Quantum-classical hybrid algorithm using an error-mitigating -representability condition to compute the Mott metal-insulator transition
Abstract
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence, connectivity, and gate errors required for their experimental realization. Here we propose a class of quantumclassical hybrid algorithms that computes the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $$N$$-representability conditions, constraints for representing an $$N$$-electron wave function, which mitigate noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H3 into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of “chemical accuracy,” even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.
- Authors:
-
- Chicago State Univ., IL (United States)
- Publication Date:
- Research Org.:
- Chicago State Univ., IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
- OSTI Identifier:
- 1559291
- Alternate Identifier(s):
- OSTI ID: 1559080
- Grant/Contract Number:
- SC0019215
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 2; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Smart, Scott E., and Mazziotti, David A. Quantum-classical hybrid algorithm using an error-mitigating N-representability condition to compute the Mott metal-insulator transition. United States: N. p., 2019.
Web. doi:10.1103/PhysRevA.100.022517.
Smart, Scott E., & Mazziotti, David A. Quantum-classical hybrid algorithm using an error-mitigating N-representability condition to compute the Mott metal-insulator transition. United States. https://doi.org/10.1103/PhysRevA.100.022517
Smart, Scott E., and Mazziotti, David A. Wed .
"Quantum-classical hybrid algorithm using an error-mitigating N-representability condition to compute the Mott metal-insulator transition". United States. https://doi.org/10.1103/PhysRevA.100.022517. https://www.osti.gov/servlets/purl/1559291.
@article{osti_1559291,
title = {Quantum-classical hybrid algorithm using an error-mitigating N-representability condition to compute the Mott metal-insulator transition},
author = {Smart, Scott E. and Mazziotti, David A.},
abstractNote = {Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence, connectivity, and gate errors required for their experimental realization. Here we propose a class of quantumclassical hybrid algorithms that computes the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $N$-representability conditions, constraints for representing an $N$-electron wave function, which mitigate noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H3 into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of “chemical accuracy,” even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.},
doi = {10.1103/PhysRevA.100.022517},
journal = {Physical Review A},
number = 2,
volume = 100,
place = {United States},
year = {Wed Aug 28 00:00:00 EDT 2019},
month = {Wed Aug 28 00:00:00 EDT 2019}
}
Web of Science
Works referenced in this record:
P y SCF: the Python-based simulations of chemistry framework : The PySCF program
journal, September 2017
- Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S.
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1
Quantum algorithm for obtaining the energy spectrum of molecular systems
journal, January 2008
- Wang, Hefeng; Kais, Sabre; Aspuru-Guzik, Alán
- Physical Chemistry Chemical Physics, Vol. 10, Issue 35
The conditions on the one-matrix for three-body fermion wavefunctions with one-rank equal to six
journal, January 1972
- Borland, R. E.; Dennis, K.
- Journal of Physics B: Atomic and Molecular Physics, Vol. 5, Issue 1
Quantum computing methods for electronic states of the water molecule
journal, February 2019
- Bian, Teng; Murphy, Daniel; Xia, Rongxin
- Molecular Physics, Vol. 117, Issue 15-16
Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian
journal, October 2008
- Gidofalvi, Gergely; Mazziotti, David A.
- The Journal of Chemical Physics, Vol. 129, Issue 13
Sparse non-orthogonal wave function expansions from the extension of the generalized Pauli constraints to the two-electron reduced density matrix
journal, April 2019
- Boyn, Jan-Niklas; Mazziotti, David A.
- The Journal of Chemical Physics, Vol. 150, Issue 14
Molecular Electronic-Structure Theory
book, August 2000
- Helgaker, Trygve; Jørgensen, Poul; Olsen, Jeppe
Pure- -representability conditions of two-fermion reduced density matrices
journal, September 2016
- Mazziotti, David A.
- Physical Review A, Vol. 94, Issue 3
A dissipatively stabilized Mott insulator of photons
journal, February 2019
- Ma, Ruichao; Saxberg, Brendan; Owens, Clai
- Nature, Vol. 566, Issue 7742
Generalized Pauli constraints in reduced density matrix functional theory
journal, April 2015
- Theophilou, Iris; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
- The Journal of Chemical Physics, Vol. 142, Issue 15
Natural Extension of Hartree–Fock Through Extremal 1-Fermion Information: Overview and Application to the Lithium Atom
journal, January 2016
- Benavides-Riveros, Carlos L.; Schilling, Christian
- Zeitschrift für Physikalische Chemie, Vol. 230, Issue 5-7
Structure of Fermionic Density Matrices: Complete -Representability Conditions
journal, June 2012
- Mazziotti, David A.
- Physical Review Letters, Vol. 108, Issue 26
Strong Electron Correlation in Nitrogenase Cofactor, FeMoco
journal, May 2018
- Montgomery, Jason M.; Mazziotti, David A.
- The Journal of Physical Chemistry A, Vol. 122, Issue 22
Quantum marginal problem and N-representability
journal, April 2006
- Klyachko, Alexander A.
- Journal of Physics: Conference Series, Vol. 36
Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm
journal, February 2018
- Colless, J. I.; Ramasesh, V. V.; Dahlen, D.
- Physical Review X, Vol. 8, Issue 1
Quantum signature of exciton condensation
journal, July 2018
- Safaei, Shiva; Mazziotti, David A.
- Physical Review B, Vol. 98, Issue 4
A variational eigenvalue solver on a photonic quantum processor
journal, July 2014
- Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
- Nature Communications, Vol. 5, Issue 1
Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics
journal, February 2011
- Mazziotti, David A.
- Physical Review Letters, Vol. 106, Issue 8
Size-consistent Brueckner theory limited to double substitutions
journal, December 1989
- Handy, Nicholas C.; Pople, John A.; Head-Gordon, Martin
- Chemical Physics Letters, Vol. 164, Issue 2-3
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
journal, December 1999
- Abrams, Daniel S.; Lloyd, Seth
- Physical Review Letters, Vol. 83, Issue 24
Structure of Fermion Density Matrices
journal, July 1963
- Coleman, A. J.
- Reviews of Modern Physics, Vol. 35, Issue 3
Experimental error mitigation via symmetry verification in a variational quantum eigensolver
journal, July 2019
- Sagastizabal, R.; Bonet-Monroig, X.; Singh, M.
- Physical Review A, Vol. 100, Issue 1
Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm
journal, May 2001
- Nakata, Maho; Nakatsuji, Hiroshi; Ehara, Masahiro
- The Journal of Chemical Physics, Vol. 114, Issue 19
Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
journal, September 1997
- Abrams, Daniel S.; Lloyd, Seth
- Physical Review Letters, Vol. 79, Issue 13
Simple All-Microwave Entangling Gate for Fixed-Frequency Superconducting Qubits
journal, August 2011
- Chow, Jerry M.; Córcoles, A. D.; Gambetta, Jay M.
- Physical Review Letters, Vol. 107, Issue 8
The Construction and Interpretation of Mcscf Wavefunctions
journal, October 1998
- Schmidt, Michael W.; Gordon, Mark S.
- Annual Review of Physical Chemistry, Vol. 49, Issue 1
Entangled Electrons Foil Synthesis of Elusive Low-Valent Vanadium Oxo Complex
journal, January 2016
- Schlimgen, Anthony W.; Heaps, Charles W.; Mazziotti, David A.
- The Journal of Physical Chemistry Letters, Vol. 7, Issue 4
Reduced density operators and theN-particle problem
journal, January 1978
- Coleman, A. J.
- International Journal of Quantum Chemistry, Vol. 13, Issue 1
Simulated Quantum Computation of Molecular Energies
journal, September 2005
- Aspuru-Guzik, A.
- Science, Vol. 309, Issue 5741
Current-constrained density-matrix theory to calculate molecular conductivity with increased accuracy
journal, May 2018
- Sajjan, Manas; Mazziotti, David A.
- Communications Chemistry, Vol. 1, Issue 1
The Pauli Principle Revisited
journal, July 2008
- Altunbulak, Murat; Klyachko, Alexander
- Communications in Mathematical Physics, Vol. 282, Issue 2
The electronic ground-state energy problem: A new reduced density matrix approach
journal, August 2006
- Cancès, Eric; Stoltz, Gabriel; Lewin, Mathieu
- The Journal of Chemical Physics, Vol. 125, Issue 6
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
journal, January 2018
- Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.
- Science Advances, Vol. 4, Issue 1
Application of fermionic marginal constraints to hybrid quantum algorithms
journal, May 2018
- Rubin, Nicholas C.; Babbush, Ryan; McClean, Jarrod
- New Journal of Physics, Vol. 20, Issue 5
Variational Two-Particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-Adapted Lifting Conditions
journal, May 2012
- Verstichel, Brecht; van Aggelen, Helen; Poelmans, Ward
- Physical Review Letters, Vol. 108, Issue 21
Generalized Pauli constraints in small atoms
journal, May 2018
- Schilling, Christian; Altunbulak, Murat; Knecht, Stefan
- Physical Review A, Vol. 97, Issue 5
Sparsity of the wavefunction from the generalized Pauli exclusion principle
journal, February 2018
- Chakraborty, Romit; Mazziotti, David A.
- The Journal of Chemical Physics, Vol. 148, Issue 5
On Multi-Particle Entanglement
journal, June 1998
- Linden, N.; Popescu, S.; Popescu, S.
- Fortschritte der Physik, Vol. 46, Issue 4-5
Strong electron correlation in the decomposition reaction of dioxetanone with implications for firefly bioluminescence
journal, October 2010
- Greenman, Loren; Mazziotti, David A.
