arXiv subjects

David E. Bernal Neira

Publications and source records attributed to David E. Bernal Neira.

At least 19 recordsLinked to original sources

arXiv2026

AI Agent Swarms as Researchers: Progress, Challenges, and Open Questions

Artificial intelligence (AI) agents, language models connected to tools and run in a loop, can now carry out long, multi-step tasks with little supervision. We gave swarms of off-the-shelf coding agents a short statement of scope, from a narrow topic to a whole field, access to the literature and to computing tools, and one standing instruction: make real, correct, useful progress, and do not stop. We supplied no scientific ideas. Within weeks, the agents produced a large body of research notes, paper-length drafts, and formal proofs in five areas of optimization theory and physical science, and proposed untested laboratory experiments in a sixth. We do not claim that all of it is correct or new, but it is not noise: in what we have checked so far, we found no major scientific error, and several results are proved in a proof assistant. The agents produced results faster than we could review them; we estimate that a full review would take us months. Together with two widely discussed 2026 results in mathematics obtained with swarms, our runs suggest that agents can already do a large part of routine theoretical research, at least in areas that we experimented with. This raises questions we cannot yet answer: how to trust results when review, not production, is the scarce resource; what credit and publication counts mean when the human input is a prompt, and why institutions would pay researchers rather than buy computing time; and how people can learn a field, add to what agents do, and stay in control of research they cannot keep up with. Research institutions are not ready: models improve faster than institutions change, so they should decide now how to respond as capabilities increase. We offer tentative positions, release the agents' unedited output as of 25 September 2026, and invite readers to repeat the experiment in their own fields.

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arXiv2026

Setting angles in quantum approximate optimization at utility-scale

The quantum approximate optimization algorithm (QAOA) is a powerful heuristic that seeks to solve combinatorial optimization problems using quantum hardware and classical optimization in tandem. Various methods exist to train the parameterized quantum circuits that serve as an ansatz in QAOA. However, which method works best to identify optimal angles for a given problem instance remains poorly understood, especially at utility-scale, i.e., $100$ qubits or more. In this work, we address this challenge through utility-scale benchmarks from which we distill operational guidance for QAOA practitioners. First, we investigate approximation techniques, such as matrix product states and Pauli propagation, to find optimal angles. Second, we train QAOA on small-scale representative problems and transfer the angles to larger ones. We then validate the results on quantum hardware for utility-scale problem instances that can be meaningfully executed. In this way, we identify insights for QAOA angle setting strategies that work best for problems at the utility scale, including as a function of resource cost for the search. Crucially, the operational implications we draw from our benchmarks will help quantum optimization practitioners execute QAOA end-to-end pipelines efficiently on current and future hardware.

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arXiv2026

Probing the Ground State of the Antiferromagnetic Heisenberg Model on the Kagome Lattice using Geometrically Informed Variational Quantum Eigensolver

This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver (VQE) algorithm on real quantum hardware. We demonstrate that the ground state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation (SPSA). We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubit-wise readout error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.

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arXiv2026

Quantum Preconditioning For Constrained Optimization Problems

We study the effect of quantum preconditioning on constrained combinatorial optimization problems, focusing on balanced graph bi-partitioning. The proposed approach uses two-point correlations between decision variables derived from the Quantum Approximate Optimization Algorithm (QAOA) to construct a modified objective function that is subsequently provided to mixed-integer programming (MIP) solvers. The preconditioned MIP formulation retains the original hard constraint, and all incumbent solutions are evaluated under the original objective. Computational experiments on dense, weighted complete-graph instances show that the preconditioned problem instances reach near-optimal solutions faster, with most of the benefit already realized at the shallowest QAOA depth tested. Solver callback trajectories show this arises from earlier discovery of high-quality incumbents during the solution search. These results support a hybrid optimization framework in which quantum algorithms provide problem-specific information to guide classical exact MIP solvers.

