arXiv subjects

Andrés Gómez

Publications and source records attributed to Andrés Gómez.

At least 37 records · Page 2Linked to original sources

arXiv2025

NetQIR: An Extension of QIR for Distributed Quantum Computing

The rapid advancement of quantum computing has highlighted the need for scalable and efficient software infrastructures to fully exploit its potential. Current quantum processors face significant scalability constraints due to the limited number of qubits per chip. In response, distributed quantum computing (DQC) -- achieved by networking multiple quantum processor units (QPUs) -- is emerging as a promising solution. To support this paradigm, robust intermediate representations (IRs) are needed to translate high-level quantum algorithms into executable instructions suitable for distributed systems. This paper presents NetQIR, an extension of Microsoft's Quantum Intermediate Representation (QIR), specifically designed to facilitate DQC by incorporating new instruction specifications. NetQIR was developed in response to the lack of abstraction at the network and hardware layers identified in the existing literature as a significant obstacle to effectively implementing distributed quantum algorithms. Based on this analysis, NetQIR introduces new essential abstraction features to support compilers in DQC contexts. It defines network communication instructions independent of specific hardware, abstracting the complexities of inter-QPU communication. Leveraging the QIR framework, NetQIR aims to bridge the gap between high-level quantum algorithm design and low-level hardware execution, thus promoting modular and scalable approaches to quantum software infrastructures for distributed applications.

quant-ph↗

arXiv2025

Density Matrix Emulation of Quantum Recurrent Neural Networks for Multivariate Time Series Prediction

Quantum Recurrent Neural Networks (QRNNs) are robust candidates for modelling and predicting future values in multivariate time series. However, the effective implementation of some QRNN models is limited by the need for mid-circuit measurements. Those increase the requirements for quantum hardware, which in the current NISQ era does not allow reliable computations. Emulation arises as the main near-term alternative to explore the potential of QRNNs, but existing quantum emulators are not dedicated to circuits with multiple intermediate measurements. In this context, we design a specific emulation method that relies on density matrix formalism. Using a compact tensor notation, we provide the mathematical formulation of the operator-sum representation involved. This allows us to show how the present and past information from a time series is transmitted through the circuit, and how to reduce the computational cost in every time step of the emulated network. In addition, we derive the analytical gradient and the Hessian of the network outputs with respect to its trainable parameters, which are needed when the outputs have stochastic noise due to hardware errors and a finite number of circuit shots (sampling). We finally test the presented methods using a hardware-efficient ansatz and four diverse datasets that include univariate and multivariate time series, with and without sampling noise. In addition, we compare the model with other existing quantum and classical approaches. Our results show how QRNNs can be trained with numerical and analytical gradients to make accurate predictions of future values by capturing non-trivial patterns of input series with different complexities.

quant-ph↗

arXiv2024

Fair and Accurate Regression: Strong Formulations and Algorithms

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially-solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times.

cs.LG↗

arXiv2024

Convexification of Multi-period Quadratic Programs with Indicators

We study a multi-period convex quadratic optimization problem, where the state evolves dynamically as an affine function of the state, control, and indicator variables in each period. We begin by projecting out the state variables using linear dynamics, resulting in a mixed-integer quadratic optimization problem with a (block-) factorizable cost matrix. We discuss the properties of these matrices and derive a closed-form expression for their inverses. Employing this expression, we construct a closed convex hull representation of the epigraph of the quadratic cost over the feasible region in an extended space. Subsequently, we establish a tight second-order cone programming formulation with $\mathcal{O}(n^2)$ conic constraints. We further propose a polynomial-time algorithm based on a reformulation of the problem as a shortest path problem on a directed acyclic graph. To illustrate the applicability of our results across diverse domains, we present case studies in statistical learning and hybrid system control.

