arXiv subjects

Víctor Valls

Publications and source records attributed to Víctor Valls.

18 recordsLinked to original sources

arXiv2026

Forecasting Quantum Observables: A Compressed Sensing Approach with Performance Guarantees

Data-driven extrapolation methods aim to extend the dynamics of quantum observables from measurements, but they often lack guarantees on prediction accuracy. We introduce a framework based on atomic norm minimization that can certify whether the spectral model learned by a forecasting algorithm -- i.e., Bohr frequencies and amplitudes -- is consistent with unitary quantum time evolution. Certification holds when the dynamics are governed by a small number of well-separated Bohr frequencies. We validate the approach on multiple forecasting algorithms applied to spin-chain Hamiltonians with 8--20 sites. Comparing with exact diagonalization, certified models yield an average forecasting error below 0.1 (observable range $[-1, 1]$) in 97\% of cases and below 0.05 in 91--99\% of cases. Even in the presence of noise, certified models remain robust at the 0.1 error threshold.

quant-ph↗

arXiv2025

Boosting Sparsity in Graph Decompositions with QAOA Sampling

We study the problem of decomposing a graph into a weighted sum of a small number of matchings, a task that arises in network resource allocation problems such as peer-to-peer energy exchange. Computing such decompositions is challenging for classical algorithms, even for small instances. To address this problem, we propose E-FCFW, a hybrid quantum-classical algorithm based on the Fully-Corrective Frank-Wolfe (FCFW) algorithm that incorporates a matching-sampling subroutine. We design a QAOA version of this subroutine and benchmark it against classical approaches (random sampling and simulated annealing) on demand graphs derived from complete, bipartite, and heavy-hex topologies. The quantum subroutine is executed using the Qiskit Aer state-vector and MPS simulators and on IBM Kingston hardware (7-111 qubits). On complete and bipartite graphs with 6-10 nodes, E-FCFW with QAOA yields consistently sparser decompositions than the classical baselines, and even beats the best-known solution for one instance. On heavy-hex graphs with 50, 70 and 100 nodes, E-FCFW with QAOA outperforms the other methods in terms of approximation error, demonstrating performance on utility-scale quantum hardware. For the largest graphs (100 nodes) E-FCFW with QAOA performs much better when using MPS circuit simulation, compared to using quantum hardware. This indicates that at this scale, the performance is severely impacted by hardware noise.

quant-ph↗

arXiv2024

Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data

Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which covariant kernels provide a provable advantage, thus establishing a separation between quantum and classical learners. However, their practical application poses two challenges: on one side, the group structure may be unknown and approximate in real-world data, and on the other side, scaling to the `utility' regime (above 100 qubits) is affected by exponential concentration. In this work, we address said challenges by applying fidelity kernels to real-world data with unknown structure, related to the scheduling of a fleet of electric vehicles, and to synthetic data generated from the union of subspaces, which is then close to many relevant real-world datasets. Furthermore, we propose a novel error mitigation strategy specifically tailored for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate the exponential concentration in our utility-scale experiments. Our multiclass classification reaches accuracies comparable to classical SVCs up to 156 qubits, thus constituting the largest experimental demonstration of quantum machine learning on IBM devices to date. For the real-world data experiments, the effect of the proposed BFT becomes manifest on 40+ qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through the union-of-subspace synthetic dataset with 156 qubits, we demonstrate a mitigated accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum, using a test set of limited size.

quant-ph↗

arXiv2024

Throughput-Optimal Scheduling via Rate Learning

We study the problem of designing scheduling policies for communication networks. This problem is often addressed with max-weight-type approaches since they are throughput-optimal. However, max-weight policies make scheduling decisions based on the network congestion, which can be sometimes unnecessarily restrictive. In this paper, we present a ``schedule as you learn'' (SYL) approach, where we learn an average rate, and then select schedules that generate such a rate in expectation. This approach is interesting because scheduling decisions do not depend on the size of the queue backlogs, and so it provides increased flexibility to select schedules based on other criteria or rules, such as serving high-priority queues. We illustrate the results with numerical experiments for a cross-bar switch and show that, compared to max-weight, SYL can achieve lower latency to certain flows without compromising throughput optimality.

cs.NI↗

arXiv2024

A Machine Learning Approach to Boost the Vehicle-2-Grid Scheduling

Electric Vehicles (EVs) are emerging as battery energy storage systems (BESSs) of increasing importance for different power grid services. However, the unique characteristics of EVs makes them more difficult to operate than dedicated BESSs. In this work, we apply a data-driven learning approach to leverage EVs as a BESS to provide capacity-related services to the grid. The approach uses machine learning to predict how to charge and discharge EVs while satisfying their operational constraints. As a paradigm application, we use flexible energy commercialization in the wholesale markets, but the approach can be applied to a broader range of capacity-related grid services. We evaluate the proposed approach numerically and show that when the number of EVs is large, we can obtain comparable objective values to CPLEX and approximate dynamic programming, but with shorter run times. These reduced run times are important because they allow us to (re)optimize frequently to adapt to the time-varying system conditions.

