Assessing Quantum Computing Performance for Energy Optimization in a Prosumer Community

In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field for near-term quantum computers, both by using gate-based QC via the Quantum Approximate Optimization Algorithm and by quantum annealing using the Ising model. However, demonstrating an advantage over classical methods in real-world applications remains an active area of research. In this work, we investigate the robustness verification of ReLU networks, which involves solving many-variable mixed-integer programs (MIPs), as a practical application. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified by classical methods. To alleviate this issue, we propose to use QC for neural network verification and introduce a hybrid quantum procedure to compute provable certificates. By applying Benders decomposition, we split the MIP into a quadratic unconstrained binary optimization and a linear program which are solved by quantum and classical computers, respectively. We further improve existing hybrid methods based on the Benders decomposition by reducing the overall number of iterations and placing a limit on the maximum number of qubits required. We show that, in a simulated environment, our certificate is sound, and provides bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulations and on quantum hardware.

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm and Quantum Annealing can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to characterize classical optimization algorithms, we analyze the solution quality obtained by solving Max-cut problems using gate-model quantum devices and a quantum annealing device. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through compelling visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. As an illustration, we explore the factors that influence quantum computing system throughput, using results obtained through execution on various quantum simulators and quantum hardware systems.

The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questions in the scaling of this algorithm. In particular, we show that for fixed number of parity-encoded QAOA layers, the performance or the output energy, vanishes towards zero (the value achieved by random guessing) with problem size N as N−1/2. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA. We perform tensor-network calculations to confirm our results, and comment on the concentration of optimal QAOA parameters over problem instances.

The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to significantly expand the breadth of applications for which quantum computers have an established advantage. A leading candidate is Farhi et al.’s quantum approximate optimization algorithm, which alternates between applying a cost function based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach, in the spirit of the quantum approximate optimization algorithm, to a wide variety of approximate optimization, exact optimization, and sampling problems. In addition to introducing the quantum alternating operator ansatz, we lay out design criteria for mixing operators, detail mappings for eight problems, and provide a compendium with brief descriptions of mappings for a diverse array of problems.

Abstract: This chapter explores the transformative potential of quantum algorithms in solving complex optimization problems across industries such as logistics, finance, and material science. Quantum algorithms, including Quantum Annealing, Quantum Approximate Optimization Algorithm (QAOA), and Variational Quantum Eigensolver (VQE), offer unprecedented computational capabilities for addressing challenges that are impractical for classical algorithms. In logistics, quantum algorithms optimize supply chains, vehicle routing, and warehouse operations, significantly reducing costs and improving efficiency. In finance, quantum optimization enables better portfolio management, risk assessment, and high-frequency trading strategies, providing faster, more accurate solutions. In material science, quantum algorithms accelerate the discovery and design of new materials, such as superconductors and catalysts, by simulating molecular interactions more efficiently. The chapter discusses real-world implementations, current technical challenges, and the future potential of quantum algorithms to revolutionize industries through faster and more scalable optimization solutions. Keywords: Quantum algorithms, Quantum Annealing, QAOA, VQE, optimization, logistics, finance, material science, portfolio optimization, risk management, supply chain, molecular simulation, quantum computing, quantum optimization, quantum chemistry, high-frequency trading.

Quantum computing is poised to transform computational paradigms across science and industry. As the field evolves, it can benefit from established classical methodologies, including promising paradigms such as Transfer of Knowledge (ToK). This work serves as a brief, self‐contained reference for ToK, unifying its core principles under a single formal framework. We introduce a joint notation that consolidates and extends prior work in Transfer Learning and Transfer Optimisation, bridging traditionally separate research lines and enabling a common language for knowledge reuse. Building on this foundation, we classify existing ToK strategies and principles into a structured taxonomy that helps researchers position their methods within a broader conceptual map. We then extend key transfer protocols to quantum computing, introducing two novel use cases—reverse annealing and multitasking Quantum Approximate Optimization Algorithm (QAOA)—alongside a sequential Variational Quantum Eigensolver (VQE) approach that supports and validates prior findings. These examples highlight ToK's potential to improve performance and generalisation in quantum algorithms. Finally, we outline challenges and opportunities for integrating ToK into quantum computing, emphasising its role in reducing resource demands and accelerating problem‐solving. This work lays the groundwork for future synergies between classical and quantum computing through a shared, transferable knowledge framework.

