Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study
Abstract
Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is well-positioned for combinatorial optimization and is particularly promising for Quadratic Unconstrained Binary Optimization (QUBO) problems. QAA is appealing due to its ability to drive the quantum system to a target state, yielding the globally optimal solution with probability over $90$+%. However, realizing QAA for application-scale optimization currently exceeds quantum hardware capacity, which is further compounded by unresolved algorithmic challenges regarding the choice of free parameters. In this study, we address these issues by utilizing a realistic traffic flow QUBO problem to investigate the implementation of QAA as a heuristic solver. Specifically, allowing the diffusion operator parameter to take non-π values expands the capabilities of QAA. This unlocks a new multiple-shot, low-iteration strategy that aims for a high cumulative probability rather than maximizing the probability of a single basis state. Using $25$-qubit simulations, our results demonstrate that heuristic QAA addresses two of the main challenges cited in previous studies. Firstly, heuristic QAA works even at a single iteration, reducing circuit depth by orders of magnitude compared to standard QAA. And secondly, we show that the problem-dependent parameters necessary for reaching optimal algorithmic performance can be reliably approximated with minimal upfront classical computing overhead.
Related
- Fewer Qubits, Better Choices: Coupling-Aware Sub-QUBO Selection for Quantum-Assisted Traffic Zone Partitioning
- Non-Orthogonal Amplitude Amplification for Hybrid CV-DV Quantum Processors
- Weakly Measured Loops for Quantum Amplitude Amplification: Oracle Savings and Adaptive Search with Unknown Target Probability
- Quantum Heuristic Separation of Comb Inequalities for the Travelling Salesman Problem
- Digital Annealer-Assisted CNOT Oriented Quantum Circuit Transpilation with Integrated QUBO Mapping and Routing
BibTeX
@misc{nieman2026heuristic,
title = {{Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study}},
author = {Kip Nieman and Daniel Koch},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13505},
eprint = {2609.13505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13505},
}
RIS
TY - UNPB
TI - Heuristic Quantum Amplitude Amplification: A Traffic QUBO Case Study
AU - Kip Nieman
AU - Daniel Koch
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13505
UR - https://arxiv.org/abs/2609.13505
AB - Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is well-positioned for combinatorial optimization and is particularly promising for Quadratic Unconstrained Binary Optimization (QUBO) problems. QAA is appealing due to its ability to drive the quantum system to a target state, yielding the globally optimal solution with probability over $90$+%. However, realizing QAA for application-scale optimization currently exceeds quantum hardware capacity, which is further compounded by unresolved algorithmic challenges regarding the choice of free parameters. In this study, we address these issues by utilizing a realistic traffic flow QUBO problem to investigate the implementation of QAA as a heuristic solver. Specifically, allowing the diffusion operator parameter to take non-π values expands the capabilities of QAA. This unlocks a new multiple-shot, low-iteration strategy that aims for a high cumulative probability rather than maximizing the probability of a single basis state. Using $25$-qubit simulations, our results demonstrate that heuristic QAA addresses two of the main challenges cited in previous studies. Firstly, heuristic QAA works even at a single iteration, reducing circuit depth by orders of magnitude compared to standard QAA. And secondly, we show that the problem-dependent parameters necessary for reaching optimal algorithmic performance can be reliably approximated with minimal upfront classical computing overhead.
ER -