Resource-Efficient Quantum Optimization via Higher-Order Encoding

TL;DR

This paper demonstrates that Higher-Order Unconstrained Binary Optimization (HUBO) significantly reduces resource requirements in quantum optimization compared to traditional QUBO encodings, making it more practical for near-term quantum devices.

Contribution

The authors introduce a systematic method for constructing HUBO Hamiltonians and provide an open-source library, showing exponential qubit reduction and substantial gate count decreases over QUBO in benchmark problems.

Findings

HUBO reduces qubit requirements exponentially compared to QUBO.

HUBO decreases CNOT gate counts by at least 89.6%.

HUBO is practical for current and near-term quantum devices.

Abstract

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and gate counts. We show that Higher-Order Unconstrained Binary Optimization (HUBO) enables a more resource-efficient formulation. Our method systematically constructs HUBO Hamiltonians and, compared to QUBO in benchmarks on Gate Assignment (GAP), Maximum k-Colorable Subgraph (MkCS), and Integer Programming (IP) problems, exponentially reduces qubit requirements and decreases CNOT gate counts by at least 89.6% after compilation to single- and two-qubit gates for all tested instances. These results highlight HUBO as a practical alternative for current and near-term devices. To promote adoption, we release an open-source Python library that automates HUBO model construction, broadening access to resource-efficient quantum optimization.