math.OC↗

arXiv2024

Real Option Pricing using Quantum Computers

In this work we present an alternative methodology to the standard Quantum Accelerated Monte Carlo (QAMC) applied to derivatives pricing. Our pipeline benefits from the combination of a new encoding protocol, referred to as the direct encoding, and a amplitude estimation algorithm, the modified Real Quantum Amplitude Estimation (mRQAE) algorithm. On the one hand, the direct encoding prepares a quantum state which contains the information about the sign of the expected payoff. On the other hand, the mRQAE is able to read all the information contained in the quantum state. Although the procedure we describe is different from the standard one, the main building blocks are almost the same. Thus, all the extensive research that has been performed is still applicable. Moreover, we experimentally compare the performance of the proposed methodology against the standard QAMC employing a quantum emulator and show that we retain the speedups.

quant-ph↗

arXiv2024

A Parametric Approach for Solving Convex Quadratic Optimization with Indicators Over Trees

This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive definite and its sparsity pattern corresponds to the adjacency matrix of a tree graph. We introduce a graph-based dynamic programming algorithm that solves this problem in time and memory complexity of $\mathcal{O}(n^2)$. Central to our algorithm is a precise parametric characterization of the cost function across various nodes of the graph corresponding to distinct variables. Our computational experiments conducted on both synthetic and real-world datasets demonstrate the superior performance of our proposed algorithm compared to existing algorithms and state-of-the-art mixed-integer optimization solvers. An important application of our algorithm is in the real-time inference of Gaussian hidden Markov models from data affected by outlier noise. Using a real on-body accelerometer dataset, we solve instances of this problem with over 30,000 variables in under a minute, and its online variant within milliseconds on a standard computer. A Python implementation of our algorithm is available at https://github.com/aareshfb/Tree-Parametric-Algorithm.git.

math.OC↗

arXiv2024

Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators

In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse graphical inference problems and others. We describe an explicit convex formulation for the problem by studying the Stieltjes polyhedron arising as part of an extended formulation and exploiting the supermodularity of a set function defined on its extreme points. Our computational results confirm that the proposed convex relaxation provides an exact optimal solution and may be an effective alternative, especially for instances with large integrality gaps that are challenging with the standard approaches.

math.OC↗

arXiv2024

Review of Distributed Quantum Computing. From single QPU to High Performance Quantum Computing

The emerging field of quantum computing has shown it might change how we process information by using the unique principles of quantum mechanics. As researchers continue to push the boundaries of quantum technologies to unprecedented levels, distributed quantum computing raises as an obvious path to explore with the aim of boosting the computational power of current quantum systems. This paper presents a comprehensive survey of the current state of the art in the distributed quantum computing field, exploring its foundational principles, landscape of achievements, challenges, and promising directions for further research. From quantum communication protocols to entanglement-based distributed algorithms, each aspect contributes to the mosaic of distributed quantum computing, making it an attractive approach to address the limitations of classical computing. Our objective is to provide an exhaustive overview for experienced researchers and field newcomers.

quant-ph↗

arXiv2024

Lorentz invariance violation and the CPT-odd electromagnetic response of a tilted anisotropic Weyl semimetal

We derive the electromagnetic response of a particular fermionic sector in the minimal QED contribution to the Standard Model Extension (SME), which can be physically realized in terms of a model describing a tilted and anisotropic Weyl semimetal (WSM). The contact is made through the identification of the Dirac-like Hamiltonian resulting from the SME with that corresponding to the WSM in the linearized tight-binding approximation. We first calculate the effective action by computing the non-perturbative vacuum polarization tensor using thermal field theory techniques, focusing upon the corrections at finite chemical potential and zero temperature. Next, we confirm our results by a direct calculation of the anomalous Hall current within a chiral kinetic theory approach. In an ideal Dirac cone picture of the WSM (isotropic and non-tilted) such response is known to be governed by axion electrodynamics, with the space-time dependent axion angle $Θ(\mathbf{r},t) = 2 (\mathbf{b} \cdot \mathbf{r} - b _{0} t)$, being $2 \mathbf{b}$ and $2b _{0}$ the separation of the Weyl nodes in momentum and energy, respectively. In this paper we demonstrate that the node tilting and the anisotropies induce novel corrections at a finite density which however preserve the structure of the axionic field theory. We apply our results to the ideal Weyl semimetal $\mathrm{EuCd}_{2}\mathrm{As}_{2}$ and to the highly anisotropic and tilted monopnictide $\mathrm{TaAs}$.

