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arXiv:2609.00881

Towards Natural Gas Contract Selection via Quantum-Guided Independent Set Reduction

Vivek Dixit, Vaibhaw Kumar, Kentaro Ohno, Alberto Maldonado Romo, Larry Bowden

quant-phSubmitted Sep 1, 2026• Announced Sep 2, 2026• 0 citations
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Abstract

Selecting mutually compatible natural gas transportation contracts is a practically important optimization task in which operators must choose from many candidate agreements subject to temporal, infrastructural, and flow-related constraints. As the number of candidates grows, the resulting search space becomes difficult to explore exhaustively. We study a pairwise abstraction of this task, formulated as a Maximum Clique problem on a contract-compatibility graph, or equivalently as a Maximum Independent Set (MIS) problem on the complement graph. Building on recent work, this paper studies a quantum-classical framework for solving large-scale MIS instances within the limitations of noisy quantum hardware. The approach combines iterative classical graph reduction with quantum-guided optimization to progressively simplify the search space while maintaining high solution quality. This enables large candidate spaces to be reduced to smaller subproblems that are more suitable for execution on current quantum computers. We evaluate the approach on fifteen benchmark instances from the Quantum Optimization Benchmarking Library (QOBLIB), obtaining an average approximation ratio of 0.996 and recovering optimal solutions for fourteen instances, including graphs with up to 186 vertices. We further evaluate the algorithm on six synthetic pairwise contract-compatibility graphs containing up to 900 contracts, where the proposed method achieves an average approximation ratio of 0.989 and obtains optimal solutions in four cases. These experiments demonstrate the ability of the hybrid MIS solver to reduce industrially motivated graphs. The pairwise abstraction serves as the first step of a two-stage screening procedure that narrows the candidate contracts to a smaller set of mutually compatible ones, which can then be verified against pipeline-capacity constraints.

