Search

Advances in sensing devices that utilize NV center ensembles in diamond are driving progress in microscale nuclear magnetic resonance spectroscopy. Utilizing quantum sensing techniques in the high-field regime significantly boosts sensitivity by increasing thermal polarization, and improve spectral quality via enhanced energy shifts. Compatible with the latter, a straightforward manner to further raise sensor sensitivity is to increase NV concentration; although, this intensifies detrimental dipole-dipole interactions among NVs. In this work, we present a method for detecting NMR signals in high-field scenarios while effectively suppressing dipole-dipole couplings in the NV ensemble. Thus, this approach enhances sensitivity by combining highly doped diamond substrates and elevated magnetic fields., Comment: 5 pages, 3 figures plus Supplemental Material

One of the first tasks we learn as children is to grasp objects based on our tactile perception. Incorporating such skill in robots will enable multiple applications, such as increasing flexibility in industrial processes or providing assistance to people with physical disabilities. However, the difficulty lies in adapting the grasping strategies to a large variety of tasks and objects, which can often be unknown. The brute-force solution is to learn new grasps by trial and error, which is inefficient and ineffective. In contrast, Bayesian optimization applies active learning by adding information to the approximation of an optimal grasp. This paper proposes the use of Bayesian optimization techniques to safely perform robotic grasping. We analyze different grasp metrics to provide realistic grasp optimization in a real system including tactile sensors. An experimental evaluation in the robotic system shows the usefulness of the method for performing unknown object grasping even in the presence of noise and uncertainty inherent to a real-world environment.

The location of the center of rotation (COR) of joints is a key parameter in multiple applications of human motion analysis. The aim of this work was to propose a novel real-time estimator of the center of fixed joints using an inertial measurement unit (IMU). Since the distance to this center commonly varies during the joint motion due to soft tissue artifacts (STA), our approach is aimed at adapting to these small variations when the COR is fixed. Our proposal, called ArVEd, to the best of our knowledge, is the first real-time estimator of the IMU-joint center vector based on one IMU. Previous works are off-line and require a complete measurement batch to be solved and most of them are not tested on the real scenario. The algorithm is based on an Extended Kalman Filter (EKF) that provides an adaptive vector to STA motion variations at each time instant, without requiring a pre-processing stage to reduce the level of noise. ArVEd has been tested through different experiments, including synthetic and real data. The synthetic data are obtained from a simulated spherical pendulum whose COR is fixed, considering both a constant and a variable IMU-joint vector, that simulates translational IMU motions due to STA. The results prove that ArVEd is adapted to obtain a vector per sample with an accuracy of 6.8$\pm$3.9 on the synthetic data, that means an error lower than 3.5% of the simulated IMU-joint vector. Its accuracy is also tested on the real scenario estimating the COR of the hip of 5 volunteers using as reference the results from an optical system. In this case, ArVEd gets an average error of 9.5% of the real vector value. In all the experiments, ArVEd outperforms the published results of the reference algorithms., Comment: \c{opyright} 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Inertial motion analysis is having a growing interest during the last decades due to its advantages over classical optical systems. The technological solution based on inertial measurement units allows the measurement of movements in daily living environments, such as in everyday life, which is key for a realistic assessment and understanding of movements. This is why research in this field is still developing and different approaches are proposed. This presents a systematic review of the different proposals for inertial motion analysis found in the literature. The search strategy has been carried out on eight different platforms, including journal articles and conference proceedings, which are written in English and published until August 2022. The results are analyzed in terms of the publishers, the sensors used, the applications, the monitored units, the algorithms of use, the participants of the studies, and the validation systems employed. In addition, we delve deeply into the machine learning techniques proposed in recent years and in the approaches to reduce the estimation error. In this way, we show an overview of the research carried out in this field, going into more detail in recent years, and providing some research directions for future work

This document introduces the PHYTMO database, which contains data from physical therapies recorded with inertial sensors, including information from an optical reference system. PHYTMO includes the recording of 30 volunteers, aged between 20 and 70 years old. A total amount of 6 exercises and 3 gait variations were recorded. The volunteers performed two series with a minimum of 8 repetitions in each one. PHYTMO includes magneto-inertial data, together with a highly accurate location and orientation in the 3D space provided by the optical system. The files were stored in CSV format to ensure its usability. The aim of this dataset is the availability of data for two main purposes: the analysis of techniques for the identification and evaluation of exercises using inertial sensors and the validation of inertial sensor-based algorithms for human motion monitoring. Furthermore, the database stores enough data to apply Machine Learning-based algorithms. The participants' age range is large enough to establish age-based metrics for the exercises evaluation or the study of differences in motions between different groups.