hep-th↗

arXiv2024

Robust support vector machines via conic optimization

We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus performing poorly in the setting considered. In contrast, using the 0-1 loss or a suitable non-convex approximation results in robust estimators, at the expense of large computational costs. In this paper we use mixed-integer optimization techniques to derive a new loss function that better approximates the 0-1 loss compared with existing alternatives, while preserving the convexity of the learning problem. In our computational results, we show that the proposed estimator is competitive with the standard SVMs with the hinge loss in outlier-free regimes and better in the presence of outliers.

cs.LG↗

arXiv2024

Interface-Driven Peptide Folding: Quantum Computations on Simulated Membrane Surfaces

Antimicrobial peptides (AMPs) play important roles in cancer, autoimmune diseases, and aging. A critical aspect of AMP functionality is their targeted interaction with pathogen membranes, which often possess altered lipid compositions. Designing AMPs with enhanced therapeutic properties relies on a nuanced understanding of these interactions, which are believed to trigger a rearrangement of these peptides from random coil to alpha-helical conformations, essential for their lytic action. Traditional supercomputing has consistently encountered difficulties in accurately modeling these structural changes, especially within membrane environments, thereby opening an opportunity for more advanced approaches. This study extends an existing quantum computing algorithm to address the complexities of antimicrobial peptide interactions at interfaces. Our approach enables the prediction of the optimal conformation of peptides located in the transition region between hydrophilic and hydrophobic phases, akin to lipid membranes. The new method has been applied to model the structure of three 10-amino-acid-long peptides, each exhibiting hydrophobic, hydrophilic, or amphipathic properties in different media and at interfaces between solvents of different polarity. Notably, our approach does not demand a higher number of qubits compared to simulations in homogeneous media, making it more feasible with current quantum computing resources. Despite existing limitations in computational power and qubit accessibility, our findings demonstrate the significant potential of quantum computing in accurately characterizing complex biomolecular processes, particularly the folding of AMPs at membrane models. This research paves the way for future advances in quantum computing to enhance the accuracy and applicability of biomolecular simulations.

quant-ph↗

arXiv2023

Bound states from the spectral Bethe-Salpeter equation

We compute the bound state properties of three-dimensional scalar $ϕ^4$ theory in the broken phase. To this end, we extend the recently developed technique of spectral Dyson-Schwinger equations to solve the Bethe-Salpeter equation and determine the bound state spectrum. We employ consistent truncations for the two-, three- and four-point functions of the theory that recover the scaling properties in the infinite coupling limit. Our result for the mass of the lowest-lying bound state in this limit agrees very well with lattice determinations.

hep-ph↗

arXiv2023

Using Differential Evolution to avoid local minima in Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era algorithms for harnessing quantum computing in diverse fields. However, the underlying optimization processes within these algorithms usually deal with local minima and barren plateau problems, preventing them from scaling efficiently. Our goal in this paper is to study alternative optimization methods that can avoid or reduce the effect of these problems. To this end, we propose to apply the Differential Evolution (DE) algorithm to VQAs optimizations. Our hypothesis is that DE is resilient to vanishing gradients and local minima for two main reasons: (i) it does not depend on gradients, and (ii) its mutation and recombination schemes allow DE to continue evolving even in these cases. To demonstrate the performance of our approach, first, we use a robust local minima problem to compare state-of-the-art local optimizers (SLSQP, COBYLA, L-BFGS-B and SPSA) against DE using the Variational Quantum Eigensolver algorithm. Our results show that DE always outperforms local optimizers. In particular, in exact simulations of a 1D Ising chain with 14 qubits, DE achieves the ground state with a 100\% success rate, while local optimizers only exhibit around 40\%. We also show that combining DE with local optimizers increases the accuracy of the energy estimation once avoiding local minima. Finally, we demonstrate how our results can be extended to more complex problems by studying DE performance in a 1D Hubbard model.

