Resource and entanglement study of a hybrid qudit-qubit quantum algorithm for solving the integer programming problem
Abstract
Recently, a hybrid qudit-qubit algorithm [1] was presented for solving the integer programming problem with a polynomial quantum advantage. In this work, we investigate the algorithm [1] to understand the role of qudits (d-dimensional quantum system) by conducting a comparative resource analysis with its qubit-only implementation and the classical simulability of the algorithm by exploring the entanglement structure. The resource analysis part is performed in terms of logical gate counts, and fault-tolerant physical resources, including non-Clifford gates. The hybrid qudit-qubit implementation has a more compact structure of the unitary operators as opposed to its qubit-only simulation which reduces the logical and fault-tolerant resource requirements. Two example problems, one with qutrits (d=3) and the other with ququint (d=5), when contrasted with their qubit-only implementation, within a simplified fault-tolerant resource model, showed $\sim 180 \times $ and ∼ 2220× fewer total resource count, respectively. For the entanglement study, volume-law-like entropy growth and signatures of multi-partite entanglement is observed leading to increasing difficulty in the classical simulation of the algorithm. The algorithm generates synergistic tri-partite entanglement even for a quadratic problem, revealing that the algorithmic structure itself can generate higher-order entanglement in the system independent of the problem.
Related
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BibTeX
@misc{goswami2026resource,
title = {{Resource and entanglement study of a hybrid qudit-qubit quantum algorithm for solving the integer programming problem}},
author = {Kapil Goswami and Rick Mukherjee and Peter Schmelcher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23243},
eprint = {2609.23243},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23243},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Resource and entanglement study of a hybrid qudit-qubit quantum algorithm for solving the integer programming problem
AU - Kapil Goswami
AU - Rick Mukherjee
AU - Peter Schmelcher
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23243
UR - https://arxiv.org/abs/2609.23243
AB - Recently, a hybrid qudit-qubit algorithm [1] was presented for solving the integer programming problem with a polynomial quantum advantage. In this work, we investigate the algorithm [1] to understand the role of qudits (d-dimensional quantum system) by conducting a comparative resource analysis with its qubit-only implementation and the classical simulability of the algorithm by exploring the entanglement structure. The resource analysis part is performed in terms of logical gate counts, and fault-tolerant physical resources, including non-Clifford gates. The hybrid qudit-qubit implementation has a more compact structure of the unitary operators as opposed to its qubit-only simulation which reduces the logical and fault-tolerant resource requirements. Two example problems, one with qutrits (d=3) and the other with ququint (d=5), when contrasted with their qubit-only implementation, within a simplified fault-tolerant resource model, showed $\sim 180 \times $ and ∼ 2220× fewer total resource count, respectively. For the entanglement study, volume-law-like entropy growth and signatures of multi-partite entanglement is observed leading to increasing difficulty in the classical simulation of the algorithm. The algorithm generates synergistic tri-partite entanglement even for a quadratic problem, revealing that the algorithmic structure itself can generate higher-order entanglement in the system independent of the problem.
ER -