Home-based physical therapies are effective if the prescribed exercises are correctly executed and patients adhere to these routines. This is specially important for older adults who can easily forget the guidelines from therapists. Inertial Measurement Units (IMUs) are commonly used for tracking exercise execution giving information of patients' motion data. In this work, we propose the use of Machine Learning techniques to recognize which exercise is being carried out and to assess if the recognized exercise is properly executed by using data from four IMUs placed on the person limbs. To the best of our knowledge, both tasks have never been addressed together as a unique complex task before. However, their combination is needed for the complete characterization of the performance of physical therapies. We evaluate the performance of six machine learning classifiers in three contexts: recognition and evaluation in a single classifier, recognition of correct exercises, excluding the wrongly performed exercises, and a two-stage approach that first recognizes the exercise and then evaluates it. We apply our proposal to a set of 8 exercises of the upper-and lower-limbs designed for maintaining elderly people health status. To do so, the motion of volunteers were monitored with 4 IMUs. We obtain accuracies of 88.4 \% and the 91.4 \% in the two initial scenarios. In the third one, the recognition provides an accuracy of 96.2 \%, whereas the exercise evaluation varies between 93.6 \% and 100.0 \%. This work proves the feasibility of IMUs for a complete monitoring of physical therapies in which we can get information of which exercise is being performed and its quality, as a basis for designing virtual coaches.

This Thesis delves into the development and implementation of quantum algorithms using the digital-analog quantum computing (DAQC) paradigm. It provides a comparative analysis of the performance of DAQC versus traditional digital approaches, particularly in the presence of noise sources from current noisy intermediate-scale quantum (NISQ) devices. The DAQC paradigm combines the strengths of digital and analog quantum computing, offering greater efficiency and precision for implementing quantum algorithms on real hardware. The Thesis focuses on the comparison of four relevant quantum algorithms using digital and digital-analog approaches, and the results show significant advantages in favor of the latter. Furthermore, the Thesis investigates the cross-resonance effect to achieve efficient and high-precision Hamiltonian simulations. The findings indicate that the digital-analog paradigm is promising for practical quantum computing applications. Its ability to deliver greater efficiency and accuracy in implementing quantum algorithms on real hardware is a significant advantage over traditional digital approaches., Comment: PhD thesis

We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal decompositions that are linear over the base. These criteria are based on the base loci of the global or relative dualizing complexes., Comment: Final version with an appendix by Shinnosuke Okawa. To appear in Collectanea Mathematica

The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps the inverse of the problem matrix $A$ into an ancillary qubit. This makes challenging the implementation in current quantum devices, forcing us to use hybrid approaches. Here, we propose a systematic manner to implement this subroutine, which can be adapted to other functions $f(A)$ of the matrix $A$, we present a co-designed quantum processor which reduces the depth of the algorithm, and we introduce its digital-analog implementation. The depth of our proposal scales with the precision $\epsilon$ as $\mathcal{O}(\epsilon^{-1})$, which is bounded by the number of samples allowed for a certain experiment. The co-design of the Harrow-Hassidim-Lloyd algorithm leads to a "kite-like" architecture, which allows us to reduce the number of required SWAP gates. Finally, merging a co-design quantum processor architecture with a digital-analog implementation contributes to the reduction of noise sources during the experimental realization of the algorithm., Comment: 7 pages, 3 figures

Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that outperforms digital quantum computation by combining the flexibility of single-qubit gates with the robustness of analog simulations. This work explores the impact of noise on both digital and DAQC paradigms and demonstrates DAQC's effectiveness in error mitigation. We compare the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single and two-qubit noise sources in superconducting processors. DAQC consistently surpasses digital approaches in fidelity, particularly as processor size increases. Moreover, zero-noise extrapolation further enhances DAQC by mitigating decoherence and intrinsic errors, achieving fidelities above 0.95 for 8 qubits, and reducing computation errors to the order of $10^{-3}$. These results establish DAQC as a viable alternative for quantum computing in the NISQ era.

Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated by the systems' underlying Hamiltonian. Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on 1D chains and 2D square lattices which, in an appropriate reference frame, results in a purely two-local Hamiltonian. By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians. We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, $XY$, and Heisenberg spin models. Our dynamics simulations are Trotter error-free for the Ising and $XY$ models in 1D. We also show that the Trotter errors for 2D $XY$ and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor. In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations. We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.

The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the post-supremacy, noisy, intermediate scale era of quantum computing. In this work, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the variational quantum approximate optimisation algorithm, due to its inherent resilience against coherent errors, by performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation times. We observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over non-variational counterparts., Comment: 14 pages, 8 figures

Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. On its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the $5$-qubit IBMQX2 quantum computer for $2\times 2$ and $3\times 3$ cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This manuscript is a first step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future.

Mobile robots are increasingly being employed for performing complex tasks in dynamic environments. Reinforcement learning (RL) methods are recognized to be promising for specifying such tasks in a relatively simple manner. However, the strong dependency between the learning method and the task to learn is a well-known problem that restricts practical implementations of RL in robotics, often requiring major modifications of parameters and adding other techniques for each particular task. In this paper we present a practical core implementation of RL which enables the learning process for multiple robotic tasks with minimal per-task tuning or none. Based on value iteration methods, this implementation includes a novel approach for action selection, called Q-biased softmax regression (QBIASSR), which avoids poor performance of the learning process when the robot reaches new unexplored states. Our approach takes advantage of the structure of the state space by attending the physical variables involved (e.g., distances to obstacles, X,Y,{\theta} pose, etc.), thus experienced sets of states may favor the decision-making process of unexplored or rarely-explored states. This improvement has a relevant role in reducing the tuning of the algorithm for particular tasks. Experiments with real and simulated robots, performed with the software framework also introduced here, show that our implementation is effectively able to learn different robotic tasks without tuning the learning method. Results also suggest that the combination of true online SARSA({\lambda}) with QBIASSR can outperform the existing RL core algorithms in low-dimensional robotic tasks., Comment: 15 pages, 10 figures, 7 tables. To be published in a scientific journal

We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by Orlov, which maps equivalences to symplectic isomorphisms, is surjective., Comment: 19 pages, to appear in Journal of Geometry and Physics

We give necessary conditions for two (including non-reduced and multiple) Kodaira curves to be derived equivalent. We classify Fourier-Mukai partners of any reduced Kodaira curve. We prove that the derived category of singularities of any non-reduced and non-multiple Kodaira curve is idempotent complete., Comment: 23 pages

The objective of the paper is to prove that, as it happens for smooth elliptic curves, any Fourier-Mukai partner of a projective reduced Gorenstein curve of genus one and trivial dualising sheaf, is isomorphic to itself., Comment: 12 pages. Final version. To appear in J. Geom. Phys

We study the group of relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano or anti-Fano fibrations. For Weierstrass and Fano or anti-Fano fibrations we are able to describe this group completely. For abelian schemes over an arbitrary base we prove that if two of them are relative Fourier-Mukai partners then there is an isometric isomorphism between the fibre products of each of them and its dual abelian scheme. If the base is normal and the slope map is surjective we show that these two conditions are equivalent. Moreover in this situation we completely determine the group of relative Fourier-Mukai transforms and we prove that the number of relative Fourier-Mukai partners of a given abelian scheme over a normal base is finite., Comment: 25 pages. Updated introduction and minor changes. Final version will appear in Mathematical Proceedings of the Cambridge Philosophical Society

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli spaces of semistable sheaves on the curve. For rank zero, the moduli spaces are symmetric powers of the curve whilst for a fixed positive rank there are only a finite number of non-isomorphic spaces. We prove similar results for the relative semistable moduli spaces on an arbitrary genus one fibration with no conditions either on the base or on the total space. For a cycle $E_N$ of projective lines, we show that the unique degree 0 stable sheaves are the line bundles having degree 0 on every irreducible component and the sheaves $\mathcal{O}(-1)$ supported on one irreducible component. We also prove that the connected component of the moduli space that contains vector bundles of rank $r$ is isomorphic to the $r$-th symmetric product of the rational curve with one node., Comment: 26 pages, 4 figures. Added the structure of the biggest component of the moduli space of sheaves of degree 0 on a cycle of projective lines. Final version; to appear en IMRS (International Mathematics Research Notices 2009)