The selection of crude oil feedstock is a critical, high-impact optimization problem in the petrochemical industry, directly influencing refinery profitability and environmental footprint. Traditional optimization methods face scalability challenges as the complexity and number of constraints increase. This paper presents an initial study on the application of quantum computing to solve a binary feedstock optimization model. We formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and employ the Quantum Approximate Optimization Algorithm (QAOA) to find low-cost solutions. To manage the probabilistic nature of quantum results, we introduce Conditional Value at Risk (CVaR) as a post-processing technique to select robust, high-quality solutions. Our results on a representative small-scale problem demonstrate the viability of this hybrid quantum-classical approach, showing its potential to identify near-optimal solutions. We conclude with a discussion of current limitations and an open call for collaboration to further explore quantum computing applications in the energy sector.

With the demonstrated ability to perform calculations in seconds that would take classical supercomputers thousands of years, quantum computers namely hold the promise of radically advancing sustainable IT. However, quantum computers face challenges due to the inherent noise in physical qubits, necessitating error correction for reliable operation in solving industrial-scale problems, which will require more computation time, energy, and electronic components than initial laboratory-scale experiments. Yet, while researchers have modeled and analyzed the environmental impacts of classical computers using Life cycle assessment the environmental performance of quantum computing remains unknown to date. This study contributes to filling this critical gap in two ways: (1) by establishing an environmental profile for quantum computers based on superconducting qubits; and (2) by comparing it to a functionally equivalent profile of a state-of-the-art supercomputer. With the comparison based on the problem size, the paper shows how the usage time can drive an environmental advantage for quantum computers under specific scaling conditions and quantum error correcting codes. The results emphasize that quantum error correction hardware has a substantial environmental impact due to the numerous electronic components needed to achieve 100 logical qubits. This paper can serve as a basis for designing more environmentally friendly quantum computers and for establishing their environmental profiles, as well as those of the human activities that will use them.

Abstract: This paper suggests a new method for improving routes in complicated logistics systems by combining cognitive modeling with quantum computing algorithms, especially the Quantum Approximate Optimization Algorithm (QAOA). In the classic Traveling Salesman Problem (TSP), the model shows major improvements, beating traditional methods by 25% in finding solutions accurately and cutting computation time by 30%. Simulations show a 15% drop in travel time and a 20% cut in CO₂ emissions, highlighting how the model helps improve efficiency and support environmental sustainability. The innovation comes from combining two usually separate fields: cognitive modeling, which mimics how humans make decisions, and quantum computing, which allows for fast and large‑scale optimization. This teamwork between different fields encourages quick, flexible, and scalable decision‑making, which is essential in fast‑changing, real‑time logistics settings. The model matches the move towards Industry 5.0, which focuses on working together with machines and being environmentally friendly. It also supports the United Nations Sustainable Development Goals, especially Goal 9 (Industry, Innovation and Infrastructure) and Goal 13 (Climate Action). To make sure the study is valid, it uses open‑access datasets and simulates real‑life situations, such as smart warehouse operations and fleet management systems. The results highlight how quantum‑enhanced cognitive systems can change the game, providing a modern tool to build smarter, greener, and stronger supply chains. This research not only pushes the boundaries of optimization science but also lays the groundwork for using quantum algorithms in industry in the future.

Abstract: This paper explores hybrid quantum-classical optimization algorithms implemented across multiple quantum software development kits (SDKs): Qiskit and Cirq,. We evaluate the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) in terms of convergence rate, final cost value, and fidelity, using both simulators and real quantum hardware backends. Our results offer comparative insights into SDK performance and propose a standardized benchmarking approach for future quantum algorithm research. Keywords: Hybrid Quantum Algorithms, Qiskit, Cirq, VQE, QAOA, Quantum SDKs, Quantum Optimization, NISQ

This work addresses the problem of energy planning optimization, focusing specifically on the regions of Baja California and Baja California Sur. To this end, a hybrid optimization approach is employed, combining classical computing and quantum computing through the Quantum Approximate Optimization Algorithm (QAOA). First, the fundamental elements of the research are presented, including the problema description, motivation, justification, objectives, hypothesis, and the proposed methodology. Subsequently, related works and basic concepts necessary for the development and understanding of the theoretical and methodological framework are reviewed. Next, a general description of the Mexican National Electric System is provided, followed by a focused analysis of the Baja California Peninsula as case studies. In this section, the technical data of the generating units in each region are presented, along with the energy demand corresponding to a day selected for the purpose of case study analysis. Subsequently, the employed methodology is described, accompanied by the mathematical and computational formulation required to address the central problem of this research. With the methodology defined and applied, the results obtained using the QAOA-based hybrid optimization algorithm are presented and compared with solutions obtained through classical optimization methods using solvers such as GLPK. Finally, the main findings related to the application of quantum computing, through the QAOA algorithm, to energy planning optimization are synthetically discussed. Additionally, current limitations and aspects requiring improvement are identified, highlighting the conditions under which quantum-based algorithms may surpass conventional classical approaches in the future.

