What Can Quantum Computers Do for You?

Quantum computing has the potential to transform many areas of computing, including – possibly – operations research (O.R.). The United Nations declared 2025 the International Year of Quantum Science and Technology, suggesting that this is a good time for INFORMS members to ask themselves if they are interested in learning about, contributing to or using this technology. This article overviews some of the areas of quantum computing that potentially overlap with operations research; while we do not aim to (and could not possibly) be exhaustive, we provide a few pointers to facilitate further investigation.

Optimization

Several potential use cases of quantum computing that have captured the attention of researchers fall within the realm of optimization; for a detailed discussion on the current state of quantum optimization research, see [1]. Quantum optimization algorithms can be broadly categorized by the type of hardware they target – near-term or fault-tolerant – and by their solution strategy: exact or approximate. For near-term devices, variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) aim to find approximate solutions to combinatorial problems using parameterized quantum circuits, although their empirical advantage remains unclear. For fault-tolerant devices, algorithms such as quantum interior point methods and quantum semidefinite optimization solvers offer theoretical speedup guarantees under specific assumptions that may not hold in practice. Fault-tolerant approximation algorithms with provable a priori performance guarantees have been suggested and in some cases, they are shown to outperform (in theory) the best known classical approximation algorithms for certain combinatorial optimization problems [2]. To demonstrate practical quantum advantage in optimization, systematic and rigorous benchmarking for challenging optimization problems is key [3].

Quantum optimization is not just about using quantum devices to solve classical problems; optimization methods are also essential to make quantum algorithms and hardware more effective. Classical optimization plays a key role in efficiently compiling quantum circuits – reducing gate depth, optimizing qubit mappings or routing operations on hardware with limited connectivity. Linear and integer programming methods are already used to schedule quantum gates and minimize cross talk or decoherence. Moreover, hybrid quantum-classical schemes rely on classical solvers to train variational circuits, often using gradient-based or derivative-free methods. As devices grow more complex, optimization will remain central in the co-design of algorithms and hardware.

Despite growing interest, demonstrating a clear quantum advantage for optimization remains an open challenge. Benchmarks often show that classical heuristics still outperform near-term quantum algorithms on practical problems, especially when accounting for noise and circuit depth constraints. As such, quantum optimization research is increasingly focused on problem instances with a specific structure – e.g., low treewidth, high degeneracy or symmetry – that may favor quantum heuristics. Continued progress will depend on tighter integration between quantum algorithm design and classical optimization insights, particularly from fields such as discrete optimization, global optimization and computational complexity.

Simulation

The simulation of quantum mechanical systems is the application for which quantum computers were initially proposed by Richard Feynman in the 1980s. Mathematically, the evolution of such a system follows the Schrodinger equation. In the simplest case – i.e., when the operator describing the energy of the system does not vary over time – the solution in closed form of the Schrodinger equation is a matrix exponential e^-iHt applied to the quantum state, where H is a matrix and t is a scalar. There are many quantum algorithms to compute matrix exponentials of that type, given a description of H. This result underpins many other quantum algorithms, including celebrated results in quantum linear algebra, such as the Harrow-Hassidim-Lloyd (HHL) algorithm for linear systems of equations. Another application of this result is the construction of Gibbs states: quantum states described by a normalized matrix exponential. Gibbs states directly generalize Gibbs distributions, so under some conditions, it is possible to sample from a Gibbs distribution more efficiently using a quantum computer than with a classical computer. Manipulation of Gibbs states and sampling from Gibbs distribution are commonly found in quantum optimization research. The intuition behind the potential advantage of quantum computers in this and related settings stems from the fact that an n x n matrix exponential e^-iHt is only a (log)-qubit operator, so there can be considerable “space” advantage, leading to – in some cases – more efficient algorithms.

Quantum computers may also be able to help with classical simulation tasks, such as estimating probabilities by Monte Carlo and related methods. The cornerstone of this potential advantage is amplitude estimation: a quantum algorithm to estimate the probability of a given event to precision ε using 0(1/ε) quantum samples instead of 0(1/ε²) classical samples. Quantum samples are more powerful than classical samples, so this is not a “plug-and-play” advantage but rather points to an area with possible applications.

Classical simulation and uncertainty quantification are extremely useful for the design and calibration of quantum hardware. The hardware is affected by several types of noise, which can occur in various phases of the device’s operation and are usually modeled based on physical principles. How to best calibrate the parameters of the noise models for a specific hardware device and how to best use the information for optimal device control are just two examples of areas in which INFORMS disciplines could be of great use for quantum computer engineering.