- The Journal of Chemical Physics, Vol. 133, Issue 16
The theory of variational hybrid quantum-classical algorithms
journal, February 2016
- McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan
- New Journal of Physics, Vol. 18, Issue 2
Error Mitigation for Short-Depth Quantum Circuits
journal, November 2017
- Temme, Kristan; Bravyi, Sergey; Gambetta, Jay M.
- Physical Review Letters, Vol. 119, Issue 18
Active-Space -Representability Constraints for Variational Two-Particle Reduced Density Matrix Calculations
journal, November 2010
- Shenvi, Neil; Izmaylov, Artur F.
- Physical Review Letters, Vol. 105, Issue 21
Quantum optimization using variational algorithms on near-term quantum devices
journal, June 2018
- Moll, Nikolaj; Barkoutsos, Panagiotis; Bishop, Lev S.
- Quantum Science and Technology, Vol. 3, Issue 3
Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
journal, April 2017
- McClean, Jarrod R.; Kimchi-Schwartz, Mollie E.; Carter, Jonathan
- Physical Review A, Vol. 95, Issue 4
An electron pair operator approach to coupled cluster wave functions. Application to He 2 , Be 2 , and Mg 2 and comparison with CEPA methods
journal, April 1981
- Chiles, Richard A.; Dykstra, Clifford E.
- The Journal of Chemical Physics, Vol. 74, Issue 8
Simulating the vibrational quantum dynamics of molecules using photonics
journal, May 2018
- Sparrow, Chris; Martín-López, Enrique; Maraviglia, Nicola
- Nature, Vol. 557, Issue 7707
The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions
journal, February 2004
- Zhao, Zhengji; Braams, Bastiaan J.; Fukuda, Mituhiro
- The Journal of Chemical Physics, Vol. 120, Issue 5
Experimental data from a quantum computer verifies the generalized Pauli exclusion principle
journal, January 2019
- Smart, Scott E.; Schuster, David I.; Mazziotti, David A.
- Communications Physics, Vol. 2, Issue 1
Three-qubit pure-state canonical forms
journal, August 2001
- Acín, A.; Andrianov, A.; Jané, E.
- Journal of Physics A: Mathematical and General, Vol. 34, Issue 35
Realization of Quantum Chemistry without Wave Functions through First-Order Semidefinite Programming
journal, November 2004
- Mazziotti, David A.
- Physical Review Letters, Vol. 93, Issue 21
Quasipinning and its relevance for -fermion quantum states
journal, February 2015
- Schilling, Christian
- Physical Review A, Vol. 91, Issue 2
Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods
journal, April 2016
- Fosso-Tande, Jacob; Nguyen, Truong-Son; Gidofalvi, Gergely
- Journal of Chemical Theory and Computation, Vol. 12, Issue 5
Enhanced Constraints for Accurate Lower Bounds on Many-Electron Quantum Energies from Variational Two-Electron Reduced Density Matrix Theory
journal, October 2016
- Mazziotti, David A.
- Physical Review Letters, Vol. 117, Issue 15
Towards quantum chemistry on a quantum computer
journal, January 2010
- Lanyon, B. P.; Whitfield, J. D.; Gillett, G. G.
- Nature Chemistry, Vol. 2, Issue 2
Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013
- Devoret, M. H.; Schoelkopf, R. J.
- Science, Vol. 339, Issue 6124
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017
- Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan
- Nature, Vol. 549, Issue 7671
Error mitigation extends the computational reach of a noisy quantum processor
journal, March 2019
- Kandala, Abhinav; Temme, Kristan; Córcoles, Antonio D.
- Nature, Vol. 567, Issue 7749
Resolving the positions of defects in superconducting quantum bits
journal, February 2020
- Bilmes, Alexander; Megrant, Anthony; Klimov, Paul
- Scientific Reports, Vol. 10, Issue 1
Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules
text, January 2014
- Chakraborty, Romit; Mazziotti, David A.
- arXiv
Generalized Pauli constraints in reduced density matrix functional theory
text, January 2015
- Theophilou, Iris; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
- arXiv
Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
text, January 2016
- McClean, Jarrod R.; Schwartz, Mollie E.; Carter, Jonathan
- arXiv
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
text, January 2016
- Santagati, R.; Wang, J.; Gentile, A. A.
- arXiv
Quantum computing methods for electronic states of the water molecule
text, January 2018
- Bian, Teng; Murphy, Daniel; Xia, Rongxin
- arXiv
A Dissipatively Stabilized Mott Insulator of Photons
text, January 2018
- Ma, Ruichao; Saxberg, Brendan; Owens, Clai
- arXiv
Experimental Data from a Quantum Computer Verifies the Generalized Pauli Exclusion Principle
text, January 2020
- Smart, Scott E.; Schuster, David I.; Mazziotti, David A.
- arXiv
Charge insensitive qubit design derived from the Cooper pair box
text, January 2007
- Koch, Jens; Yu, Terri M.; Gambetta, Jay
- arXiv
A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
text, January 1998
- Abrams, Daniel S.; Lloyd, Seth
- arXiv