Combinatorial Optimization by Decomposition on Hybrid CPU–non-CPU Solver Architectures
By Ali Narimani, Seyed Saeed Rezaei, & Arman Zaribafiyan
The advent of special-purpose hardware such as FPGA- or ASIC-based annealers and quantum processors has shown potential in solving certain families of complex combinatorial optimization problems more efficiently than conventional CPUs. We show that to address an industrial optimization problem, a hybrid architecture of CPUs and non-CPU devices is inevitable. In this paper, we propose problem decomposition as an effective method for designing a hybrid CPU–non-CPU optimization problem solver. We introduce the required algorithmic elements for making problem decomposition a viable approach in meeting real-world constraints such as communication time and the potential higher cost of using non-CPU hardware. We then turn to the well-known maximum clique problem, and propose a new decomposition method for this problem. Our method enables us to solve the maximum clique problem on very large graphs using non-CPU hardware that is considerably smaller in size than the graph. As an example, we demonstrate that the maximum clique problem on the com-Amazon graph, with 334,863 vertices and 925,872 edges, can be solved using a single problem embedding on fully connected hardware with at least 21 nodes, such as the D-Wave 2000Q. We also show that our proposed problem decomposition approach can improve the runtime of two of the best-known classical algorithms for large, sparse graphs, namely PMC and BBMCSP, by orders of magnitude. In the light of our study, we believe that even new non-CPU hardware that is small in size could become competitive with CPUs if it could be either mass produced and highly parallelized, or able to provide high-quality solutions to specific problems significantly faster than CPUs.
PDF ARXIV PREPRINT
Most Recent Papers
Neural Error Mitigation of Near-Term Quantum Simulations
By Elizabeth R. Bennewitz, Florian Hopfmueller, Bohdan Kulchytskyy, Juan Carrasquilla, & Pooya Ronagh
One of the promising applications of early quantum computers is the simulation of quantum systems. Variational methods for near-term quantum computers, such as the variational quantum eigensolver (VQE), are a promising approach to finding ground states of quantum systems relevant in physics, chemistry, and materials science…
Benchmark Study of Quantum Algorithms for Combinatorial Optimization: Unitary versus Dissipative
By Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, & Yoshihisa Yamamoto
We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr-Hoyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover’s search. We use MaxCut problems as our reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms…
Scaling Up Electronic Structure Calculations on Quantum Computers: The Frozen Natural Orbital Based Method of Increments
By Prakash Verma, Lee Huntington, Marc Coons, Yukio Kawashima, Takeshi Yamazaki, & Arman Zaribafiyan
The method of increments and frozen natural orbital (MI-FNO) framework is introduced to help expedite the application of noisy, intermediate-scale quantum (NISQ) devices for quantum chemistry simulations. The MI-FNO framework provides a systematic reduction of the occupied and virtual orbital spaces for quantum chemistry simulations. The correlation energies of the resulting increments from the MI-FNO reduction can then be solved by various algorithms, including quantum algorithms such as the phase estimation algorithm and the variational quantum eigensolver (VQE)…
Variationally Scheduled Quantum Simulation
By Shunji Matsuura, Samantha Buck, Valentin Senicourt, & Arman Zaribafiyan
Eigenstate preparation is ubiquitous in quantum computing, and a standard approach for generating the lowest-energy states of a given system is by employing adiabatic state preparation (ASP). In the present work, we investigate a variational method for determining the optimal scheduling procedure within the context of ASP. In the absence of quantum error correction, running a quantum device for any meaningful amount of time causes a system to become susceptible to the loss of relevant information…
Efficient and Accurate Electronic Structure Simulation Demonstrated on a Trapped-Ion Quantum Computer
By Yukio Kawashima, Marc P. Coons, Yunseong Nam, Erika Lloyd, Shunji Matsuura, Alejandro J. Garza, Sonika Johri, Lee Huntington, Valentin Senicourt, Andrii O. Maksymov, Jason H. V. Nguyen, Jungsang Kim, Nima Alidoust, Arman Zaribafiyan, & Takeshi Yamazaki
Quantum computers have the potential to perform accurate and efficient electronic structure calculations, enabling the simulation of properties of materials. However, today’s noisy, intermediate-scale quantum (NISQ) devices have a limited number of qubits and gate operations due to the presence of errors. Here, we propose a systematically improvable end-to-end pipeline to alleviate these limitations…