arXiv subjects

Martin J. A. Schuetz

Publications and source records attributed to Martin J. A. Schuetz.

At least 19 recordsLinked to original sources

arXiv2026

Quantum-Informed Portfolio Selection: An End-to-End Pipeline Validated on Trapped-Ion Hardware with Real Market Data

Portfolio diversification - a cornerstone of modern investment management - can be formulated as a Maximum Independent Set (MIS) problem on asset correlation graphs. Solving this problem at scale is computationally challenging, motivating the exploration of quantum algorithms for practical financial optimization. We propose an end-to-end pipeline leveraging qReduMIS, a recursive hybrid quantum-classical algorithm. Rather than using quantum optimization to directly produce a final solution, qReduMIS leverages independent set measurements from the Quantum Approximate Optimization Algorithm (QAOA) to identify frozen nodes - vertices likely to belong to optimal solutions - thereby guiding and unblocking subsequent (provably optimal) classical reductions on the remaining graph. We benchmark qReduMIS on real financial data from four major market indices with up to 225 assets, executing experiments on Quantinuum's 98-qubit trapped-ion Helios system, with QAOA circuits acting on kernels of up to 78 qubits and 1016 two-qubit gates. While standalone QAOA fails to find the optimal solution for two of the largest indices (S&P 100 and Nikkei 225), qReduMIS achieves success probabilities of $0.40$ and $0.95$, respectively, with average approximation ratios $\geq 0.96$ across all four indices. We perform a systematic benchmark on the Quantinuum H2-1 noisy emulator over 73 asset correlation graphs of varying size showing that, for $p=2$ QAOA layers, the optimal time-to-solution scaling exponent of qReduMIS is $3.2$ times smaller than that of standalone QAOA.

quant-ph↗

arXiv2026

qReduMIS: A Quantum-Informed Reduction Algorithm for the Maximum Independent Set Problem

We propose and implement a quantum-informed reduction algorithm for the maximum independent set problem that integrates classical kernelization techniques with information extracted from quantum devices. Our larger framework consists of dedicated application, algorithm, and hardware layers, and easily generalizes to the maximum weight independent set problem. In this hybrid quantum-classical framework, which we call qReduMIS, the quantum computer is used as a co-processor to inform classical reduction logic about frozen vertices that are likely (or unlikely) to be in large independent sets, thereby opening up the reduction space after removal of targeted subgraphs. We systematically assess the performance of qReduMIS based on experiments with up to 231 qubits run on Rydberg quantum hardware available through Amazon Braket. Our experiments show that qReduMIS can help address fundamental performance limitations faced by a broad set of (quantum) solvers including Rydberg quantum devices. We outline implementations of qReduMIS with alternative platforms, such as superconducting qubits or trapped ions, and we discuss potential future extensions.

quant-ph↗

arXiv2026

Crystal structure prediction using graph neural combinatorial optimization

Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in computational approaches aiming to accelerate this process. Previously, CSP has been approached from a combinatorial optimization perspective, with the core challenge of allocating atoms on a fine grid of predefined discrete positions within a unit cell while minimizing their interaction energy. Exact mathematical optimization methods provide guaranteed solutions, but they become computationally expensive for large-scale instances, where the atomic configuration space grows rapidly, particularly in the absence of additional symmetry constraints. In this work, we introduce a neural combinatorial optimization approach to the atom allocation challenge and, subsequently, CSP, based on graph neural networks (GNNs), which can effectively sample from the distribution of feasible structures in an unsupervised manner. We leverage expander graphs to construct computational graphs over discrete positions that capture both short- and long-range interactions between atoms, and employ the Gumbel-Sinkhorn approach to enforce the desired stoichiometry of the generated structures. We demonstrate that our method outperforms classical heuristic approaches and is competitive with a commercial optimization solver across a range of chemical compositions. This enables the use of ever-expanding GPU infrastructure to tackle the inherent combinatorial challenges of CSP, paving the way for scaling beyond current capabilities.

cs.LG↗

arXiv2026

Applying a Random-Key Optimizer on Mixed Integer Programs

Mixed-Integer Programs (MIPs) are NP-hard optimization models that arise in a broad range of decision-making applications, including finance, logistics, energy systems, and network design. Although modern commercial solvers have achieved remarkable progress and perform effectively on many small- and medium-sized instances, their performance often degrades when confronted with large-cale or highly constrained formulations. This paper explores the use of the Random-Key Optimizer (RKO) framework as a flexible, metaheuristic alternative for computing high-quality solutions to MIPs through the design of problem-specific decoders. The proposed approach separates the search process from feasibility enforcement by operating in a continuous random-key space while mapping candidate solutions to feasible integer solutions via efficient decoding procedures. We evaluate the methodology on two representative and structurally distinct benchmark problems: the mean-variance Markowitz portfolio optimization problem with buy-in and cardinality constraints, and the Time-Dependent Traveling Salesman Problem. For each formulation, tailored decoders are developed to reduce the effective search space, promote feasibility, and accelerate convergence. Computational experiments demonstrate that RKO consistently produces competitive, and in several cases superior, solutions compared to a state-of-the-art commercial MIP solver, both in terms of solution quality and computational time. These results highlight the potential of RKO as a scalable and versatile heuristic framework for tackling challenging large-scale MIPs.

