Solving Large‐Scale Linear Systems of Equations by a Quantum Hybrid Algorithm

Today's intermediate‐scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum‐enabled large‐scale solutions have been realized only for limited set of problems. Here...

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Bibliographic Details
Published in:Annalen der Physik Vol. 534; no. 7
Main Authors: Perelshtein, M. R., Pakhomchik, A. I., Melnikov, A. A., Novikov, A. A., Glatz, A., Paraoanu, G. S., Vinokur, V. M., Lesovik, G. B.
Format: Journal Article
Language:English
Published: Weinheim Wiley Subscription Services, Inc 01.07.2022
Wiley Blackwell (John Wiley & Sons)
Subjects:
Algorithms
Circuits
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
linear equation systems
linear equation systems
Linear systems
Optimization
quantum algorithms
Quantum computers
Quantum computing
Quantum entanglement
Supercomputers
ISSN:0003-3804, 1521-3889
Online Access:Get full text
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Summary:Today's intermediate‐scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum‐enabled large‐scale solutions have been realized only for limited set of problems. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. A classification of linear systems based on the entanglement properties of the associated phase‐estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix‐to‐circuit map. A 217‐dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record‐breaking result for a linear system solved by a quantum computer. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution. One of the most pressing computational problems omnipresent in the broadest scope of natural phenomena and industrial applications is solving systems of linear equations. Here, a solution via a hybrid algorithm enables the current generation of quantum computers to solve a 130,000‐dimensional problem using public superconducting devices, which is a record‐breaking result for a linear system solution on quantum computers.
Bibliography:ObjectType-Article-1
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Academy of Finland
USDOE
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
Terra Quantum
AC02-06CH11357; AC05-00OR22725
ISSN:0003-3804
1521-3889
DOI:10.1002/andp.202200082