Many challenging scheduling, planning, and resource allocation problems come with real-world input data and hard problem constraints, and reduce to optimizing a cost function over a combinatorially defined feasible set, such as colorings of a graph. Toward tackling such problems with quantum computers using quantum approximate optimization algorithms, we present novel efficient quantum alternating operator ansatz (QAOA) constructions for optimization problems over proper colorings of chordal graphs. As our primary application, we consider the flight-gate assignment problem , where flights are assigned to airport gates as to minimize the total transit time of all passengers, and feasible assignments correspond to proper graph colorings of a conflict graph derived instancewise from the input data. We leverage ideas from classical algorithms and graph theory to show our constructions have the desirable properties of restricting quantum state evolution to the feasible subspace, and satisfying a particular reachability condition for most problem parameter regimes. Using classical preprocessing we show that we can always find and construct a suitable initial quantum (superposition) state efficiently. We show our constructions in detail, including explicit decompositions to a universal set of basic quantum gates, which we use to bound the required resource scaling as low-degree polynomials of the input parameters. In particular, we derive novel QAOA mixing operators and show that their implementation cost is commensurate with that of the QAOA phase operator for flight-gate assignment. A number of quantum circuit diagrams are included such that our constructions may be used as a template toward development and implementation of quantum gate-model approaches for a wider variety of potentially impactful real-world applications.

Automatic optical inspection (AOI) systems for drones are increasingly becoming core tools for intelligent operation and maintenance of industrial infrastructure. However, their traditional implementation paradigms face fundamental technical bottlenecks in communication security, collaborative control, and harsh environment perception. This paper aims to provide a systematic review and analysis of research progress in enabling nextgeneration UAV AOI systems through emerging quantum technologies, including quantum communication, quantum computing, and quantum sensing. The article first provides a comprehensive overview of the unique potential and current engineering challenges faced by technologies such as quantum key distribution (QKD), quantum approximate optimization algorithms (QAOA), and quantum imaging in addressing the limitations of classical systems. Furthermore, this analysis delved into the cutting-edge concept of a “quantum-classical hybrid architecture” that integrates quantum modules with mature classical systems, analyzing its integration mechanisms and performance gains across three dimensions: communication, computation, and sensing. The review indicates that while this fusion paradigm can theoretically significantly enhance system security, optimize efficiency, and improve robustness, its practical deployment remains constrained by the environmental sensitivity of quantum devices, high costs, and complex system integration. Finally, this paper offers a forward-looking discussion on future development directions in hardware miniaturization, algorithmic collaboration frameworks, and standardization research within this field, providing a framework for researchers to comprehensively understand the opportunities and challenges in this interdisciplinary domain.

The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work (Lloyd, arXiv:1812.11075) argued that for one-dimensional local cost Hamiltonians, composed of nearest neighbour ZZ terms, this set-up is quantum computationally universal and provides a universal gate set, i.e. all unitaries can be reached up to arbitrary precision. In the present paper, we complement this work by giving a complete proof and the precise conditions under which such a one-dimensional QAOA might produce a universal gate set. We further generalize this type of gate-set universality for certain cost Hamiltonians with ZZ and ZZZ terms arranged according to the adjacency structure of certain graphs and hypergraphs.

In this work we investigate the performance of greedy randomised search (GRS) techniques to the problem of compiling quantum circuits that solve instances of the Graph Coloring problem. Quantum computing uses quantum gates that manipulate multi-valued bits (qubits). A quantum circuit is composed of a number of qubits and a series of quantum gates that operate on those qubits, and whose execution realises a specific quantum algorithm. Current quantum computing technologies limit the qubit interaction distance allowing the execution of gates between adjacent qubits only. This has opened the way to the exploration of possible techniques aimed at guaranteeing nearest-neighbor (NN) compliance in any quantum circuit through the addition of a number of so-called swap gates between adjacent qubits. In addition, technological limitations (decoherence effect) impose that the overall duration (i.e., depth) of the quantum circuit realization be minimized. One core contribution of the paper is the application of an upgraded version of the greedy randomized search (GRS) technique originally introduced in the literature that synthesises NN-compliant quantum circuits realizations, starting from a set of benchmark instances of different size belonging to the Quantum Approximate Optimization Algorithm (QAOA) class tailored for the Graph Coloring problem. We propose a comparison between the presented method and the SABRE compiler, one of the best-performing compilation procedures present in Qiskit, an open-source SDK for quantum development, both from the CPU efficiency and from the solution quality standpoint.