Correlating AGP on a quantum computer
Abstract
For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. Furthermore, the results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.
- Authors:
-
[1];
[2];
[1]
- Rice University, Houston, TX (United States)
- Emory University, Atlanta, GA (United States)
- Publication Date:
- Research Org.:
- Emory Univ., Atlanta, GA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1677415
- Grant/Contract Number:
- SC0019374
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Quantum Science and Technology
- Additional Journal Information:
- Journal Volume: 6; Journal Issue: 1; Journal ID: ISSN 2058-9565
- Publisher:
- IOPscience
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Khamoshi, Armin, Evangelista, Francesco A., and Scuseria, Gustavo E.. Correlating AGP on a quantum computer. United States: N. p., 2020.
Web. https://doi.org/10.1088/2058-9565/abc1bb.
Khamoshi, Armin, Evangelista, Francesco A., & Scuseria, Gustavo E.. Correlating AGP on a quantum computer. United States. https://doi.org/10.1088/2058-9565/abc1bb
Khamoshi, Armin, Evangelista, Francesco A., and Scuseria, Gustavo E.. Wed .
"Correlating AGP on a quantum computer". United States. https://doi.org/10.1088/2058-9565/abc1bb. https://www.osti.gov/servlets/purl/1677415.
@article{osti_1677415,
title = {Correlating AGP on a quantum computer},
author = {Khamoshi, Armin and Evangelista, Francesco A. and Scuseria, Gustavo E.},
abstractNote = {For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. Furthermore, the results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.},
doi = {10.1088/2058-9565/abc1bb},
journal = {Quantum Science and Technology},
number = 1,
volume = 6,
place = {United States},
year = {2020},
month = {11}
}
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Works referenced in this record:
Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian
journal, April 2019
- Qiu, Y.; Henderson, T. M.; Duguet, T.
- Physical Review C, Vol. 99, Issue 4
�ber das Paulische �quivalenzverbot
journal, September 1928
- Jordan, P.; Wigner, E.
- Zeitschrift f�r Physik, Vol. 47, Issue 9-10
Exact eigenstates of the pairing-force Hamiltonian
journal, March 1964
- Richardson, R. W.; Sherman, N.
- Nuclear Physics, Vol. 52
Exact parameterization of fermionic wave functions via unitary coupled cluster theory
journal, December 2019
- Evangelista, Francesco A.; Chan, Garnet Kin-Lic; Scuseria, Gustavo E.
- The Journal of Chemical Physics, Vol. 151, Issue 24
Theory of Superconductivity
journal, December 1957
- Bardeen, J.; Cooper, L. N.; Schrieffer, J. R.
- Physical Review, Vol. 108, Issue 5
Efficient evaluation of AGP reduced density matrices
journal, November 2019
- Khamoshi, Armin; Henderson, Thomas M.; Scuseria, Gustavo E.
- The Journal of Chemical Physics, Vol. 151, Issue 18
New perspectives on unitary coupled-cluster theory
journal, January 2006
- Taube, Andrew G.; Bartlett, Rodney J.
- International Journal of Quantum Chemistry, Vol. 106, Issue 15
Error analysis and improvements of coupled-cluster theory
journal, January 1991
- Kutzelnigg, Werner
- Theoretica Chimica Acta, Vol. 80, Issue 4-5
A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
journal, February 2020
- Stair, Nicholas H.; Huang, Renke; Evangelista, Francesco A.
- Journal of Chemical Theory and Computation, Vol. 16, Issue 4
Quantum computational chemistry
journal, March 2020
- McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alán
- Reviews of Modern Physics, Vol. 92, Issue 1
Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
journal, November 2019
- Grimsley, Harper R.; Claudino, Daniel; Economou, Sophia E.
- Journal of Chemical Theory and Computation, Vol. 16, Issue 1
The Bravyi-Kitaev transformation for quantum computation of electronic structure
journal, December 2012
- Seeley, Jacob T.; Richard, Martin J.; Love, Peter J.
- The Journal of Chemical Physics, Vol. 137, Issue 22
A variational eigenvalue solver on a photonic quantum processor
journal, July 2014
- Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
- Nature Communications, Vol. 5, Issue 1
Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions
journal, August 2018
- Barkoutsos, Panagiotis Kl.; Gonthier, Jerome F.; Sokolov, Igor
- Physical Review A, Vol. 98, Issue 2
On the Theory of Automorphic Functions of a Matrix Variable, II-The Classification of Hypercircles Under the Symplectic Group
journal, October 1944
- Hua, Loo-Keng
- American Journal of Mathematics, Vol. 66, Issue 4
Geminal-based configuration interaction
journal, August 2019
- Henderson, Thomas M.; Scuseria, Gustavo E.
- The Journal of Chemical Physics, Vol. 151, Issue 5
Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors
journal, October 1962
- Yang, C. N.
- Reviews of Modern Physics, Vol. 34, Issue 4
Elementary gates for quantum computation
journal, November 1995
- Barenco, Adriano; Bennett, Charles H.; Cleve, Richard
- Physical Review A, Vol. 52, Issue 5
Low-Depth Quantum Simulation of Materials
journal, March 2018
- Babbush, Ryan; Wiebe, Nathan; McClean, Jarrod
- Physical Review X, Vol. 8, Issue 1
A derivation of the pairing-correlation method
journal, February 1960
- Bayman, B. F.
- Nuclear Physics, Vol. 15
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
Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy
journal, July 2011
- Bytautas, Laimutis; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A.
- The Journal of Chemical Physics, Vol. 135, Issue 4
Pair extended coupled cluster doubles
journal, June 2015
- Henderson, Thomas M.; Bulik, Ireneusz W.; Scuseria, Gustavo E.
- The Journal of Chemical Physics, Vol. 142, Issue 21
Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
journal, November 2018
- Lee, Joonho; Huggins, William J.; Head-Gordon, Martin
- Journal of Chemical Theory and Computation, Vol. 15, Issue 1
On the order problem in construction of unitary operators for the variational quantum eigensolver
journal, January 2020
- Izmaylov, Artur F.; Díaz-Tinoco, Manuel; Lang, Robert A.
- Physical Chemistry Chemical Physics, Vol. 22, Issue 23
Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions
journal, April 2018
- Jiang, Zhang; Sung, Kevin J.; Kechedzhi, Kostyantyn
- Physical Review Applied, Vol. 9, Issue 4
Projected quasiparticle theory for molecular electronic structure
journal, September 2011
- Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.
- The Journal of Chemical Physics, Vol. 135, Issue 12
Alternative single-reference coupled cluster approaches for multireference problems: The simpler, the better
journal, June 2011
- Evangelista, Francesco A.
- The Journal of Chemical Physics, Vol. 134, Issue 22
Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
journal, October 2018
- Romero, Jonathan; Babbush, Ryan; McClean, Jarrod R.
- Quantum Science and Technology, Vol. 4, Issue 1
Can Single-Reference Coupled Cluster Theory Describe Static Correlation?
journal, June 2015
- Bulik, Ireneusz W.; Henderson, Thomas M.; Scuseria, Gustavo E.
- Journal of Chemical Theory and Computation, Vol. 11, Issue 7
Complete multi-configuration self-consistent field theory
journal, January 1967
- Veillard, A.; Clementi, E.
- Theoretica Chimica Acta, Vol. 7, Issue 2
Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
journal, March 2016
- Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo
- Physical Review B, Vol. 93, Issue 12
Exact study of the effect of level statistics in ultrasmall superconducting grains
journal, May 2000
- Sierra, G.; Dukelsky, J.; Dussel, G. G.
- Physical Review B, Vol. 61, Issue 18
Benchmark studies of variational, unitary and extended coupled cluster methods
journal, December 2010
- Cooper, Bridgette; Knowles, Peter J.
- The Journal of Chemical Physics, Vol. 133, Issue 23
Half-Projection of the Strongly Orthogonal Unrestricted Geminals’ Product Wave Function
journal, December 2019
- Mihálka, Zs. É.; Surján, P. R.; Szabados, Á.
- Journal of Chemical Theory and Computation, Vol. 16, Issue 2
Efficient Variational Quantum Simulator Incorporating Active Error Minimization
journal, June 2017
- Li, Ying; Benjamin, Simon C.
- Physical Review X, Vol. 7, Issue 2
Barren plateaus in quantum neural network training landscapes
journal, November 2018
- McClean, Jarrod R.; Boixo, Sergio; Smelyanskiy, Vadim N.
- Nature Communications, Vol. 9, Issue 1
A restricted class of exact eigenstates of the pairing-force Hamiltonian
journal, February 1963
- Richardson, R. W.
- Physics Letters, Vol. 3, Issue 6
A Limited Memory Algorithm for Bound Constrained Optimization
journal, September 1995
- Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge
- SIAM Journal on Scientific Computing, Vol. 16, Issue 5
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial
journal, March 2008
- Aharonov, Dorit; Jones, Vaughan; Landau, Zeph
- Algorithmica, Vol. 55, Issue 3
Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers
journal, September 1965
- Coleman, A. J.