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arXiv2026

Optimizing QAOA circuit transpilation with parity twine and SWAP network encodings

Mapping quantum approximate optimization algorithm (QAOA) circuits with non-trivial connectivity in fixed-layout quantum platforms, such as superconducting quantum processing units (QPUs), requires a transpilation process to match the circuit to the hardware layout. This step is critical for reducing error rates on noisy QPUs. Two approaches that improve the resources required for such transpilation are the SWAP network and parity twine chains (PTC), which reduce the two-qubit gate count and circuit depth needed to represent fully connected circuits. In this work, we introduce a simulated annealing-based method that further reduces the encoding overhead of PTC and SWAP networks for QAOA circuits with non-fully connected two-qubit interactions. The method is benchmarked against various transpilers, including the Qiskit SAT mapper, demonstrating that beyond specific connectivity thresholds it achieves significant reductions in both two-qubit gate count and circuit depth. For example, for a 120-qubit QAOA instance with 25% connectivity, our method achieves an 87\% reduction in depth and a 29% reduction in two-qubit gates compared to the Qiskit transpiler. Finally, the practical impact of PTC encoding is validated by benchmarking QAOA on the ibm_fez and ibm_kingston devices, showing improved performance for systems of up to 20 qubits.

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arXiv2026

QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization

We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of optimization problems in JuMP, Julia's mathematical programming package, for straightforward application in many physics and physics-inspired solution methods whose standard model form is equivalent to QUBO. These methods include quantum annealing, quantum gate-circuit optimization algorithms (Quantum Optimization Alternating Ansatz, Variational Quantum Eigensolver), other hardware-accelerated platforms, such as Coherent Ising Machines and Simulated Bifurcation Machines, and more traditional methods such as simulated annealing. In addition to working with reformulations, QUBO.jl allows its users to interface with the aforementioned hardware, sending QUBO models to these devices and retrieving results for subsequent analysis. QUBO.jl was written as a JuMP / MathOptInterface (MOI) layer that automatically maps between the input and output frames, thus providing a smooth modeling experience.

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arXiv2026

Leveraging Classical and Quantum Computing for Process Systems Engineering Applications: Decomposition Algorithm with Ising Solvers for Efficient Discrete Landscape Exploration

Conceptual process design is a crucial aspect of chemical engineering that involves process synthesis. Mixed-integer nonlinear programming is a powerful framework for modeling such design problems by combining discrete and continuous variables; however, the combinatorial complexity of discrete choices, coupled with nonlinearities, presents challenging monolithic problems. Using decomposition, discrete subproblems can potentially benefit from Ising solvers, while simulators and nonlinear solvers offer powerful tools for handling nonlinearities. This work aims to: evaluate use of Ising-based solvers for discrete optimization and holistic process optimization through two case studies: an ionic liquid selection and its process design, and a more complex problem of drug manufacturing process optimization. The discrete subproblem is formulated as an integer program or quadratic unconstrained binary optimization and solved using a commercial classical or Ising solvers such as simulated annealing (SA), quantum annealing (QA), and entropy computing (EC) respectively. The commercial classical solver had the shortest runtime, whereas EC took the longest, followed by QA and SA, in reaching feasible and optimal solutions. The heuristics identified all or most feasible solutions in a single run, demonstrating advantages in solution diversity and efficient and broad exploration of the solution space over the classical solver, while the classical solver provides an optimality guarantee and rapid convergence speed. In process design, where insights of alternative designs and cost comparisons are more valuable than an optimal solution, heuristics offer a better-suited decision-making strategy. The comparative analysis highlights the strengths of each method and underscores the potential of this heterogeneous computing approach that leverages different methods to address practical optimization problems.

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arXiv2026

Exact Hull Reformulation for Quadratically Constrained Generalized Disjunctive Programs

