist of the following. - We construct an SSL scheme for pseudorandom functions from the LWE assumption against quantum adversaries. - We construct an SSL scheme for a subclass of evasive functions from the LWE assumption against sub-exponential quantum adversaries. - We construct SSL schemes for the functionalities above with classical communication from the LWE assumption against (sub-exponential) quantum adversaries. SSL with classical communication means that entities exchange only classical information though they run quantum computation locally. Our crucial tool is two-tier quantum lightning, which is introduced in this work and a relaxed version of quantum lighting. In two-tier quantum lightning schemes, we have a public verification algorithm called semi-verification and a private verification algorithm called full-verification. An adversary cannot generate possibly entangled two quantum states whose serial numbers are the same such that one passes the semi-verification, and the other also passes the full-verification. We show that we can construct a two-tier quantum lightning scheme from the LWE assumption.

In this paper, we initiate the study of isogeometric analysis (IGA) of a quantum three-body problem that has been well-known to be difficult to solve. In the IGA setting, we represent the wavefunctions by linear combinations of B-spline basis functions and solve the problem as a matrix eigenvalue problem. The eigenvalue gives the eigenstate energy while the eigenvector gives the coefficients of the B-splines that lead to the eigenstate. The major difficulty of isogeometric or other finite-element-method-based analyses lies in the lack of boundary conditions and a large number of degrees of freedom for accuracy. For a typical many-body problem with attractive interaction, there are bound and scattering states where bound states have negative eigenvalues. We focus on bound states and start with the analysis for a two-body problem. We demonstrate through various numerical experiments that IGA provides a promising technique to solve the three-body problems.

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into $N = 2^{n-p-1} \tbinom{n}{p}$ physical qubits and displays local testability with a soundness of $\Omega(1/\log(N))$ beating the current state-of-the-art of $1/\log^{2}(N)$ due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors. We then extend this code family by considering the quotient of the $n$-cube by arbitrary linear classical codes of length $n$. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be constant, similarly to the ordinary $n$-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension.

Distance measures provide the foundation for many popular algorithms in Machine Learning and Pattern Recognition. Different notions of distance can be used depending on the types of the data the algorithm is working on. For graph-shaped data, an important notion is the Graph Edit Distance (GED) that measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. As the complexity of computing GED is the same as NP-hard problems, it is reasonable to consider approximate solutions. In this paper we present a QUBO formulation of the GED problem. This allows us to implement two different approaches, namely quantum annealing and variational quantum algorithms that run on the two types of quantum hardware currently available: quantum annealer and gate-based quantum computer, respectively. Considering the current state of noisy intermediate-scale quantum computers, we base our study on proof-of-principle tests of their performance.

Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This "spin alignment conjecture", which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In a companion paper, we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

We present a classical algorithm that, for any $D$-dimensional geometrically-local, quantum circuit $C$ of polylogarithmic-depth, and any bit string $x \in {0,1}^n$, can compute the quantity $|<x|C|0^{\otimes n}>|^2$ to within any inverse-polynomial additive error in quasi-polynomial time, for any fixed dimension $D$. This is an extension of the result [CC21], which originally proved this result for $D = 3$. To see why this is interesting, note that, while the $D = 1$ case of this result follows from standard use of Matrix Product States, known for decades, the $D = 2$ case required novel and interesting techniques introduced in [BGM19]. Extending to the case $D = 3$ was even more laborious and required further new techniques introduced in [CC21]. Our work here shows that, while handling each new dimension has historically required a new insight, and fixed algorithmic primitive, based on known techniques for $D \leq 3$, we can now handle any fixed dimension $D > 3$. Our algorithm uses the Divide-and-Conquer framework of [CC21] to approximate the desired quantity via several instantiations of the same problem type, each involving $D$-dimensional circuits on about half the number of qubits as the original. This division step is then applied recursively, until the width of the recursively decomposed circuits in the $D^{th}$ dimension is so small that they can effectively be regarded as $(D-1)$-dimensional problems by absorbing the small width in the $D^{th}$ dimension into the qudit structure at the cost of a moderate increase in runtime. The main technical challenge lies in ensuring that the more involved portions of the recursive circuit decomposition and error analysis from [CC21] still hold in higher dimensions, which requires small modifications to the analysis in some places.

Fast developing artificial intelligence (AI) technology has enabled various applied systems deployed in the real world, impacting people's everyday lives. However, many current AI systems were found vulnerable to imperceptible attacks, biased against underrepresented groups, lacking in user privacy protection, etc., which not only degrades user experience but erodes the society's trust in all AI systems. In this review, we strive to provide AI practitioners a comprehensive guide towards building trustworthy AI systems. We first introduce the theoretical framework of important aspects of AI trustworthiness, including robustness, generalization, explainability, transparency, reproducibility, fairness, privacy preservation, alignment with human values, and accountability. We then survey leading approaches in these aspects in the industry. To unify the current fragmented approaches towards trustworthy AI, we propose a systematic approach that considers the entire lifecycle of AI systems, ranging from data acquisition to model development, to development and deployment, finally to continuous monitoring and governance. In this framework, we offer concrete action items to practitioners and societal stakeholders (e.g., researchers and regulators) to improve AI trustworthiness. Finally, we identify key opportunities and challenges in the future development of trustworthy AI systems, where we identify the need for paradigm shift towards comprehensive trustworthy AI systems.

Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the graph topology is learned from the data. A particular emphasis is on graph topology definition based on the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the smoothness or sparsity of graph connections. For learning sparse graphs (with small number of edges), the least absolute shrinkage and selection operator, known as LASSO is employed, along with its graph specific variant, graphical LASSO. For completeness, both variants of LASSO are derived in an intuitive way, and explained. An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems. As many graph neural networks (GNN) and convolutional graph networks (GCN) are emerging, we have also reviewed the main trends in GNNs and GCNs, from the perspective of graph signal filtering. Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside on a high-dimensional regular lattice structure. This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling.