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

Journal Article · · Annalen der Physik (Leipzig)
 [1];  [2];  [2];  [3];  [4];  [5]; ORCiD logo [6];  [2]
  1. Terra Quantum AG St. Gallerstrasse 16A Rorschach 9400 Switzerland, Department of General and Applied Physics Moscow Institute of Physics and Technology Institutskii Per. 9, Dolgoprudny, Moscow Distr. 141700 Russian Federation, QTF Centre of Excellence Department of Applied Physics Aalto University School of Science P.O. Box 15100 AALTO FI‐00076 Finland
  2. Terra Quantum AG St. Gallerstrasse 16A Rorschach 9400 Switzerland, Department of General and Applied Physics Moscow Institute of Physics and Technology Institutskii Per. 9, Dolgoprudny, Moscow Distr. 141700 Russian Federation
  3. Department of General and Applied Physics Moscow Institute of Physics and Technology Institutskii Per. 9, Dolgoprudny, Moscow Distr. 141700 Russian Federation
  4. Materials Science Division Argonne National Laboratory 9700 S. Cass Avenue Argonne IL 60637 USA, Department of Physics Northern Illinois University DeKalb IL 60115 USA
  5. Terra Quantum AG St. Gallerstrasse 16A Rorschach 9400 Switzerland, QTF Centre of Excellence Department of Applied Physics Aalto University School of Science P.O. Box 15100 AALTO FI‐00076 Finland
  6. Terra Quantum AG St. Gallerstrasse 16A Rorschach 9400 Switzerland, Physics Department City College of the City University of New York 160 Convent Ave New York NY 10031 USA
+ Show Author Affiliations

Abstract 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 2 17 ‐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.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
Academy of Finland; Terra Quantum; USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
Grant/Contract Number:
AC02-06CH11357; AC05-00OR22725
OSTI ID:
1868124
Journal Information:
Annalen der Physik (Leipzig), Journal Name: Annalen der Physik (Leipzig) Journal Issue: 7 Vol. 534; ISSN 0003-3804
Publisher:
Wiley Blackwell (John Wiley & Sons)Copyright Statement
Country of Publication:
Germany
Language:
English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
linear equation systems
quantum algorithms
quantum computing