- Journal of Mathematical Physics, Vol. 6, Issue 9
Error Mitigation for Short-Depth Quantum Circuits
journal, November 2017
- Temme, Kristan; Bravyi, Sergey; Gambetta, Jay M.
- Physical Review Letters, Vol. 119, Issue 18
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
Fermionic Quantum Computation
journal, May 2002
- Bravyi, Sergey B.; Kitaev, Alexei Yu.
- Annals of Physics, Vol. 298, Issue 1
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
Quasiparticle coupled cluster theory for pairing interactions
journal, May 2014
- Henderson, Thomas M.; Scuseria, Gustavo E.; Dukelsky, Jorge
- Physical Review C, Vol. 89, Issue 5
On the difference between variational and unitary coupled cluster theories
journal, January 2018
- Harsha, Gaurav; Shiozaki, Toru; Scuseria, Gustavo E.
- The Journal of Chemical Physics, Vol. 148, Issue 4
Colloquium : Exactly solvable Richardson-Gaudin models for many-body quantum systems
journal, August 2004
- Dukelsky, J.; Pittel, S.; Sierra, G.
- Reviews of Modern Physics, Vol. 76, Issue 3
Structure of the number-projected BCS wave function
journal, March 2016
- Dukelsky, J.; Pittel, S.; Esebbag, C.
- Physical Review C, Vol. 93, Issue 3
Quantum supremacy using a programmable superconducting processor
journal, October 2019
- Arute, Frank; Arya, Kunal; Babbush, Ryan
- Nature, Vol. 574, Issue 7779
On Construction of Projection Operators
journal, March 2019
- Izmaylov, Artur F.
- The Journal of Physical Chemistry A, Vol. 123, Issue 15
Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits
journal, January 2020
- Matsuzawa, Yuta; Kurashige, Yuki
- Journal of Chemical Theory and Computation, Vol. 16, Issue 2
Quantum algorithms for fermionic simulations
journal, July 2001
- Ortiz, G.; Gubernatis, J. E.; Knill, E.
- Physical Review A, Vol. 64, Issue 2
Projected Hartree–Fock theory
journal, April 2012
- Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Tsuchimochi, Takashi
- The Journal of Chemical Physics, Vol. 136, Issue 16
Entanglement Generation in Superconducting Qubits Using Holonomic Operations
journal, January 2019
- Egger, D. J.; Ganzhorn, M.; Salis, G.
- Physical Review Applied, Vol. 11, Issue 1
Half-Projected and Projected Hartree-Fock Calculations for Singlet Ground States. i. four-Electron Atomic Systems
journal, July 1973
- Smeyers, Yves G.; Doreste-Suarez, L.
- International Journal of Quantum Chemistry, Vol. 7, Issue 4
Alternative coupled-cluster ansätze II. The unitary coupled-cluster method
journal, February 1989
- Bartlett, Rodney J.; Kucharski, Stanislaw A.; Noga, Jozef
- Chemical Physics Letters, Vol. 155, Issue 1
Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
journal, January 2020
- Gard, Bryan T.; Zhu, Linghua; Barron, George S.
- npj Quantum Information, Vol. 6, Issue 1
Symmetry-projected Hartree–Fock–Bogoliubov equations
journal, February 2000
- Sheikh, Javid A.; Ring, Peter
- Nuclear Physics A, Vol. 665, Issue 1-2
A new approach to density matrix functional theory
journal, September 2003
- Kollmar, Christian; Heß, Bernd A.
- The Journal of Chemical Physics, Vol. 119, Issue 9
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
Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer
journal, October 2019
- Yen, Tzu-Ching; Lang, Robert A.; Izmaylov, Artur F.
- The Journal of Chemical Physics, Vol. 151, Issue 16
Not All Qubits Are Created Equal: A Case for Variability-Aware Policies for NISQ-Era Quantum Computers
conference, April 2019
- Tannu, Swamit S.; Qureshi, Moinuddin K.
- ASPLOS '19: Architectural Support for Programming Languages and Operating Systems, Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems
Generalized Molecular Orbital Theory II
journal, September 1997
- Couty, Marc; Hall, Michael B.
- The Journal of Physical Chemistry A, Vol. 101, Issue 37
Quantum Chemistry in the Age of Quantum Computing
journal, August 2019
- Cao, Yudong; Romero, Jonathan; Olson, Jonathan P.
- Chemical Reviews, Vol. 119, Issue 19
An adaptive variational algorithm for exact molecular simulations on a quantum computer
journal, July 2019
- Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin
- Nature Communications, Vol. 10, Issue 1