math.OC↗

arXiv2024

A Brief Introduction to Quantum Network Control

Quantum networking is an emerging area with the potential to transform information processing and communications. In this paper, we present a brief introduction to quantum network control, an area in quantum networking dedicated to designing algorithms for distributing entanglement (i.e., entangled qubits). We start by explaining what qubits and entanglement are and how they furnish quantum network control operations such as entanglement swapping and teleportation. With those operations, we present a model for distributing entanglement in a multi-hop quantum network to enable applications such as quantum key distribution and distributed quantum computing. We conclude the paper by presenting open research problems in the field, including the characterization of the quantum network capacity region and the design of throughput-optimal policies.

math.OC↗

arXiv2024

On the Capacity of the Quantum Switch with and without Entanglement Decoherence

This paper studies the capacity of the quantum switch for two decoherence models: when link-level entanglements last (i) for a time slot, or (ii) until they are used to serve a request (i.e., there is no decoherence). The two models are important as they set lower and upper bounds on the capacity region for any other decoherence model. The paper's contributions are to characterize the switch capacity region for both decoherence models and to propose throughput-optimal policies based on gradient descent.

math.OC↗

arXiv2023

Otter-Knowledge: benchmarks of multimodal knowledge graph representation learning from different sources for drug discovery

Recent research on predicting the binding affinity between drug molecules and proteins use representations learned, through unsupervised learning techniques, from large databases of molecule SMILES and protein sequences. While these representations have significantly enhanced the predictions, they are usually based on a limited set of modalities, and they do not exploit available knowledge about existing relations among molecules and proteins. In this study, we demonstrate that by incorporating knowledge graphs from diverse sources and modalities into the sequences or SMILES representation, we can further enrich the representation and achieve state-of-the-art results for drug-target binding affinity prediction in the established Therapeutic Data Commons (TDC) benchmarks. We release a set of multimodal knowledge graphs, integrating data from seven public data sources, and containing over 30 million triples. Our intention is to foster additional research to explore how multimodal knowledge enhanced protein/molecule embeddings can improve prediction tasks, including prediction of binding affinity. We also release some pretrained models learned from our multimodal knowledge graphs, along with source code for running standard benchmark tasks for prediction of biding affinity.

cs.LG↗

arXiv2023

Information Flow in Graph Neural Networks: A Clinical Triage Use Case

Graph Neural Networks (GNNs) have gained popularity in healthcare and other domains due to their ability to process multi-modal and multi-relational graphs. However, efficient training of GNNs remains challenging, with several open research questions. In this paper, we investigate how the flow of embedding information within GNNs affects the prediction of links in Knowledge Graphs (KGs). Specifically, we propose a mathematical model that decouples the GNN connectivity from the connectivity of the graph data and evaluate the performance of GNNs in a clinical triage use case. Our results demonstrate that incorporating domain knowledge into the GNN connectivity leads to better performance than using the same connectivity as the KG or allowing unconstrained embedding propagation. Moreover, we show that negative edges play a crucial role in achieving good predictions, and that using too many GNN layers can degrade performance.

cs.LG↗

arXiv2023

Full Exploitation of Limited Memory in Quantum Entanglement Switching

We study the problem of operating a quantum switch with memory constraints. In particular, the switch has to allocate quantum memories to clients to generate link-level entanglements (LLEs), and then use these to serve end-to-end entanglements requests. The paper's main contributions are (i) to characterize the switch's capacity region, and (ii) to propose a memory allocation policy (MEW) that is throughput optimal. The worst-case time complexity of MEW is exponential on the system parameters. However, when the requests are bipartite and the LLE attempts are always successful, we propose a variant of MEW (MEW2) that has polynomial time complexity. We evaluate the proposed policies numerically and illustrate their performance depending on the requests arrivals characteristics and the time available to obtain a memory allocation.

cs.NI↗

arXiv2022

Accelerated Convex Optimization with Stochastic Gradients: Generalizing the Strong-Growth Condition

This paper presents a sufficient condition for stochastic gradients not to slow down the convergence of Nesterov's accelerated gradient method. The new condition has the strong-growth condition by Schmidt \& Roux as a special case, and it also allows us to (i) model problems with constraints and (ii) design new types of oracles (e.g., oracles for finite-sum problems such as SAGA). Our results are obtained by revisiting Nesterov's accelerated algorithm and are useful for designing stochastic oracles without changing the underlying first-order method.

math.OC↗

arXiv2020

Birkhoff's Decomposition Revisited: Sparse Scheduling for High-Speed Circuit Switches

