Correlating AGP on a quantum computer

Khamoshi, Armin; Evangelista, Francesco A.; Scuseria, Gustavo E.

doi:10.1088/2058-9565/abc1bb

Title: 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:: 2020-11-11

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.  doi:10.1088/2058-9565/abc1bb.

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                    Khamoshi, Armin, Evangelista, Francesco A., & Scuseria, Gustavo E.. Correlating AGP on a quantum computer.  United States.  https://doi.org/10.1088/2058-9565/abc1bb

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                    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.

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@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}

}

Copy to clipboard

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Title: Correlating AGP on a quantum computer

Abstract

Citation Formats

Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian journal, April 2019

Exact parameterization of fermionic wave functions via unitary coupled cluster theory journal, December 2019

Efficient evaluation of AGP reduced density matrices journal, November 2019

New perspectives on unitary coupled-cluster theory journal, January 2006

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons journal, February 2020

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A variational eigenvalue solver on a photonic quantum processor journal, July 2014

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On the Theory of Automorphic Functions of a Matrix Variable, II-The Classification of Hypercircles Under the Symplectic Group journal, October 1944

Geminal-based configuration interaction journal, August 2019

Elementary gates for quantum computation journal, November 1995

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Quantum Computing in the NISQ era and beyond journal, August 2018

Projected quasiparticle theory for molecular electronic structure journal, September 2011

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Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz journal, October 2018

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Barren plateaus in quantum neural network training landscapes journal, November 2018

A restricted class of exact eigenstates of the pairing-force Hamiltonian journal, February 1963

A Limited Memory Algorithm for Bound Constrained Optimization journal, September 1995

A Polynomial Quantum Algorithm for Approximating the Jones Polynomial journal, March 2008

Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers journal, September 1965

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On the difference between variational and unitary coupled cluster theories journal, January 2018

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On Construction of Projection Operators journal, March 2019

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Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm journal, January 2020

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Efficient evaluation of AGP reduced density matrices
journal, November 2019

New perspectives on unitary coupled-cluster theory
journal, January 2006

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
journal, February 2020

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
journal, November 2019

The Bravyi-Kitaev transformation for quantum computation of electronic structure
journal, December 2012

A variational eigenvalue solver on a photonic quantum processor
journal, July 2014

Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions
journal, August 2018

On the Theory of Automorphic Functions of a Matrix Variable, II-The Classification of Hypercircles Under the Symplectic Group
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journal, August 2019

Elementary gates for quantum computation
journal, November 1995

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A derivation of the pairing-correlation method
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journal, July 2011

Pair extended coupled cluster doubles
journal, June 2015

Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
journal, November 2018

Quantum Computing in the NISQ era and beyond
journal, August 2018

Projected quasiparticle theory for molecular electronic structure
journal, September 2011

Alternative single-reference coupled cluster approaches for multireference problems: The simpler, the better
journal, June 2011

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
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Can Single-Reference Coupled Cluster Theory Describe Static Correlation?
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Complete multi-configuration self-consistent field theory
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journal, March 2008

Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers
journal, September 1965

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On the difference between variational and unitary coupled cluster theories
journal, January 2018

Quantum supremacy using a programmable superconducting processor
journal, October 2019

On Construction of Projection Operators
journal, March 2019

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits
journal, January 2020

Projected Hartree–Fock theory
journal, April 2012

Half-Projected and Projected Hartree-Fock Calculations for Singlet Ground States. i. four-Electron Atomic Systems
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