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Objective. To develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV) and gradient performance compared to existing low-weight configurations. Approach. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly-packed distribution of magnetic Nd$_2$Fe$_14$B cubes with differential evolution algorithms, and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. Main result. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10 & 14 cm and the magnet generates a field of 87 mT homogeneous down to 5,700 ppm (parts per million) in a 20 cm diameter FoV, it weighs 216 kg and has a width of 65 cm and a height of 72 cm. Gradient efficiencies go up to around 0.8 mT/m/A, for a maximum of 12 mT/m with in 0.5 ms with 15 A & 15 V amplifier. The distance between lobes is 28 cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25 W at maximum power, and gradient deviations from linearity are below 20% in a 20 cm sphere.

Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at edge endpoints. These port labels greatly simplify pattern matching. A pre-requisite for graph rewriting is the ability to find subgraphs of the input that match known graph identities: the pattern matching problem. We propose a new solution to pattern matching in port graphs. Its novelty lies in the use of a pre-computed data structure that makes the pattern matching runtime complexity independent of the number of patterns. The runtime is bound by the maximum width $w$ and depth $d$ of the patterns, as well as the input graph size $|G|$ as $O(|G| \cdot c^w / w^{1/2} \cdot d)$ with $c = 6.75$. This offers a significant advantage over existing solutions for use cases where patterns have low width and the set of patterns is large and fixed ahead of time. In the context of quantum circuits, pattern width can be limited to qubit number. Quantum superoptimisers may use thousands of rewrite rules on circuits with less than 5 qubits, making them an ideal use case. We provide benchmarks showing that our algorithm offers a 20x speedup over current implementations on a dataset of 10'000 real world patterns describing quantum circuits.

We consider sets with infinite addition, called $\Sigma$-monoids, and contribute to their literature in three ways. First, our definition subsumes those from previous works and allows us to relate them in terms of adjuctions between their categories. In particular, we discuss $\Sigma$-monoids with additive inverses. Second, we show that every Hausdorff commutative monoid is a $\Sigma$-monoid, and that there is a free Hausdorff commutative monoid for each $\Sigma$-monoid. Third, we prove that $\Sigma$-monoids have well-defined tensor products, unlike topological abelian groups.

Large language models (LLMs) have been massively applied to many tasks, often surpassing state-of-the-art approaches. While their effectiveness in code generation has been extensively studied (e.g., AlphaCode), their potential for code detection remains unexplored. This work presents the first analysis of code detection using LLMs. Our study examines essential kernels, including matrix multiplication, convolution, and fast-fourier transform, implemented in C/C++. We propose both a preliminary, naive prompt and a novel prompting strategy for code detection. Results reveal that conventional prompting achieves great precision but poor accuracy (68.8%, 22.3%, and 79.2% for GEMM, convolution, and FFT, respectively) due to a high number of false positives. Our novel prompting strategy substantially reduces false positives, resulting in excellent overall accuracy (91.1%, 97.9%, and 99.7%, respectively). These results pose a considerable challenge to existing state-of-the-art code detection methods.

We consider a heterogeneous network of quantum computing modules, sparsely connected via Bell states. Operations across these connections constitute a computational bottleneck and they are likely to add more noise to the computation than operations performed within a module. We introduce several techniques for transforming a given quantum circuit into one implementable on a network of the aforementioned type, minimising the number of Bell states required to do so. We extend previous works on circuit distribution over fully connected networks to the case of heterogeneous networks. On the one hand, we extend the hypergraph approach of [Andres-Martinez & Heunen. 2019] to arbitrary network topologies. We additionally make use of Steiner trees to find efficient realisations of the entanglement sharing within the network, reusing already established connections as often as possible. On the other hand, we extend the embedding techniques of [Wu, et al. 2022] to networks with more than two modules. Furthermore, we discuss how these two seemingly incompatible approaches can be made to cooperate. Our proposal is implemented and benchmarked; the results confirming that, when orchestrated, the two approaches complement each other's weaknesses., Comment: 30 pages, 18 figures, comments welcome; v2 - Add link to experiment data; v3 - 31 pages, small updates to discussion and references

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field $\phi(x)$ locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional $\lambda\phi^4$ terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling $\lambda$. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the $\lambda\phi^4$ QFT.

Last years we have witnessed the uprising of location based applications, which depend on the devices ability to accurately obtain their position. IEEE 802.11, foretelling the need for such applications, started the IEEE 802.11az work on Next Generation Positioning. Although this standard provides positioning enhancements for sub-6GHz and mmWave bands, high accuracy in the order of centimeters can only be obtained in the latter band, thanks to the beamforming information available at mmWave operation. This work presents a detailed analysis on the new techniques provided by IEEE 802.11az for enhanced secured positioning in the mmWave band, assessing them through experimentation., Comment: 8 pages, 6 figures, magazine submission

