FastHare: Fast Hamiltonian Reduction for Large-scale Quantum Annealing

TL;DR

FastHare is a novel, efficient Hamiltonian reduction method for quantum annealing that significantly reduces qubits and outperforms existing techniques, enabling larger problem instances to be tackled.

Contribution

We introduce FastHare, a new reduction algorithm based on non-separable groups, with provable efficiency and superior performance over existing methods.

Findings

FastHare achieves 62% qubit reduction on average.

It runs in $O(eta n^2)$ time, with $eta$ depending on user parameters.

Outperforms roof duality with 3.6x higher reduction ratio.

Abstract

Quantum annealing (QA) that encodes optimization problems into Hamiltonians remains the only near-term quantum computing paradigm that provides sufficient many qubits for real-world applications. To fit larger optimization instances on existing quantum annealers, reducing Hamiltonians into smaller equivalent Hamiltonians provides a promising approach. Unfortunately, existing reduction techniques are either computationally expensive or ineffective in practice. To this end, we introduce a novel notion of non-separable~group, defined as a subset of qubits in a Hamiltonian that obtains the same value in optimal solutions. We develop a theoretical framework on non-separability accordingly and propose FastHare, a highly efficient reduction method. FastHare, iteratively, detects and merges non-separable groups into single qubits. It does so within a provable worst-case time complexity of only $O(\alpha n^2)$, for some user-defined parameter $\alpha$. Our extensive benchmarks for the feasibility of the reduction are done on both synthetic Hamiltonians and 3000+ instances from the MQLIB library. The results show FastHare outperforms the roof duality, the implemented reduction method in D-Wave's SDK library, with 3.6x higher average reduction ratio. It demonstrates a high level of effectiveness with an average of 62% qubits saving and 0.3s processing time, advocating for Hamiltonian reduction as an inexpensive necessity for QA.