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quant-pharXiv:2605.03524•IEEE International Conference on Quantum Computing and Engineering (QCE)•May 6, 2026•6 citations
Selecting mutually compatible natural gas transportation contracts is a practically important optimization task in which operators must choose from many candidate agreements subject to temporal, infrastructural, and flow-related constraints. As the number of candidates grows, the resulting search space becomes difficult to explore exhaustively. We study a pairwise abstraction of this task, formulated as a Maximum Clique problem on a contract-compatibility graph, or equivalently as a Maximum Independent Set (MIS) problem on the complement graph.
Building on recent work, this paper studies a quantum-classical framework for solving large-scale MIS instances within the limitations of noisy quantum hardware. The approach combines iterative classical graph reduction with quantum-guided optimization to progressively simplify the search space while maintaining high solution quality. This enables large candidate spaces to be reduced to smaller subproblems that are more suitable for execution on current quantum computers.
We evaluate the approach on fifteen benchmark instances from the Quantum Optimization Benchmarking Library (QOBLIB), obtaining an average approximation ratio of 0.996 and recovering optimal solutions for fourteen instances, including graphs with up to 186 vertices. We further evaluate the algorithm on six synthetic pairwise contract-compatibility graphs containing up to 900 contracts, where the proposed method achieves an average approximation ratio of 0.989 and obtains optimal solutions in four cases. These experiments demonstrate the ability of the hybrid MIS solver to reduce industrially motivated graphs. The pairwise abstraction serves as the first step of a two-stage screening procedure that narrows the candidate contracts to a smaller set of mutually compatible ones, which can then be verified against pipeline-capacity constraints.
Maximizing gas throughput in transmission networks under hydraulic and operational constraints is a combinatorial problem whose complexity grows exponentially with network size, making it computationally intensive to solve exactly. This paper addresses the graph-based optimization problem by optimizing nodal-pressure assignments under the Panhandle-B hydraulic equation. By framing the problem as a search over discretized nodal-pressure assignments coupled with a cost Hamiltonian that encodes both the delivery objective and physical-constraint penalties, we establish a unified formulation suitable for the Quantum Approximate Optimization Algorithm (QAOA). The mathematical model is adapted to a Quadratic Unconstrained Binary Optimization (QUBO) formulation and implemented using the Classiq quantum software platform. In simulator-based experiments, QAOA recovered the maximum-throughput valid operating point, consistent with classical exhaustive evaluation and classical hydraulic simulation reference solutions. A distinctive contribution of this work is the end-to-end execution of a reduced problem instance on the IonQ Forte-1 trapped-ion quantum processor. Remarkably, the hardware implementation used only p=2p=2p=2 QAOA layers, substantially fewer than the p=30p=30p=30 layers used in the simulator-based study. Despite this significant reduction in circuit depth, the QPU produced physically valid and interpretable candidate solutions that bracketed the continuous classical optimum, with each located within one pressure-discretization step of it. These results demonstrate that meaningful gas-network optimization behavior can be obtained using considerably shallower QAOA circuits than initially expected and provide an end-to-end proof of concept for near-term quantum-assisted gas-network optimization.
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 subsecond timescales, 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 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.
We investigate a hybrid quantum-classical algorithm for solving the Maximum Independent Set (MIS) problem on regular graphs, combining the Quantum Approximate Optimization Algorithm (QAOA) with a minimal degree classical greedy algorithm. The method leverages pre-computed QAOA angles, derived from depth-ppp QAOA circuits on regular trees, to compute local expectation values and inform sequential greedy decisions that progressively build an independent set. This hybrid approach maintains shallow quantum circuit and avoids instance-specific parameter training, making it well-suited for implementation on current quantum hardware: we have implemented the algorithm on a 20 qubit IQM superconducting device to find independent sets in graphs with thousands of nodes. We perform tensor network simulations to evaluate the performance of the algorithm beyond the reach of current quantum hardware and compare to established classical heuristics. Our results show that even at low depth (p=4p=4p=4), the quantum-enhanced greedy method significantly outperforms purely classical greedy baselines as well as more sophisticated approximation algorithms. The modular structure of the algorithm and relatively low quantum resource requirements make it a compelling candidate for scalable, hybrid optimization in the NISQ era and beyond.
Abstract The quantum alternating operator ansatz algorithm (QAOA+) is widely used for constrained combinatorial optimization problems (CCOPs) due to its ability to construct feasible solution spaces. In this paper, we propose a progressive quantum algorithm (PQA) to reduce qubit requirements for QAOA+ in solving the maximum independent set (MIS) problem. PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution. Specifically, PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies. After each expansion, PQA solves the MIS problem on the newly generated subgraph using QAOA+. In each run, PQA repeats the expansion and solving process until a predefined stopping condition is reached. Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57% (2.17%) of the qubits and 17.59% (6.43%) of the runtime compared with directly solving the original problem with QAOA+ on Erdös–Rényi (3-regular) graphs, highlighting the efficiency and scalability of PQA.
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of COPs, while preserving problem structure. Our approach introduces three key ideas: (i) constraint-aware shrinking that prevents merges that will likely violate problem-specific feasibility constraints, (ii) a verification-and-repair pipeline to correct infeasible solutions post-optimization, and (iii) adaptive strategies for recalculating correlations and controlling the graph shrinking process. We apply our approach to three standard benchmark problems: Multidimensional Knapsack (MDKP), Maximum Independent Set (MIS), and the Quadratic Assignment Problem (QAP). Empirical results show that our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances. These findings demonstrate a scalable pathway for applying near-term quantum algorithms to classically challenging constrained optimization problems.
Among the limitations of current quantum machines, the qubits count represents one of the most critical challenges for porting reasonably large computational problems, such as those coming from real-world applications, to the scale of the quantum hardware. In this regard, one possibility is to decompose the problems at hand and exploit parallelism over multiple size-limited quantum resources. To this purpose, we designed a hybrid quantum-classical algorithm, i.e., BBQ-mIS, to solve graph coloring problems on Rydberg atoms quantum machines. The BBQ-mIS algorithm combines the natural representation of Maximum Independent Set (MIS) problems onto the machine Hamiltonian with a Branch&Bound (BB) approach to identify a proper graph coloring. In the proposed solution, the graph representation emerges from qubit interactions (qubits represent vertexes of the graph), and the coloring is then retrieved by iteratively assigning one color to a maximal set of independent vertexes of the graph, still minimizing the number of colors with the Branch&Bound approach. We emulated real quantum hardware onto an IBM Power9-based cluster, with 32 cores/node and 256 GB/node, and exploited an MPI-enhanced library to implement the parallelism for the BBQ-mIS algorithm. Considering this use case, we also identify some technical requirements and challenges for an effective HPC-QC integration. The results show that our problem decomposition is effective in terms of graph coloring solutions quality, and provide a reference for applying this methodology to other quantum technologies or applications.