Data centers are increasingly using high-speed circuit switches to cope with the growing demand and reduce operational costs. One of the fundamental tasks of circuit switches is to compute a sparse collection of switching configurations to support a traffic demand matrix. Such a problem has been addressed in the literature with variations of the approach proposed by Birkhoff in 1946 to decompose a doubly stochastic matrix exactly. However, the existing methods are heuristic and do not have theoretical guarantees on how well a collection of switching configurations (i.e., permutations) can approximate a traffic matrix (i.e., a scaled doubly stochastic matrix). In this paper, we revisit Birkhoff's approach and make three contributions. First, we establish the first theoretical bound on the sparsity of Birkhoff's algorithm (i.e., the number of switching configurations necessary to approximate a traffic matrix). In particular, we show that by using a subset of the admissible permutation matrices, Birkhoff's algorithm obtains an $ε$-approximate decomposition with at most $O( \log(1 / ε))$ permutations. Second, we propose a new algorithm, Birkhoff+, which combines the wealth of Frank-Wolfe with Birkhoff's approach to obtain sparse decompositions in a fast manner. And third, we evaluate the performance of the proposed algorithm numerically and study how this affects the performance of a circuit switch. Our results show that Birkhoff+ is superior to previous algorithms in terms of throughput, running time, and number of switching configurations.

math.OC↗

arXiv2019

Online Convex Optimization with Perturbed Constraints

This paper addresses Online Convex Optimization (OCO) problems where the constraints have additive perturbations that (i) vary over time and (ii) are not known at the time to make a decision. Perturbations may not be i.i.d. generated and can be used to model a time-varying budget or commodity in resource allocation problems. The problem is to design a policy that obtains sublinear regret while ensuring that the constraints are satisfied on average. To solve this problem, we present a primal-dual proximal gradient algorithm that has $O(T^ε\vee T^{1-ε})$ regret and $O(T^ε)$ constraint violation, where $ε\in [0,1)$ is a parameter in the learning rate. Our results match the bounds of previous work on OCO with time-varying constraints when $ε= 1/2$; however, we (i) define the regret using a time-varying set of best fixed decisions; (ii) can balance between regret and constraint violation; and (iii) use an adaptive learning rate that allows us to run the algorithm for any time horizon.

math.OC↗

arXiv2018

A Convex Optimization Approach to Discrete Optimal Control

In this paper, we bring the celebrated max-weight features (myopic and discrete actions) to mainstream convex optimization. Myopic actions are important in control because decisions need to be made in an online manner and without knowledge of future events, and discrete actions because many systems have a finite (so non-convex) number of control decisions. For example, whether to transmit a packet or not in communication networks. Our results show that these two features can be encompassed in the subgradient method for the Lagrange dual problem by the use of stochastic and $ε$-subgradients. One of the appealing features of our approach is that it decouples the choice of a control action from a specific choice of subgradient, which allows us to design control policies without changing the underlying convex updates. Two classes of discrete control policies are presented: one that can make discrete actions by looking only at the system's current state, and another that selects actions using blocks. The latter class is useful for handling systems that have constraints on the order in which actions are selected.

math.OC↗

arXiv2015

Descent With Approximate Multipliers is Enough: Generalising Max-Weight

We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is orthogonal to the choice of multipliers. Using the Skorokhod representation for a queueing process we show that approximate multipliers can be constructed in a number of ways. These observations lead to the generalisation of (i) essentially any descent method to encompass use of discrete actions and queues and (ii) max-weight scheduling to encompass new descent methods including those with unsynchronised updates such as block coordinate descent. This also allows consideration of communication delays and of updates at varying time-scales within the same clean and consistent framework.

math.OC↗

arXiv2015

Max-Weight Revisited: Sequences of Non-Convex Optimisations Solving Convex Optimisations

We investigate the connections between max-weight approaches and dual subgradient methods for convex optimisation. We find that strong connections exist and we establish a clean, unifying theoretical framework that includes both max-weight and dual subgradient approaches as special cases. Our analysis uses only elementary methods, and is not asymptotic in nature. It also allows us to establish an explicit and direct connection between discrete queue occupancies and Lagrange multipliers.

math.OC↗

arXiv2014

Proportional Fair MU-MIMO in 802.11 WLANs

We consider the proportional fair rate allocation in an 802.11 WLAN that supports multi-user MIMO (MU-MIMO) transmission by one or more stations. We characterise, for the first time, the proportional fair allocation of MU-MIMO spatial streams and station transmission opportunities. While a number of features carry over from the case without MU-MIMO, in general neither flows nor stations need to be allocated equal airtime when MU-MIMO is available.

cs.NI↗

arXiv2012

Hierarchical Range Sectoring and Bidirectional Link Quality Estimation for On-demand Collections in WSNs

The paper presents two mechanisms for designing an on-demand, reliable and efficient collection protocol for Wireless Sensor Networks. The former is the Bidirectional Link Quality Estimation, which allows nodes to easily and quickly compute the quality of a link between a pair of nodes. The latter, Hierarchical Range Sectoring, organizes sensors in different sectors based on their location within the network. Based on this organization, nodes from each sector are coordinated to transmit in specific periods of time to reduce the hidden terminal problem. To evaluate these two mechanisms, a protocol called HBCP (Hierarchical-Based Collection Protocol), that implements both mechanisms, has been implemented in TinyOS 2.1, and evaluated in a testbed using TelosB motes. The results show that the HBCP protocol is able to achieve a very high reliability, especially in large networks and in scenarios with bottlenecks.

cs.NI↗