Work

Imposing Constraints on Driver Hamiltonians and Mixing Operators: From Theory to Practical Implementation

Year: 2026

Type: article

Abstract: Driver Hamiltonians and Mixing Operators that satisfy constraints is an important part of ansatz construction for many quantum algorithms. In this manuscript, we give general algebraic expressions for finding Hamiltonian terms and analogously unitary primitives, that satisfy constraint embeddings and use these to give complexity characterizations of the related problems. We prove that knowing if operators exist that enforce classical constraints is NP-Complete in the general case, but give algorithmic procedures with worst-case polynomial runtime to find any operators with a constant locality bound; a useful result since many constraints imposed admit local operators to enforce them in practice. We then give algorithmic procedures to turn these algebraic primitives into Hamiltonian drivers and unitary mixers that can be used for Constrained Quantum Annealing (CQA) and Quantum Alternating Operator Ansatz (QAOA) constructions by tackling practical problems related to finding an appropriate set of reduced generators and defining corresponding drivers and mixers accordingly. We consider a new QAOA approach based on the maximally disjoint subset as well as higher order constraint satisfaction terms for 1-in-3 SAT, which dramatically outperform the X-mixer.

Source: ACM Transactions on Quantum Computing

DOI: 10.1145/3821414

Authors: Hannes Leipold, Federico Spedalieri, Stuart Hadfield, Eleanor Rieffel

Institutions: University of Southern California, Ames Research Center, Research Institute for Advanced Computer Science, Universities Space Research Association

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid