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Quantum annealing (QA) that encodes optimization problems into Hamiltonians remains the only near-term quantum computing paradigm that provides sufficient 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 non-separability theory 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(αn^2), for some user-defined parameter α. 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 in D-Wave’s library. 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.
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This content will become publicly available on August 5, 2026
A Haskell Adiabatic DSL: Solving Classical Optimization Problems on Quantum Hardware
In physics and chemistry, quantum systems are typically modeled using energy constraints formulated as Hamiltonians. Investigations into such systems often focus on the evolution of the Hamiltonians under various initial conditions, an approach summarized as Adiabatic Quantum Computing (AQC). Although this perspective may initially seem foreign to functional programmers, we demonstrate that conventional functional programming abstractions—specifically, the Traversable and Monad type classes—naturally capture the essence of AQC. To illustrate this connection, we introduce EnQ, a functional programming library designed to express diverse optimization problems as energy constraint computations (ECC). The library comprises three core components: generating the solution space, associating energy costs with potential solutions, and searching for optimal or near-optimal solutions. Because EnQ is implemented using standard Haskell, it can be executed directly through conventional classical Haskell compilers. More interestingly, we develop and implement a process to compile EnQ programs into circuits executable on quantum hardware. We validate EnQ’s effectiveness through a number of case studies, demonstrating its capacity to express and solve classical optimization problems on quantum hardware, including search problems, type inference, number partitioning, clique finding, and graph coloring.
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- Award ID(s):
- 2435255
- PAR ID:
- 10628284
- Publisher / Repository:
- Association for Computing Machinery
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 9
- Issue:
- ICFP
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 479 to 509
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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