Gradients and frequency profiles of quantum re-uploading models

Quantum re-uploading models have been extensively investigated as a form of machine learning within the context of variational quantum algorithms. Their trainability and expressivity are not yet fully understood and are critical to their performance. In this work, we address trainability through the lens of the magnitude of the gradients of the cost function. We prove bounds for the differences between gradients of the better-studied data-less parameterized quantum circuits and re-uploading models. We coin the concept of {\sl absorption witness} to quantify such difference. For the expressivity, we prove that quantum re-uploading models output functions with vanishing high-frequency components and upper-bounded derivatives with respect to data. As a consequence, such functions present limited sensitivity to fine details, which protects against overfitting. We performed numerical experiments extending the theoretical results to more relaxed and realistic conditions. Overall, future designs of quantum re-uploading models will benefit from the strengthened knowledge delivered by the uncovering of absorption witnesses and vanishing high frequencies

Analyzing variational quantum landscapes with information content

The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of information content, a measure of the variability between points in parameter space. Our major contribution connects the information content to the average norm of the gradient, for which we provide robust analytical bounds on its estimators. This result holds for any (classical or quantum) variational landscape. We validate the analytical understating by numerically studying the scaling of the gradient in an instance of the barren plateau problem. In such instance we are able to estimate the scaling pre-factors in the gradient. Our work provides a new way to analyze variational quantum algorithms in a data-driven fashion well-suited for near-term quantum computers.Comment: 8 pages + 6 pages appendix + 2 pages references, 5 figures, 6 tables. Peer-reviewed version published in npj quantum informatio

Measuring the tangle of three-qubit states

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses the validity of the method

Reducing-effect of chloride for the dissolution of black copper

Oxidized black copper ores are known for their difficulty in dissolving their components of interest through conventional methods. This is due to its non-crystalline and amorphous structure. Among these minerals, copper pitch and copper wad are of great interest because of their considerable concentrations of copper and manganese. Currently, these minerals are not incorporated into the extraction circuits or left untreated, whether in stock, leach pads, or waste. For the recovery of its main elements of interest (Cu and Mn), it is necessary to use reducing agents that dissolve the present MnO2, while allowing the recovery of Cu. In this research, the results for the dissolution of Mn and Cu from a black copper mineral are exposed, evaluating the reducing e↵ect of NaCl for MnO2 through pre-treatment of agglomerate and curing, and subsequently leaching in standard condition with the use of a reducing agent (Fe2+). High concentrations of chloride in the agglomerate process and prolonged curing times would favor the reduction of MnO2, increasing the dissolution of Mn, while the addition of NaCl did not benefit Cu extractions. Under standard conditions, low Mn extractions were obtained, while in an acid-reducing medium, a significant dissolution of MnO2 was achieved, which supports the removal of Cu

Proteína C reactiva, marcador inflamatorio asociado con ANCA en tuberculosis pulmonar

Antecedentes: la proteína C reactiva es uno de los marcadores inflamatorios denominados “reactantes de fase aguda” que se produce en el hígado en respuesta a procesos infecciosos o inflamatorios. En los pacientes con tuberculosis se ha descrito la formación de anticuerpos anticitoplasma de neutrófi los (ANCA). Objetivo: determinar la concentración de proteína C reactiva, evaluar su comportamiento como marcador de la respuesta inflamatoria y analizar su correlación con los ANCA en los pacientes con tuberculosis pulmonar, antes y después de iniciar el tratamiento antifímico. Pacientes: se eligieron pacientes con sospecha de tuberculosis pulmonar. Una vez confirmado el diagnóstico, se obtuvieron las muestras de suero para analizar los datos clínicos y de laboratorios. La determinación de ANCA se realizó con estuches comerciales de inmunofluorescencia y la de proteína C reactiva con ELISA, antes y después de iniciar el tratamiento antifímico. Resultados: se obtuvieron 50 muestras de suero de pacientes con tuberculosis pulmonar. En la primera (94%) y segunda obtención (90%) de los sueros se registró un valor de proteína C reactiva menor de 5 mg/L. El valor promedio de proteína C reactiva fue de 3.05 ± 8.27 mg/L en la primera muestra y de 4.49 ± 11.2 mg/L en la segunda (p = 0.46). Los pacientes positivos a ANCA tuvieron valores más altos de proteína C reactiva en su segunda muestra (p = 0.001). Discusión: existe una asociación entre la proteína C reactiva y la producción de anticuerpos anticitoplasma de neutrófilos en un subgrupo de pacientes con tuberculosis pulmonar. Su significación es incierta, pero quizá desempeñan alguna función patogénica en la respuesta inflamatoria pulmonar

Quantum unary approach to option pricing

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude distribution corresponding to the asset value at maturity is generated using a low depth circuit; second, the computation of the expected return is computed with simple controlled gates; and third, standard Amplitude Estimation is used to gain quantum advantage. On the positive side, unary representation remarkably simplifies the structure and depth of the quantum circuit. Amplitude distributions uses quantum superposition to bypass the role of classical Monte Carlo simulation. The unary representation also provides a post-selection consistency check that allows for a substantial mitigation in the error of the computation. On the negative side, unary representation requires linearly many qubits to represent a target probability distribution, as compared to the logarithmic scaling of binary algorithms. We compare the performance of both unary vs. binary option pricing algorithms using error maps, and find that unary representation may bring a relevant advantage in practice for near-term devices.Comment: 14 (main) + 10 (appendix) pages, 22 figures. Final peer-reviewed version, published in PRA. All suggestions from the referees have been considered. We thank the referees and the journal for all the wor

A RISC-V simulator and benchmark suite for designing and evaluating vector architectures

Vector architectures lack tools for research. Consider the gem5 simulator, which is possibly the leading platform for computer-system architecture research. Unfortunately, gem5 does not have an available distribution that includes a flexible and customizable vector architecture model. In consequence, researchers have to develop their own simulation platform to test their ideas, which consume much research time. However, once the base simulator platform is developed, another question is the following: Which applications should be tested to perform the experiments? The lack of Vectorized Benchmark Suites is another limitation. To face these problems, this work presents a set of tools for designing and evaluating vector architectures. First, the gem5 simulator was extended to support the execution of RISC-V Vector instructions by adding a parameterizable Vector Architecture model for designers to evaluate different approaches according to the target they pursue. Second, a novel Vectorized Benchmark Suite is presented: a collection composed of seven data-parallel applications from different domains that can be classified according to the modules that are stressed in the vector architecture. Finally, a study of the Vectorized Benchmark Suite executing on the gem5-based Vector Architecture model is highlighted. This suite is the first in its category that covers the different possible usage scenarios that may occur within different vector architecture designs such as embedded systems, mainly focused on short vectors, or High-Performance-Computing (HPC), usually designed for large vectors.This work is partially supported by CONACyT Mexico under Grant No. 472106 and the DRAC project, which is co-financed by the European Union Regional Development Fund within the framework of the ERDF Operational Program of Catalonia 2014-2020 with a grant of 50% of total cost eligible.Peer ReviewedPostprint (published version