Machine Learning

Quantum machine learning (QML) aims to leverage quantum algorithms to improve performance or efficiency in data-driven tasks. Many QML algorithms mirror classical counterparts, such as quantum support vector machines, quantum principal component analysis and quantum Boltzmann machines, but often assume idealized or fault-tolerant settings [4, 5]. One often-cited motivation is representational efficiency: Quantum states over n qubits can encode 2ⁿ amplitudes, enabling compact representations of complex functions or distributions. However, this does not guarantee a speedup by itself.

On near-term devices, most QML methods rely on parameterized quantum circuits trained via classical optimizers. These hybrid models face practical challenges such as barren plateaus, vanishing gradients and high estimator variance [4]. This creates a role for classical O.R. techniques – e.g., derivative-free optimization, robust training or bilevel optimization – to improve reliability.

Amplitude estimation (discussed earlier) also provides a speedup that could benefit applications such as risk assessment or Bayesian inference. In more engineering-focused tasks, O.R. tools can help manage hybrid QML workflows by designing experiments, allocating compute resources or incorporating uncertainty. As entry points for further reading, we refer to two recent reviews on the opportunities and limitations of QML [4,5].

Applications

Quantum computing is being explored in multiple domains in which OR/MS plays a central role, including finance, chemical engineering and transportation. These areas provide structured problems that are natural candidates for quantum techniques and serve as inspiration for other potential applications.

In finance, quantum algorithms are being developed for stochastic modeling, optimization and machine learning. Techniques such as quantum Monte Carlo integration and gradient estimation offer asymptotic speedups, even though practical feasibility requires reduced quantum resource demands. Financial optimization problems span continuous, discrete and mixed-variable formulations, and quantum machine learning approaches face training and interpretability challenges similar to those in other fields [6].

In chemical engineering, quantum computing is being investigated for molecular simulations relevant to catalysis and materials discovery. These simulations feed into larger process design and optimization frameworks and may be integrated with classical surrogate modeling tools. While current hardware remains limited, hybrid approaches might be able to enhance modeling of chemical systems [7].

In transportation, a broad range of quantum applications has been identified across road, rail, aviation, maritime and pipeline systems. These include predictive maintenance, congestion management, supply chain optimization, emergency planning and simulation tasks such as fuel efficiency, crash modeling and weather forecasting. These use cases reflect core OR/MS problems such as large-scale scheduling, network design and decision-making under uncertainty; many are naturally suited for hybrid quantum-classical implementations in digital twin environments [8].

These examples reflect the broader potential for OR/MS to guide the modeling, benchmarking and deployment of quantum computing tools. As the field progresses, identifying problem structures that match quantum capabilities will be key to realizing impact. OR/MS expertise is also essential for building effective hybrid solutions that tackle real-world complexity through collaboration with quantum algorithm designers.

Acknowledgments

The INFORMS Quantum Computing and Operations Research Ad Hoc committee was formed in October 2024. This article is written by its members.

Disclaimer

This paper was prepared for informational purposes with contributions from the Global Technology Applied Research center of JPMorgan Chase. This paper is not a product of the Research Department of JPMorgan Chase or its affiliates. Neither JPMorgan Chase nor any of its affiliates makes any explicit or implied representation or warranty and none of them accept any liability in connection with this paper, including, without limitation, with respect to the completeness, accuracy, or reliability of the information contained herein and the potential legal, compliance, tax, or accounting effects thereof. This document is not intended as investment research or investment advice, or as a recommendation, offer, or solicitation for the purchase or sale of any security, financial instrument, financial product or service, or to be used in any way for evaluating the merits of participating in any transaction.

References

1. Abbas, A., A. Ambainis, B. Augustino, A. Bartschi, H. Buhrman, C. Coffrin, et al., 2024, “Challenges and opportunities in quantum optimization,” Nature Reviews Physics, 1-18.
2. Jordan, S.P., N. Shutty, M. Wootters, A. Zalcman, A. Schmidhuber, R. King, et al., 2024, “Optimization by decoded quantum interferometry,” arXiv: 2408.08292.
3. Koch, T., D.E. Bernal Neira, Y. Chen, G. Cortiana, D.J. Egger, R. Heese, et al., 2025, “Quantum Optimization Benchmark Library – The Intractable Decathlon,” arXiv: 2504.03832, https://git.zib.de/qopt/qoblib-quantum-optimization-benchmarking-library.
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8. LeMaster, D.A. and P. Vakharia, 2024, “Quantum technologies in transportation,” Office of the Assistant Secretary for Research and Technology, S. Department of Transportation, https://www.transportation.gov/sites/dot.gov/files/2024-12/Quantum%20Workshop_Report_121024.pdf.