math.OC↗

arXiv2025

Quantum-Guided Cluster Algorithms for Combinatorial Optimization

Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a Monte Carlo (MC)-based algorithm that updates spins one at a time. Yet, these localized updates can cause the system to become trapped in local minima. Cluster algorithms (CAs) were developed to address this limitation and have demonstrated considerable success in studying ferromagnetic systems; however, they tend to encounter percolation issues when applied to generic spin glasses. In this work, we introduce a novel CA designed to tackle these challenges by leveraging precomputed two-point correlations, aiming solve combinatorial optimization problems in the form of Max-Cut more efficiently. In our approach, clusters are formed probabilistically based on these correlations. Various classical and quantum algorithms can be employed to generate correlations that embody information about the energy landscape of the problem. By utilizing this information, the algorithm aims to identify groups of spins whose simultaneous flipping induces large transitions in configuration space with high acceptance probability -- even at low energy levels -- thereby escaping local minima more effectively. Notably, clusters generated using correlations from the Quantum Approximate Optimization Algorithm exhibit high acceptance rates at low temperatures. These acceptance rates often increase with circuit depth, accelerating the algorithm and enabling more efficient exploration of the solution space.

quant-ph↗

arXiv2025

A Random-Key Optimizer for Combinatorial Optimization

This paper introduces the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys that are subsequently decoded into feasible solutions via problem-specific decoders. The RKO framework is able to combine a plethora of classic metaheuristics, each capable of operating independently or in parallel, with solution sharing facilitated through an elite solution pool. This modular approach allows for the adaptation of various metaheuristics, including simulated annealing, iterated local search, and greedy randomized adaptive search procedures, among others. The efficacy of the RKO framework, implemented in C++ and publicly available (Github public repository: github.com/RKO-solver), is demonstrated through its application to three NP-hard combinatorial optimization problems: the alpha-neighborhood p-median problem, the tree of hubs location problem, and the node-capacitated graph partitioning problem. The results highlight the framework's ability to produce high-quality solutions across diverse problem domains, underscoring its potential as a robust tool for combinatorial optimization.

cs.AI↗

arXiv2025

Modern Computational Methods in Reinsurance Optimization: From Simulated Annealing to Quantum Branch & Bound

We propose and implement modern computational methods to enhance catastrophe excess-of-loss reinsurance contracts in practice. The underlying optimization problem involves attachment points, limits, and reinstatement clauses, and the objective is to maximize the expected profit while considering risk measures and regulatory constraints. We study the problem formulation, paving the way for practitioners, for two very different approaches: A local search optimizer using simulated annealing, which handles realistic constraints, and a branch & bound approach exploring the potential of a future speedup via quantum branch & bound. On the one hand, local search effectively generates contract structures within several constraints, proving useful for complex treaties that have multiple local optima. On the other hand, although our branch & bound formulation only confirms that solving the full problem with a future quantum computer would require a stronger, less expensive bound and substantial hardware improvements, we believe that the designed application-specific bound is sufficiently strong to serve as a basis for further works. Concisely, we provide insurance practitioners with a robust numerical framework for contract optimization that handles realistic constraints today, as well as an outlook and initial steps towards an approach which could leverage quantum computers in the future.

math.OC↗

arXiv2025

Optimization of Next-Day Delivery Coverage using Constraint Programming and Random Key Optimizers

We consider the logistics network of an e-commerce retailer, specifically the so-called "middle mile" network, that routes inventory from supply warehouses to distribution stations to be ingested into the terminal ("last mile") delivery network. The speed of packages through this middle mile network is a key determinant for the ultimate delivery speed to the end user. An important target for a retailer is to maximize the fraction of user orders that can be serviced within one day, i.e., next-day delivery. As such, we formulate the maximization of expected next-day delivery coverage within the middle-mile network as an optimization problem, involving a set of temporal and capacity-based constraints on the network and requiring the use of a black-box model to evaluate the objective function. We design both exact constraint programming (CP) and heuristic random-key optimizer (RKO) approaches, the former of which uses a proxy objective function. We perform experiments on large-scale, real-world problem instances and show that both approaches have merit, in that they can match or outperform the baseline solution, a bespoke greedy solver with integrated local search, in expected next-day delivery coverage. Our experiments focus on two high-level problem definitions, starting with a base problem and then adding more complexity, and also explore the generalization of the solvers across a range of problem instance sizes. We find that a hybrid model using RKO and a bespoke local search protocol performs best on the full problem definition with respect to expected next-day delivery (increase of +50 basis points [bps] over baseline) but can take days to run, whereas the hybrid model using CP and local search is slightly less competitive (+20 bps) but takes only hours to run.

