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Abstract Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.
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FastHare: Fast Hamiltonian Reduction for Large-scale Quantum Annealing
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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- Award ID(s):
- 2229075
- PAR ID:
- 10477830
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- 2022 IEEE International Conference on Quantum Computing and Engineering (QCE)
- ISBN:
- 978-1-6654-9113-6
- Page Range / eLocation ID:
- 114 to 124
- Subject(s) / Keyword(s):
- Qubit-reduction Ising Hamiltonian Quantum annealing non-separable group
- Format(s):
- Medium: X
- Location:
- Broomfield, CO, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/QCE53715.2022.00030
