Scaling Overhead of Locality Reduction in Binary Optimization Problems
By Elisabetta Valiante, Maritza Hernandez, Amin Barzegar, & Helmut G. Katzgraber
Recently, there has been considerable interest in solving optimization problems by mapping these onto a binary representation, sparked mostly by the use of quantum annealing machines. Such binary representation is reminiscent of a discrete physical two-state system, such as the Ising model. As such, physics-inspired techniques—commonly used in fundamental physics studies—are ideally suited to solve optimization problems in a binary format. While binary representations can be often found for paradigmatic optimization problems, these typically result in k-local higher-order unconstrained binary optimization cost functions. In this work, we discuss the effects of locality reduction needed for solvers such as the D-Wave quantum annealer, the Fujitsu Digital Annealer, or the Toshiba Simulated Bifurcation Machine that can only accommodate 2-local (quadratic) cost functions. General locality reduction approaches require the introduction of ancillary variables which cause an overhead over the native problem. Using a parallel tempering Monte Carlo solver on Azure Quantum, as well as k-local binary problems with planted solutions, we show that post reduction to a corresponding 2-local representation the problems become considerably harder to solve. We further quantify the increase in computational hardness introduced by the reduction algorithm by measuring the variation of number of variables, statistics of the coefficient values, and the entropic family size. Our results demonstrate the importance of avoiding locality reduction when solving optimization problems.
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…