math.OC↗

arXiv2025

Quantum Compilation Toolkit for Rydberg Atom Arrays with Implications for Problem Hardness and Quantum Speedups

We propose and implement a comprehensive quantum compilation toolkit for solving the maximum independent set (MIS) problem on quantum hardware based on Rydberg atom arrays. Our end-to-end pipeline involves three core components to efficiently map generic MIS instances onto Rydberg arrays with unit-disk connectivity, with modules for graph reduction, hardware compatibility checks, and graph embedding. The first module (reducer) provides hardware-agnostic and deterministic reduction logic that iteratively reduces the problem size via lazy clique removals. We find that real-world networks can typically be reduced by orders of magnitude on sub-second time scales, thus significantly cutting down the eventual load for quantum devices. Moreover, we show that reduction techniques may be an important tool in the ongoing search for potential quantum speedups, given their ability to identify hard problem instances. In particular, for Rydberg-native MIS instances, we observe signatures of an easy-hard-easy transition and quantify a critical degree indicating the onset of a hard problem regime. The second module (compatibility checker) implements a hardware compatibility checker that quickly determines whether or not a given input graph may be compatible with the restrictions imposed by Rydberg quantum hardware. The third module (embedder) describes hardware-efficient graph embedding routines to generate (approximate) encodings with controllable overhead and optimized ancilla placements. We exemplify our pipeline with experiments run on the QuEra Aquila device available on Amazon Braket. In aggregate, our work provides a set of tools that extends the class of problems that can be tackled with near-term Rydberg atom arrays.

quant-ph↗

arXiv2024

Scalable iterative pruning of large language and vision models using block coordinate descent

Pruning neural networks, which involves removing a fraction of their weights, can often maintain high accuracy while significantly reducing model complexity, at least up to a certain limit. We present a neural network pruning technique that builds upon the Combinatorial Brain Surgeon, but solves an optimization problem over a subset of the network weights in an iterative, block-wise manner using block coordinate descent. The iterative, block-based nature of this pruning technique, which we dub ``iterative Combinatorial Brain Surgeon'' (iCBS) allows for scalability to very large models, including large language models (LLMs), that may not be feasible with a one-shot combinatorial optimization approach. When applied to large models like Mistral and DeiT, iCBS achieves higher performance metrics at the same density levels compared to existing pruning methods such as Wanda. This demonstrates the effectiveness of this iterative, block-wise pruning method in compressing and optimizing the performance of large deep learning models, even while optimizing over only a small fraction of the weights. Moreover, our approach allows for a quality-time (or cost) tradeoff that is not available when using a one-shot pruning technique alone. The block-wise formulation of the optimization problem enables the use of hardware accelerators, potentially offsetting the increased computational costs compared to one-shot pruning methods like Wanda. In particular, the optimization problem solved for each block is quantum-amenable in that it could, in principle, be solved by a quantum computer.

cs.LG↗

arXiv2024

Decomposition Pipeline for Large-Scale Portfolio Optimization with Applications to Near-Term Quantum Computing

Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman's algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization.

math.OC↗

arXiv2024

End-to-end resource analysis for quantum interior point methods and portfolio optimization

We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant pre-factors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage.

quant-ph↗

arXiv2024

Quantum-Informed Recursive Optimization Algorithms

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We demonstrate the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow (depth $p=1$) circuits of the quantum approximate optimization algorithm (QAOA), solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor available online on Amazon Braket to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics, such as simulated annealing and greedy algorithms, even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms, highlighting the potential of QIRO. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a blueprint for designing a broader class of hybrid quantum-classical algorithms for combinatorial optimization.

quant-ph↗

arXiv2024

Hardness of the Maximum Independent Set Problem on Unit-Disk Graphs and Prospects for Quantum Speedups