Generalized Disjunctive Programming (GDP) provides a natural framework for optimization models that combine logical decisions with nonlinear constraints. The Hull Reformulation (HR) is attractive because it yields tight continuous relaxations, but for nonlinear disjunctive constraints, it is commonly implemented using an epsilon-approximation of the closure of the perspective function. This approximation introduces fractional expressions, enlarges the relaxation for any non-zero value, can cause numerical instability, and may hinder solver convexity recognition. This paper develops a framework for constructing exact hull reformulations for GDPs with quadratic disjunctive constraints that avoids approximations while preserving solver-friendly structure. For general (possibly non-convex) quadratic constraints, we derive a General Exact Hull Reformulation (GEHR) that eliminates perspective division and preserves quadratic degree, and we prove that it is equivalent to the standard closed-perspective hull in lifted space. For convex quadratic constraints, we propose using a Conic Exact Hull Reformulation (CEHR), re-derived in this work, that represents the perspective term with rotated second-order cone constraints, enabling conic-capable solvers to certify and exploit convexity directly. We implement both reformulations in Pyomo.GDP and evaluate them on random convex and non-convex instances, a CSTR network benchmark, k-means clustering, and constrained layout problems using Gurobi, SCIP, and BARON. Across these benchmarks, the proposed exact formulations reduce numerical failures and often improve runtime relative to the epsilon-approximation. In particular, CEHR is consistently the most reliable and typically the fastest hull reformulation on convex benchmarks, while GEHR performs best on non-convex benchmarks, improving both robustness and overall performance.

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arXiv2026

Multi-GPU Quantum Circuit Simulation and the Impact of Network Performance

As is intrinsic to the fundamental goal of quantum computing, classical simulation of quantum algorithms is notoriously demanding in resource requirements. Nonetheless, simulation is critical to the success of the field and a requirement for algorithm development and validation, as well as hardware design. GPU-acceleration has become standard practice for simulation, and due to the exponential scaling inherent in classical methods, multi-GPU simulation can be required to achieve representative system sizes. In this case, inter-GPU communications can bottleneck performance. In this work, we present the introduction of MPI into the QED-C Application-Oriented Benchmarks to facilitate benchmarking on HPC systems. We review the advances in interconnect technology and the APIs for multi-GPU communication. We benchmark using a variety of interconnect paths, including the recent NVIDIA Grace Blackwell NVL72 architecture that represents the first product to expand high-bandwidth GPU-specialized interconnects across multiple nodes. We show that while improvements to GPU architecture have led to speedups of over 4.5X across the last few generations of GPUs, advances in interconnect performance have had a larger impact with over 16X performance improvements in time to solution for multi-GPU simulations.

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arXiv2026

Mixed-Integer Reaggregated Hull Reformulation of Special Structured Generalized Linear Disjunctive Programs

Generalized Disjunctive Programming (GDP) provides a powerful framework for combining algebraic constraints with logical disjunctions. To solve these problems, mixed-integer reformulations are required, but traditional reformulation schemes, such as Big-M and Hull, either yield a weak continuous relaxation or result in a bloated model size. Castro and Grossmann showed that scheduling problems can be formulated as GDP by modeling task orderings as disjunctions with algebraic timing constraints. Moreover, in their work, a particular representation of the single-unit scheduling problem, namely using a time-slot concept, can be reformulated as a tight yet compact mixed-integer linear program with notable computational performance. Based on that observation, and focusing on the case where the constraints in disjunctions are linear and share the same coefficients, we connect the characterization of the convex hull of these disjunctive sets by Jeroslow and Blair with Castro and Grossmann's time-slot reaggregation strategy to derive a unified reformulation methodology. We test this reformulation in two problems, single-unit scheduling and two-dimensional strip-packing. We derive new formulations of the general precedence concept of single-unit scheduling and symmetry-breaking formulations of the strip-packing problem, yielding mixed-integer programs with strong theoretical guarantees, particularly compact formulations in terms of continuous variables, and efficient computational performance when solving them with commercial mixed-integer solvers for these problems.

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arXiv2025

Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization

Quantum algorithms have shown promise in solving Quadratic Unconstrained Binary Optimization (QUBO) problems, benefiting from their connection to the transverse field Ising model. Various Ising solvers, both classical and quantum, have emerged to tackle such problems efficiently but lack global optimality guarantees and often suffer from hardware limitations such as limited qubit availability. In this work, we propose a hybrid branch-and-bound (B&B) framework that integrates Ising solvers as heuristics within a classical B&B algorithm. Unlike prior theoretical studies, our work presents a practical implementation, available as open-source on GitHub. We explore when and where to apply Ising solvers in the search tree and introduce a custom branching rule optimized QUBO embedding. Our method is evaluated on hundreds of QUBO instances from QUBOLib.jl using Gurobi and the D-Wave quantum annealer. Our results show up to 11% less solution time and 17% fewer nodes compared to default Gurobi, an off-the-shelf commercial optimization solver. These findings demonstrate the value of hybrid quantum-classical strategies for enhancing exact optimization.

