About

David Bernal Neira is an Assistant Professor of Chemical Engineering at Purdue University, having joined the institution in August 2023. His research interests encompass optimization software and theory, quantum computing as solution methods to problems in combinatorial optimization and chemistry, and chemical and process systems engineering. His work focuses on the mathematical modeling and optimization of discrete nonlinear systems through novel algorithms, theory, and computational methods, with applications in process and energy systems engineering. Bernal Neira's academic background includes a PhD in Chemical Engineering from Carnegie Mellon University, a B.A.Sc. in Physics, a M.Sc., and a B.A.Sc. in Chemical Engineering from Universidad de Los Andes. His research group explores the intersection of optimization, quantum computing, and chemical engineering, contributing to advancements in computational methods for complex systems.

Research topics

• Computer Science
• Mathematical optimization
• Mathematics
• Computer engineering
• Algorithm
• Physics
• Distributed computing
• Statistical physics
• Business
• Quantum mechanics

Selected publications

• Multi-GPU quantum circuit simulation and the impact of network performance

  Computer Physics Communications · 2026-03-18

  preprintOpen accessSenior author
  PublisherOA PDFDOI

• A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations

  IEEE Transactions on Quantum Engineering · 2025-01-01 · 4 citations

  articleOpen access

  Quantum Hamiltonian simulation is one of the most promising applications of quantum computing and forms the basis for many quantum algorithms. Benchmarking them is an important gauge of progress in quantum computing technology. We present a methodology and software framework to evaluate various facets of the performance of gate-based quantum computers on Trotterized quantum Hamiltonian evolution. We propose three distinct modes for benchmarking: (i) comparing simulation on a real device to that on a noiseless classical simulator, (ii) comparing simulation on a real device with exact diagonalization results, and (iii) using scalable mirror circuit techniques to assess hardware performance in scenarios beyond classical simulation methods. We demonstrate this framework on five Hamiltonian models from the HamLib library: the Fermi and Bose-Hubbard models, the transverse field Ising model, the Heisenberg model, and the Max3SAT problem. Experiments were conducted using Qiskit's Aer simulator, BlueQubit's CPU cluster and GPU simulators, and IBM's quantum hardware. Our framework, extendable to other Hamiltonians, provides comprehensive performance profiles that reveal hardware and algorithmic limitations and measure both fidelity and execution times, identifying crossover points where quantum hardware outperforms CPU/GPU simulators.

  PublisherDOI

• Benchmarking the operation of quantum heuristics and Ising machines: scoring parameter setting strategies on optimization applications

  Quantum Machine Intelligence · 2025-09-05 · 3 citations

  articleOpen access1st authorCorresponding

  We discuss guidelines for evaluating the performance of parameterized stochastic solvers for optimization problems, with particular attention to systems that employ novel hardware, such as digital quantum processors running variational algorithms, analog processors performing quantum annealing, or coherent Ising machines. We illustrate through an example a benchmarking procedure grounded in the statistical analysis of the expectation of a given performance metric measured in a test environment. In particular, we discuss the necessity and cost of setting parameters that affect the algorithm's performance. The optimal value of these parameters could vary significantly between instances of the same target problem. We present an open-source software package that facilitates the design, evaluation, and visualization of practical parameter tuning strategies for the complex use of the heterogeneous components of the solver. We examine in detail an example using parallel tempering and a simulator of a photonic coherent Ising machine computing and display the scoring of an illustrative baseline family of parameter setting strategies that feature an exploration-exploitation trade-off.

  PublisherOA PDFDOI

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

  Industrial & Engineering Chemistry Research · 2025-12-23

  articleOpen accessSenior authorCorresponding

  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 Grossmann1 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 this 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 Jeroslow2 and Blair3 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 (also worked by Castro and Grossmann4). 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.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-04-14

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Intensified production of butyl citrates from a calcium citrate salt via solid-liquid reaction

  Chemical Engineering Journal · 2025-05-21

  article
  PublisherDOI

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

  2025-08-30 · 1 citations

  article

  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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex>-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 opensource HamLib collection. Our results demonstrate a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{2 7. 1} \boldsymbol{\%}$</tex> 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.

  PublisherDOI

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

  ArXiv.org · 2025-02-10

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

• Quantum Optimization Benchmarking Library - The Intractable Decathlon

  ArXiv.org · 2025-04-04 · 2 citations

  preprintOpen access

  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.

  PublisherOA PDFDOI

• A Multilevel Approach For Solving Large-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

  arXiv (Cornell University) · 2024-08-14

  preprintOpen access

  Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are relatively small, and canonical mappings of QUBO via the Ising model require one qubit per variable, rendering direct large-scale optimization infeasible. In classical optimization, a general strategy for addressing many large-scale problems is via multilevel/multigrid methods, where the large target problem is iteratively coarsened, and the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentally test how existing QPUs perform as a sub-solver within such a multilevel strategy. We combine and extend (via additional classical processing) the recent Noise-Directed Adaptive Remapping (NDAR) and Quantum Relax $\&amp;$ Round (QRR) algorithms. We first demonstrate the effectiveness of our heuristic extensions on Rigetti's transmon device Ankaa-2. We find approximate solutions to $10$ instances of fully connected $82$-qubit Sherrington-Kirkpatrick graphs with random integer-valued coefficients obtaining normalized approximation ratios (ARs) in the range $\sim 0.98-1.0$, and the same class with real-valued coefficients (ARs $\sim 0.94-1.0$). Then, we implement the extended NDAR and QRR algorithms as subsolvers in the multilevel algorithm for $6$ large-scale graphs with at most $\sim 27,000$ variables. The QPU (with classical post-processing steps) is used to find approximate solutions to dozens of problems, at most $82$-qubit, which are iteratively used to construct the global solution. We observe that quantum optimization results are competitive regarding the quality of solutions compared to classical heuristics used as subsolvers within the multilevel approach.

  PublisherOA PDFDOI

Frequent coauthors

• Davide Venturelli

  NASA Research Park

  20 shared

• Farshud Sorourifar

  The Ohio State University

  11 shared

• Ignacio E. Grossmann

  Carnegie Mellon University

  10 shared

• Zoe Gonzalez Izquierdo

  Research Institute for Advanced Computer Science

  10 shared

• Andres F. Cabeza

  Universidad Nacional de Colombia

  9 shared

• Diana Chamaki

  8 shared

• Phillip A. Kerger

  Johns Hopkins University

  7 shared

• Eleanor Rieffel

  Quantum Group (United States)

  7 shared

Labs

• David Bernal Neira - Davidson School of Chemical EngineeringPI