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arXiv:2607.27509

Quantum Interference as a Proposal Mechanism for Combinatorial Optimization

Donald J. Jacobs

quant-phSubmitted Jul 29, 2026• Announced Jul 31, 2026• 0 citations
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Abstract

Quantum Interference Proposal Search (QIPS) uses seed-conditioned quantum circuits to generate localized interference patterns as finite-shot proposal distributions for QUBO/Ising optimization. Candidate $n_b$-bit strings are sampled from these distributions, scored classically and used to update an elite frontier of low-energy solutions. QIPS uses a fixed two-layer gate-based circuit architecture with 100 shots per circuit while the Hilbert-space dimension grows as $2^{n_b}$. Across six benchmark families with $18 \le n_b \le 29$, QIPS maintains competitive progress relative to a matched classical control that preserves the same search loop, frontier update rule and proposal budget, with total proposals proportional to $n_b$. Performance is assessed using top-$K$ coverage, hit rate, multiplicity, Hilbert-space coverage and dyadic-rank metrics. The results identify localized quantum interference as a resource-efficient proposal mechanism for computational quantum optimization.

Comments
Main article with Supplementary Information; 5 main figures and 34 supplementary figures

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Quantum Interference Proposal Search (QIPS) uses seed-conditioned quantum circuits to generate localized interference patterns as finite-shot proposal distributions for QUBO/Ising optimization. Candidate nbn_bnb​-bit strings are sampled from these distributions, scored classically and used to update an elite frontier of low-energy solutions. QIPS uses a fixed two-layer gate-based circuit architecture with 100 shots per circuit while the Hilbert-space dimension grows as 2nb2^{n_b}2nb​. Across six benchmark families with 18≤nb≤2918 \le n_b \le 2918≤nb​≤29, QIPS maintains competitive progress relative to a matched classical control that preserves the same search loop, frontier update rule and proposal budget, with total proposals proportional to nbn_bnb​. Performance is assessed using top-KKK coverage, hit rate, multiplicity, Hilbert-space coverage and dyadic-rank metrics. The results identify localized quantum interference as a resource-efficient proposal mechanism for computational quantum optimization.
Large-scale combinatorial optimization is a challenge for near-term quantum computing because dense Quadratic Unconstrained Binary Optimization (QUBO) formulations yield interaction graphs that exceed the limits of NISQ processors. This work introduces Hybrid Quantum Neighborhood Selection (HQNS), a hybrid framework mitigating this via stochastic frontier decomposition. Instead of encoding all N variables into a monolithic circuit, HQNS selects a compact frontier of F << N active variables per stage, freezing the rest into reduced QUBO coefficients. A multi-stage crawling procedure rotates these frontiers, letting local quantum subproblems refine a global solution. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP) across six scales, N up to 1000. Circuit burden is reduced from the dense QAOA requirement of O(N^2) two-qubit terms per layer to O(F^2) per stage, with total complexity governed by the number of stages and classical overhead. Benchmarks show that HQNS achieves competitive solution quality relative to parallel simulated annealing (SA) while maintaining bounded circuit width and stable QPU time. In the N=1000 benchmark over ten executions, HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel SA baseline, while reducing wall-clock time by 65.03%, peak CPU usage by 55.97%, and peak memory by 35.21%. Ablation shows performance depends on frontier size, warm-starts, CVaR filtering, and stochastic rotation. These results demonstrate that structured frontier decomposition makes variational optimization executable for dense QUBO instances unsuitable for direct QAOA on present hardware.
Large-scale combinatorial optimization remains demanding for classical heuristics, particularly when dense Quadratic Unconstrained Binary Optimization (QUBO) formulations induce large memory footprints, high CPU utilization, and long execution times. While near-term quantum processors cannot yet deliver unconditional quantum advantage, hybrid architectures can provide practical value by reducing the resource burden. This paper presents a resource-efficiency study of Hybrid Quantum Neighborhood Selection (HQNS), a framework that decomposes large dense QUBO instances into bounded-width quantum subproblems via stochastic frontier selection. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP), focusing on the trade-off between solution quality retention and resource consumption. Benchmarks up to N=1000 candidates show that HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel Simulated Annealing baseline, while reducing wall-clock time by 94.91%, peak CPU utilization by 64.68%, and peak memory usage by 88.61%. The QPU execution time remains bounded within a 6-7 second envelope across scales, indicating that the quantum component is decoupled from the global QUBO dimension when the frontier size is fixed. These results suggest that HQNS provides a resource-aware pathway for deploying hybrid quantum optimization in practical large-scale settings, serving as an efficient architecture for incorporating near-term quantum processors into classical optimization pipelines.