quant-ph↗

arXiv2023

Compact extended formulations for low-rank functions with indicator variables

We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are defined as compositions of low-dimensional nonlinear functions with affine functions Extended formulations describing the convex hull of such sets can easily be constructed via disjunctive programming, although a direct application of this method often yields prohibitively large formulations, whose size is exponential in the number of variables. In this paper, we propose a new disjunctive representation of the sets under study, which leads to compact formulations with size exponential in the dimension of the nonlinear function, but polynomial in the number of variables. Moreover, we show how to project out the additional variables for the case of dimension one, recovering or generalizing known results for the convex hulls of such sets (in the original space of variables). Our computational results indicate that the proposed approach can significantly improve the performance of solvers in structured problems.

math.OC↗

arXiv2023

Influence of Initial Entangled States on the Temperature-Dependent CHSH Inequality

We demonstrate that the temperature affects the validity of the CHSH inequality in an open bipartite two-qubit system. Specifically, for initial entangled states within the decoherence-free subspace (DFS), the CHSH inequality remains temperature-independent. In contrast, other entangled states exhibit a temperature threshold beyond which the inequality holds.

quant-ph↗

arXiv2023

Learning Optimal Fair Classification Trees: Trade-offs Between Interpretability, Fairness, and Accuracy

The increasing use of machine learning in high-stakes domains -- where people's livelihoods are impacted -- creates an urgent need for interpretable, fair, and highly accurate algorithms. With these needs in mind, we propose a mixed integer optimization (MIO) framework for learning optimal classification trees -- one of the most interpretable models -- that can be augmented with arbitrary fairness constraints. In order to better quantify the "price of interpretability", we also propose a new measure of model interpretability called decision complexity that allows for comparisons across different classes of machine learning models. We benchmark our method against state-of-the-art approaches for fair classification on popular datasets; in doing so, we conduct one of the first comprehensive analyses of the trade-offs between interpretability, fairness, and predictive accuracy. Given a fixed disparity threshold, our method has a price of interpretability of about 4.2 percentage points in terms of out-of-sample accuracy compared to the best performing, complex models. However, our method consistently finds decisions with almost full parity, while other methods rarely do.

cs.LG↗

arXiv2023

Learning Optimal Prescriptive Trees from Observational Data

We consider the problem of learning an optimal prescriptive tree (i.e., an interpretable treatment assignment policy in the form of a binary tree) of moderate depth, from observational data. This problem arises in numerous socially important domains such as public health and personalized medicine, where interpretable and data-driven interventions are sought based on data gathered in deployment -- through passive collection of data -- rather than from randomized trials. We propose a method for learning optimal prescriptive trees using mixed-integer optimization (MIO) technology. We show that under mild conditions our method is asymptotically exact in the sense that it converges to an optimal out-of-sample treatment assignment policy as the number of historical data samples tends to infinity. Contrary to existing literature, our approach: 1) does not require data to be randomized, 2) does not impose stringent assumptions on the learned trees, and 3) has the ability to model domain specific constraints. Through extensive computational experiments, we demonstrate that our asymptotic guarantees translate to significant performance improvements in finite samples, as well as showcase our uniquely flexible modeling power by incorporating budget and fairness constraints.

cs.LG↗

arXiv2023

Strong Optimal Classification Trees

Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary classification trees with univariate splits. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer optimization (MIO) technology. Yet, existing MIO-based approaches from the literature do not leverage the power of MIO to its full extent: they rely on weak formulations, resulting in slow convergence and large optimality gaps. To fill this gap in the literature, we propose an intuitive flow-based MIO formulation for learning optimal binary classification trees. Our formulation can accommodate side constraints to enable the design of interpretable and fair decision trees. Moreover, we show that our formulation has a stronger linear optimization relaxation than existing methods in the case of binary data. We exploit the decomposable structure of our formulation and max-flow/min-cut duality to derive a Benders' decomposition method to speed-up computation. We propose a tailored procedure for solving each decomposed subproblem that provably generates facets of the feasible set of the MIO as constraints to add to the main problem. We conduct extensive computational experiments on standard benchmark datasets on which we show that our proposed approaches are 29 times faster than state-of-the-art MIO-based techniques and improve out-of-sample performance by up to 8%.

cs.LG↗