We study a variant of the subgraph isomorphism problem that is of high interest to the quantum computing community. Our results give an algorithm to perform pattern matching in quantum circuits for many patterns simultaneously, independently of the number of patterns. After a pre-computation step in which the patterns are compiled into a decision tree, the running time is linear in the size of the input quantum circuit. More generally, we consider connected port graphs, in which every edge $e$ incident to $v$ has a label $L_v(e)$ unique in $v$. Jiang and Bunke showed that the subgraph isomorphism problem $H \subseteq G$ for such graphs can be solved in time $O(|V(G)| \cdot |V(H)|)$. We show that if in addition the graphs are directed acyclic, then the subgraph isomorphism problem can be solved for an unbounded number of patterns simultaneously. We enumerate all $m$ pattern matches in time $O(P)^{P+3/2} \cdot |V(G)| + O(m)$, where $P$ is the number of vertices of the largest pattern. In the case of quantum circuits, we can express the bound obtained in terms of the maximum number of qubits $N$ and depth $\delta$ of the patterns : $O(N)^{N + 1/2} \cdot \delta \log \delta \cdot |V(G)| + O(m)$., Comment: The main bound of thm 1 is asymptotically very close to previous work, significantly reducing the novelty and motivation for this work. A new approach to this problem is presented in 2402.13065

Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier to wider scale adoption. Recent work overcomes this by matching and replacing patterns within code, but such approaches are fragile and fail to cope with the diversity of real-world codes. We develop ATC, a compiler that uses program synthesis to map regions of code to specific APIs. The mapping space that ATC explores is combinatorially large, requiring the development of program classification, dynamic analysis, variable constraint generation and lexical distance matching techniques to make it tractable. We apply ATC to real-world tensor and linear algebra codes and evaluate them against four state-of-the-art approaches. We accelerate between 2.6x and 7x more programs, leading to over an order of magnitude performance improvement., Comment: This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Proceedings of the 32nd ACM SIGPLAN International Conference on Compiler Construction (CC '23), February 25-26, 2023, Montr\'eal, QC, Canada, https://doi.org/10.1145/3578360.3580262

In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits., Comment: Published version: 30+10 pages, 22+2 figures, updated with numerical benchmarking of the packing algorithm

Control flow of quantum programs is often divided into two different classes: classical and quantum. Quantum programs with classical control flow have their conditional branching determined by the classical outcome of measurements, and these collapse quantum data. Conversely, quantum control flow is coherent, i.e. it does not perturb quantum data; quantum walk-based algorithms are practical examples where coherent quantum feedback plays a major role. This dissertation has two main contributions: (i) a categorical study of coherent quantum iteration and (ii) the introduction of weak while loops. (i) The objective is to endow categories of quantum processes with a traced monoidal structure capable of modelling iterative quantum loops. To this end, the trace of a morphism is calculated via the execution formula, which adds up the contribution of all possible paths of the control flow. Haghverdi's unique decomposition categories are generalised to admit additive inverses and equipped with convergence criteria using basic topology. In this setting, it is possible to prove the validity of the execution formula as a categorical trace on certain categories of quantum processes. (ii) A weak while loop is a classical control flow primitive that offers a trade-off between the collapse caused on each iteration and the amount of information gained. The trade-off may be adjusted by tuning a parameter and, in certain situations, it is possible to set its value so that we may control the algorithm without sacrificing its quantum speed-up. As an example, it is shown that Grover's search problem can be implemented using a weak while loop, maintaining the same time complexity as the standard Grover's algorithm (as previously shown by Mizel)., Comment: PhD Thesis

Heterogeneous computing is becoming mainstream in all scopes. This new era in computer architecture brings a new paradigm called Accelerator Level Parallelism (ALP). In ALP, accelerators are used concurrently to provide unprecedented levels of performance and energy efficiency. To reach that, there are many problems to be solved, one of the most challenging being co-execution. This paper develops a scheduling framework called POAS, a general method for providing co-execution to generic applications. Unlike other scheduling approaches, POAS does not directly schedule applications. Instead, it is a generic model that transforms any application to make it suitable for co-execution, so that it can be executed in ALP environments. Our proposal is composed of four differentiated steps: predict, optimize, adapt and schedule. During these phases, different modifications are implemented in the application to make it suitable to be executed in ALP environments. In this work we also apply our framework to a matrix multiplication case study, outlining the critical and most important steps to port the application with POAS. We evaluate our POAS-based implementation for matrix multiplication on a CPU/GPU/XPU environment using CPU cores, CUDA cores and tensor cores (XPU). Our experiments prove that co-execution in the studied scenario can benefit from ALP, yielding speedups of up to 45% with respect to using only one accelerator. The proven flexibility and potential of POAS make it an excellent candidate to reach ALP in future computer systems.

The A.I. disruption and the need to compete on innovation are impacting cities that have an increasing necessity to become innovation hotspots. However, without proven solutions, experimentation, often unsuccessful, is needed. But experimentation in cities has many undesirable effects not only for its citizens but also reputational if unsuccessful. Digital Twins, so popular in other areas, seem like a promising way to expand experimentation proposals but in simulated environments, translating only the half-baked ones, the ones with higher probability of success, to real environments and therefore minimizing risks. However, Digital Twins are data intensive and need highly localized data, making them difficult to scale, particularly to small cities, and with the high cost associated to data collection. We present an alternative based on synthetic data that given some conditions, quite common in Smart Cities, can solve these two problems together with a proof-of-concept based on NO2 pollution.