Rydberg atom arrays are among the leading contenders for the demonstration of quantum speedups. Motivated by recent experiments with up to 289 qubits [Ebadi et al., Science 376, 1209 (2022)] we study the maximum independent set problem on unit-disk graphs with a broader range of classical solvers beyond the scope of the original paper. We carry out extensive numerical studies and assess problem hardness, using both exact and heuristic algorithms. We find that quasi-planar instances with Union-Jack-like connectivity can be solved to optimality for up to thousands of nodes within minutes, with both custom and generic commercial solvers on commodity hardware, without any instance-specific fine-tuning. We also perform a scaling analysis, showing that by relaxing the constraints on the classical simulated annealing algorithms considered in Ebadi et al., our implementation is competitive with the quantum algorithms. Conversely, instances with larger connectivity or less structure are shown to display a time-to-solution potentially orders of magnitudes larger. Based on these results we propose protocols to systematically tune problem hardness, motivating experiments with Rydberg atom arrays on instances orders of magnitude harder (for established classical solvers) than previously studied.

quant-ph↗

arXiv2023

Explainable AI using expressive Boolean formulas

We propose and implement an interpretable machine learning classification model for Explainable AI (XAI) based on expressive Boolean formulas. Potential applications include credit scoring and diagnosis of medical conditions. The Boolean formula defines a rule with tunable complexity (or interpretability), according to which input data are classified. Such a formula can include any operator that can be applied to one or more Boolean variables, thus providing higher expressivity compared to more rigid rule-based and tree-based approaches. The classifier is trained using native local optimization techniques, efficiently searching the space of feasible formulas. Shallow rules can be determined by fast Integer Linear Programming (ILP) or Quadratic Unconstrained Binary Optimization (QUBO) solvers, potentially powered by special purpose hardware or quantum devices. We combine the expressivity and efficiency of the native local optimizer with the fast operation of these devices by executing non-local moves that optimize over subtrees of the full Boolean formula. We provide extensive numerical benchmarking results featuring several baselines on well-known public datasets. Based on the results, we find that the native local rule classifier is generally competitive with the other classifiers. The addition of non-local moves achieves similar results with fewer iterations, and therefore using specialized or quantum hardware could lead to a speedup by fast proposal of non-local moves.

cs.AI↗

arXiv2023

Designing Quantum Annealing Schedules using Bayesian Optimization

We propose and analyze the use of Bayesian optimization techniques to design quantum annealing schedules with minimal user and resource requirements. We showcase our scheme with results for two paradigmatic spin models. We find that Bayesian optimization is able to identify schedules resulting in fidelities several orders of magnitude better than standard protocols for both quantum and reverse annealing, as applied to the $p$-spin model. We also show that our scheme can help improve the design of hybrid quantum algorithms for hard combinatorial optimization problems, such as the maximum independent set problem, and illustrate these results via experiments on a neutral atom quantum processor available on Amazon Braket.

quant-ph↗

arXiv2023

Reply to: Inability of a graph neural network heuristic to outperform greedy algorithms in solving combinatorial optimization problems

We provide a comprehensive reply to the comment written by Stefan Boettcher [arXiv:2210.00623] and argue that the comment singles out one particular non-representative example problem, entirely focusing on the maximum cut problem (MaxCut) on sparse graphs, for which greedy algorithms are expected to perform well. Conversely, we highlight the broader algorithmic development underlying our original work, and (within our original framework) provide additional numerical results showing sizable improvements over our original data, thereby refuting the comment's original performance statements. Furthermore, it has already been shown that physics-inspired graph neural networks (PI-GNNs) can outperform greedy algorithms, in particular on hard, dense instances. We also argue that the internal (parallel) anatomy of graph neural networks is very different from the (sequential) nature of greedy algorithms, and (based on their usage at the scale of real-world social networks) point out that graph neural networks have demonstrated their potential for superior scalability compared to existing heuristics such as extremal optimization. Finally, we conclude highlighting the conceptual novelty of our work and outline some potential extensions.

cs.LG↗

arXiv2023

Reply to: Modern graph neural networks do worse than classical greedy algorithms in solving combinatorial optimization problems like maximum independent set

We provide a comprehensive reply to the comment written by Chiara Angelini and Federico Ricci-Tersenghi [arXiv:2206.13211] and argue that the comment singles out one particular non-representative example problem, entirely focusing on the maximum independent set (MIS) on sparse graphs, for which greedy algorithms are expected to perform well. Conversely, we highlight the broader algorithmic development underlying our original work, and (within our original framework) provide additional numerical results showing sizable improvements over our original results, thereby refuting the comment's performance statements. We also provide results showing run-time scaling superior to the results provided by Angelini and Ricci-Tersenghi. Furthermore, we show that the proposed set of random d-regular graphs does not provide a universal set of benchmark instances, nor do greedy heuristics provide a universal algorithmic baseline. Finally, we argue that the internal (parallel) anatomy of graph neural networks is very different from the (sequential) nature of greedy algorithms and emphasize that graph neural networks have demonstrated their potential for superior scalability compared to existing heuristics such as parallel tempering. We conclude by discussing the conceptual novelty of our work and outline some potential extensions.

cond-mat.dis-nn↗