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arXiv2025

Quantum Optimization Benchmarking Library - The Intractable Decathlon

Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms are heuristics - it is key to empirically analyze their performance on hardware and track progress towards quantum advantage. To this extent, we present ten optimization problem classes that are difficult for existing classical algorithms and can (mostly) be linked to practically relevant applications, with the goal to enable systematic, fair, and comparable benchmarks for quantum optimization methods. Further, we introduce the Quantum Optimization Benchmarking Library (QOBLIB) where the problem instances and solution track records can be found. The individual properties of the problem classes vary in terms of objective and variable type, coefficient ranges, and density. Crucially, they all become challenging for established classical methods already at system sizes ranging from less than 100 to, at most, an order of 100,000 decision variables, allowing to approach them with today's quantum computers. We reference the results from state-of-the-art solvers for instances from all problem classes and demonstrate exemplary baseline results obtained with quantum solvers for selected problems. The baseline results illustrate a standardized form to present benchmarking solutions, which has been designed to ensure comparability of the used methods, reproducibility of the respective results, and trackability of algorithmic and hardware improvements over time. We encourage the optimization community to explore the performance of available classical or quantum algorithms and hardware platforms with the benchmarking problem instances presented in this work toward demonstrating quantum advantage in optimization.

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arXiv2025

Spectral Outer-Approximation Algorithms for Binary Semidefinite Problems

Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However, it remains unclear whether this reformulation effectively uses existing ISDP solvers to address BQCQPs. To the best of our knowledge, no specialized ISDP algorithms exploit the unique structure of BSDPs derived from BQCQPs. This paper proposes a novel spectral outer approximation algorithm tailored for BSDPs derived from BQCQP reformulations. Our approach is inspired by polyhedral and second-order representable regions that outer approximate the feasible set of a semidefinite program relying on a spectral decomposition of a matrix that simultaneously diagonalizes the objective matrix and an aggregation of the constraint matrices. Computational experiments show that our algorithm is competitive with, and in some cases outperforms, state-of-the-art ISDP solvers such as SCIP-SDP and PAJARITO, highlighting ISDP's potential for solving BQCQPs.

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arXiv2025

Evaluating the performance of quantum processing units at large width and depth

Quantum computers have now surpassed classical simulation limits, yet noise continues to limit their practical utility. As the field shifts from proof-of-principle demonstrations to early deployments, there is no standard method for meaningfully and scalably comparing heterogeneous quantum hardware. Existing benchmarks typically focus on gate-level fidelity or constant-depth circuits, offering limited insight into algorithmic performance at depth. Here we introduce a benchmarking protocol based on the linear ramp quantum approximate optimization algorithm (LR-QAOA), a fixed-parameter, deterministic variant of QAOA. LR-QAOA quantifies a QPU's ability to preserve a coherent signal as circuit depth increases, identifying when performance becomes statistically indistinguishable from random sampling. We apply this protocol to 24 quantum processors from six vendors, testing problems with up to 156 qubits and 10,000 layers across 1D-chains, native layouts, and fully connected topologies. This constitutes the most extensive cross-platform quantum benchmarking effort to date, with circuits reaching a million two-qubit gates. LR-QAOA offers a scalable, unified benchmark across platforms and architectures, making it a tool for tracking performance in quantum computing.

