O(N^3) Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians
Variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of O(N 4 ) terms. This quartic scaling appears to be a significant obstacle to practical applications. H...
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| Published in | IEEE transactions on quantum engineering Vol. 1; pp. 1 - 24 |
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| Main Authors | , , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
IEEE
01.01.2020
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2689-1808 2689-1808 |
| DOI | 10.1109/TQE.2020.3035814 |
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| Abstract | Variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of O(N 4 ) terms. This quartic scaling appears to be a significant obstacle to practical applications. However, we note that it empirically reduces to O(N 3 ) when we partition the terms into linear-sized commuting families that can be measured simultaneously. We confirm these empirical observations by studying the MIN-COMMUTING-PARTITION problem at the level of the fermionic Hamiltonian and its encoding into qubits. Moreover, we provide a fast, precomputable procedure for creating linearly sized commuting partitions by solving a round-robin scheduling problem via flow networks. In addition, we demonstrate how to construct the quantum circuits necessary for simultaneous measurement, and we discuss the statistical implication of simultaneous measurement. Our results are experimentally validated by a ground state estimation of deuteron with low shot budget on a 20-qubit IBM machine. |
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| AbstractList | Variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of O(N 4 ) terms. This quartic scaling appears to be a significant obstacle to practical applications. However, we note that it empirically reduces to O(N 3 ) when we partition the terms into linear-sized commuting families that can be measured simultaneously. We confirm these empirical observations by studying the MIN-COMMUTING-PARTITION problem at the level of the fermionic Hamiltonian and its encoding into qubits. Moreover, we provide a fast, precomputable procedure for creating linearly sized commuting partitions by solving a round-robin scheduling problem via flow networks. In addition, we demonstrate how to construct the quantum circuits necessary for simultaneous measurement, and we discuss the statistical implication of simultaneous measurement. Our results are experimentally validated by a ground state estimation of deuteron with low shot budget on a 20-qubit IBM machine. Variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of O(N4) terms. This quartic scaling appears to be a significant obstacle to practical applications. However, we note that it empirically reduces to O(N3) when we partition the terms into linear-sized commuting families that can be measured simultaneously. We confirm these empirical observations by studying the MIN-COMMUTING-PARTITION problem at the level of the fermionic Hamiltonian and its encoding into qubits. Moreover, we provide a fast, precomputable procedure for creating linearly sized commuting partitions by solving a round-robin scheduling problem via flow networks. In addition, we demonstrate how to construct the quantum circuits necessary for simultaneous measurement, and we discuss the statistical implication of simultaneous measurement. Our results are experimentally validated by a ground state estimation of deuteron with low shot budget on a 20-qubit IBM machine. |
| Author | Gui, Kaiwen Ding, Yongshan Chong, Frederic T. Suchara, Martin Gokhale, Pranav Angiuli, Olivia Tomesh, Teague Martonosi, Margaret |
| Author_xml | – sequence: 1 givenname: Pranav orcidid: 0000-0003-1946-4537 surname: Gokhale fullname: Gokhale, Pranav email: pranav@super.tech organization: Super.tech, Chicago, IL, USA – sequence: 2 givenname: Olivia orcidid: 0000-0002-0785-5605 surname: Angiuli fullname: Angiuli, Olivia email: oangiuli@berkeley.edu organization: University of California, Berkeley, CAUSA – sequence: 3 givenname: Yongshan orcidid: 0000-0002-2338-1315 surname: Ding fullname: Ding, Yongshan email: yongshan@uchicago.edu organization: University of Chicago, Chicago, IL, USA – sequence: 4 givenname: Kaiwen surname: Gui fullname: Gui, Kaiwen email: kgui@uchicago.edu organization: University of Chicago, Chicago, IL, USA – sequence: 5 givenname: Teague surname: Tomesh fullname: Tomesh, Teague email: teaguetomesh@gmail.com organization: Princeton University, Princeton, NJ, USA – sequence: 6 givenname: Martin orcidid: 0000-0001-8808-1367 surname: Suchara fullname: Suchara, Martin email: msuchara@anl.gov organization: Argonne National Laboratory, Lemont, IL, USA – sequence: 7 givenname: Margaret orcidid: 0000-0001-9683-8032 surname: Martonosi fullname: Martonosi, Margaret email: mrm@princeton.edu organization: Princeton University, Princeton, NJ, USA – sequence: 8 givenname: Frederic T. orcidid: 0000-0001-9282-4645 surname: Chong fullname: Chong, Frederic T. email: chong@cs.uchicago.edu organization: University of Chicago, Chicago, IL, USA |
| BackLink | https://www.osti.gov/servlets/purl/1808691$$D View this record in Osti.gov |
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| Snippet | Variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule... |
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| SubjectTerms | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Energy measurement Extraterrestrial measurements Quantum computing Qubit Rotation measurement Stationary state variational quantum eigensolver (VQE) |
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| Title | O(N^3) Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians |
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