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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Benchmarking Chain Strength: An Optimal Approach for Quantum Annealing
Quantum annealing (QA) is a promising optimization technique used to find global optimal solution of a combinatorial optimization problem by leveraging quantum fluctuations. In QA, the problem being solved is mapped onto the quantum processing unit (QPU) composed of qubits through a procedure called minor-embedding. The qubits are connected by a network of couplers, which determine the strength of the interactions between the qubits. The strength of the couplers that connect qubits within a chain is often referred to as the chain strength. The appropriate balance of chain strength is equally imperative in enabling the qubits to interact with one another in a way that is strong enough to obtain the optimal solution, but not excessively strong so as not to bias the original problem terms. To this end, we address the problem of identifying the optimal chain strength through the utilization of Path Integral Monte Carlo (PIMC) quantum simulation algorithm. The results indicate that our judicious choice of chain strength parameter facilitates enhancements in quantum annealer performance and solution quality, thereby paving the way for QA to compete with, or potentially outperform, classical optimization algorithms.
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- PAR ID:
- 10477832
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)
- ISBN:
- 979-8-3503-4323-6
- Page Range / eLocation ID:
- 397 to 406
- Subject(s) / Keyword(s):
- quantum annealing chain strength minor embedding
- Format(s):
- Medium: X
- Location:
- Bellevue, WA, USA
- Sponsoring Org:
- National Science Foundation
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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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We present the Hybrid Polar Decoder (HyPD), a hybrid classical-quantum decoder design for Polar error correction codes, which are becoming widespread in today’s 5G and tomorrow’s 6G networks. HyPD employs CMOS processing for the Polar decoder’s binary tree traversal, and Quantum Annealing (QA) processing for the Quantum Polar Decoder (QPD)-a Maximum-Likelihood QA-based Polar decoder submodule. QPD’s design efficiently transforms a Polar decoder into a quadratic polynomial optimization form, then maps this polynomial on to the physical QA hardware via QPD-MAP, a customized problem mapping scheme tailored to QPD. We have experimentally evaluated HyPD on a state-of-the-art QA device with 5,627 qubits, for 5G-NR Polar codes with block length of 1,024 bits, in Rayleigh fading channels. Our results show that HyPD outperforms Successive Cancellation List decoders of list size eight by half an order of bit error rate magnitude, and achieves a 1,500-bytes frame delivery rate of 99.1%, at 1 dB signal-to-noise ratio. Further studies present QA compute time considerations. We also propose QPD-HW, a novel QA hardware topology tailored for the task of decoding Polar codes. QPD-HW is sparse, flexible to code rate and block length, and may be of potential interest to the designers of tomorrow’s 6G wireless networks.more » « less
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We present the Hybrid Polar Decoder (HyPD), a hybrid of classical CMOS and quantum annealing (QA) computational structures for decoding Polar error correction codes, which are becoming widespread in today’s 5G and tomorrow’s 6G networks. HyPD considers CMOS for the Polar code’s binary tree traversal, and QA for executing a Quantum Polar Decoder (QPD)–a novel QA-based maximum likelihood submodule. Our QPD design efficiently transforms a Polar decoder into a quadratic polynomial optimization form amenable to the QA’s optimization process. We experimentally evaluate HyPD on a state-of-the-art QA device with 5,627 qubits, for Polar codes of block length 1,024 bits, in Rayleigh fading channels. Our results show that HyPD outperforms successive cancellation list decoders of list size eight by half an order of bit error rate magnitude at 1 dB SNR. Further experimental studies address QA compute time at various code rates, and with increased QA qubit numbers.more » « less
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Gilbert, Seth (Ed.)Quantum computing hardware is improving in robustness, but individual computers still have small number of qubits (for storing quantum information). Computations needing a large number of qubits can only be performed by distributing them over a network of smaller quantum computers. In this paper, we consider the problem of distributing a quantum computation, represented as a quantum circuit, over a homogeneous network of quantum computers, minimizing the number of communication operations needed to complete every step of the computation. We propose a two-step solution: dividing the given circuit’s qubits among the computers in the network, and scheduling communication operations, called migrations, to share quantum information among the computers to ensure that every operation can be performed locally. While the first step is an intractable problem, we present a polynomial-time solution for the second step in a special setting, and a O(log n)-approximate solution in the general setting. We provide empirical results which show that our two-step solution outperforms existing heuristic for this problem by a significant margin (up to 90%, in some cases).more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/QCE57702.2023.00052