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arXiv2025

A Practical Framework for Assessing the Performance of Observable Estimation in Quantum Simulation

Simulating dynamics of physical systems is a key application of quantum computing, with potential impact in fields such as condensed matter physics and quantum chemistry. However, current quantum algorithms for Hamiltonian simulation yield results that are inadequate for real use cases and suffer from lengthy execution times when implemented on near-term quantum hardware. In this work, we introduce a framework for evaluating the performance of quantum simulation algorithms, focusing on the computation of observables, such as energy expectation values. Our framework provides end-to-end demonstrations of algorithmic optimizations that utilize Pauli term groups based on k-commutativity, generate customized Clifford measurement circuits, and implement weighted shot distribution strategies across these groups. These demonstrations span multiple quantum execution environments, allowing us to identify critical factors influencing runtime and solution accuracy. We integrate enhancements into the QED-C Application-Oriented Benchmark suite, utilizing problem instances from the open-source HamLib collection. Our results demonstrate a 27.1% error reduction through Pauli grouping methods, with an additional 37.6% improvement from the optimized shot distribution strategy. Our framework provides an essential tool for advancing quantum simulation performance using algorithmic optimization techniques, enabling systematic evaluation of improvements that could maximize near-term quantum computers' capabilities and advance practical quantum utility as hardware evolves.

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arXiv2025

A Greedy Quantum Route-Generation Algorithm

Routing and scheduling problems with time windows have long been important optimization problems for logistics and planning. Many classical heuristics and exact methods exist for such problems. However, there are no satisfactory methods for generating routes using quantum computing (QC), for mainly two reasons: inequality constraints, and the trade-off of feasibility and solution quality. Inequality constraints are typically handled using slack variables; and feasible solutions are found by filtering samples. These challenges are amplified in the presence of noise inherent in QC. Here, we propose a greedy algorithm that generates routes by using information from all samples obtained from the quantum computer. By noticing the relationship between qubits in our formulation as a directed acyclic graph (DAG), we designed an algorithm that adaptively constructs a feasible solution. We prove its convergence to a feasible solution, and illustrate its efficacy by solving the Fleet Sizing Vehicle Routing Problem with Time Windows (FSVRPTW). Our computational results show that this method obtains a lower objective value than the current state-of-the-art annealing approaches, both classical and hybrid, for the same amount of time using D-Wave Hybrid Solvers. We also show its robustness to noise on D-Wave Advantage2 through computational results as compared to the filtering approach on DWaveSampler, even when the filtering approach is given a longer annealing time, and a larger sample size.

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arXiv2025

Benchmarking Quantum Optimization for the Maximum-Cut Problem on a Superconducting Quantum Computer

Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the performance of a hybrid quantum-classical algorithm inspired by semidefinite programming approaches for solving the maximum-cut problem on 3-regular graphs up to several thousand variables. We leverage the structure of the input problems to address sizes beyond what current quantum machines can naively handle. We attain an average approximation ratio of 99% over a random ensemble of thousands of problem instances. We benchmark the quantum solver against similarly high-performing classical heuristics, including the Gurobi optimizer, simulated annealing, and the Burer-Monteiro algorithm. A run-time analysis shows that the quantum solver on large-scale problems is competitive against Gurobi but short of others on a projected 100-qubit quantum computer. We explore multiple leads to close the gap and discuss prospects for a practical quantum speedup.

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arXiv2025

Logic-Based Discrete-Steepest Descent: A Solution Method for Process Synthesis Generalized Disjunctive Programs

The optimization of chemical processes is challenging due to the nonlinearities arising from process physics and discrete design decisions. In particular, optimal synthesis and design of chemical processes can be posed as a Generalized Disjunctive Programming (GDP) superstructure problem. Various solution methods are available to address these problems, such as reformulating them as Mixed-Integer Nonlinear Programming (MINLP) problems; nevertheless, algorithms explicitly designed to solve the GDP problem and potentially leverage its structure remain scarce. This paper presents the Logic-based Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP problems involving ordered Boolean variables. The LD-SDA reformulates these ordered Boolean variables into integer decisions called external variables. The LD-SDA solves the reformulated GDP problem using a two-level decomposition approach where the upper-level subproblem determines external variable configurations. Subsequently, the remaining continuous and discrete variables are solved as a subproblem only involving those constraints relevant to the given external variable arrangement, effectively taking advantage of the structure of the GDP problem. The advantages of LD-SDA are illustrated through a batch processing case study, a reactor superstructure, a distillation column, and a catalytic distillation column, and its open-source implementation is available online. The results show convergence efficiency and solution quality improvements compared to conventional GDP and MINLP solvers.

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