We study the separation of geometric effects from quantum interference in quantum optimization algorithms. Constrained optimization problems such as routing, assignment, and scheduling are often encoded as product spaces of local variables, together with global feasibility penalties. The central algorithmic question we address is how a constraint-preserving mixing operator transports quantum amplitude across an exponential search space in the presence of local and global constraints. We develop a framework that separates three effects that are usually intermixed: amplitude transport, coherent interference among transported amplitudes, and problem-dependent classical postprocessing. We show that the mixing operator alone does not have a target-seeking ability. Concretely, the normalized distribution induced by its amplitude transport moves toward the distance profile of a uniformly random configuration. Thus, quantum sampling advantage may only arise when the phases of the many computational paths reaching a target configuration are sufficiently aligned for their amplitudes to reinforce. We show that, when the cost phases are engineered so that these paths add coherently, a number of circuit alternations growing only logarithmically with problem size suffices to convert the sum of their absolute contributions into a lower bound on the target amplitude, yielding a certified success probability independent of the ambient Hilbert-space dimension, the search-space size, or the feasible-set cardinality. We develop applications to problem-specific transpilation diagnostics, scalable hardware probes, constraint-induced classical maps of quantum-generated samples, the attribution of solution quality between the quantum distribution and classical post-processing in hybrid quantum-classical workflows and connections to distance-partitioned product spaces from classical coding theory.
This paper explores a novel approach to randomized search algorithms, termed Quantum-Inspired Randomized Search (QIRS). The core premise is that the principles of quantum superposition and interference, traditionally associated with quantum computing, can be effectively translated into classical algorithms to enhance their efficiency. The proposed methodology involves representing candidate solutions as quantum states and utilizing interference patterns to strategically guide the search process. This departs from traditional randomized search which relies solely on random sampling, introducing a layer of probabilistic control mimicking quantum behavior. The effectiveness of QIRS is evaluated through theoretical analysis and conceptual demonstrations, highlighting the potential for significant improvements in algorithm design, particularly in complex, high-dimensional search spaces. We demonstrate a shift in the search strategy from purely stochastic exploration to a more informed, interference-driven process. The key contribution lies in adapting quantum concepts to optimize the exploration process within randomized search, offering a new direction for algorithm design and optimization.
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This paper explores the application of quantum-inspired concepts to the field of combinatorial optimization. Traditional search algorithms often struggle with the complexity of problems involving numerous possible solutions. We propose a novel approach that leverages the principles of quantum superposition and interference, albeit within a classical computing framework, to enhance the efficiency of search processes. The core of our method involves a hybrid algorithm that combines established classical search techniques with probabilistic sampling strategies informed by quantum mechanics. We aim to demonstrate that by mimicking these quantum phenomena, we can significantly improve the speed and effectiveness of solving complex combinatorial optimization problems. The algorithm's performance is evaluated through theoretical analysis and conceptual design, focusing on the potential for achieving performance gains without requiring actual quantum hardware. The key contribution lies in the strategic application of probabilistic sampling to explore solution spaces in a manner analogous to quantum superposition, followed by interference-like mechanisms to guide the search towards promising regions. This approach represents a new direction in optimization, bridging the gap between classical and quantum computing paradigms.