An adaptive variational algorithm for exact molecular simulations on a quantum computer

Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin; Mayhall, Nicholas J.

doi:10.1038/s41467-019-10988-2

Title: An adaptive variational algorithm for exact molecular simulations on a quantum computer

Abstract

Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.

Authors:

Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin;

Publication Date:: 2019-07-08

Research Org.:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Science Foundation (NSF)

OSTI Identifier:: 1619531

Alternate Identifier(s):: OSTI ID: 1613145

Grant/Contract Number:: SC0019199; SC0019318; 1839136

Resource Type:: Published Article

Journal Name:: Nature Communications

Additional Journal Information:: Journal Name: Nature Communications Journal Volume: 10 Journal Issue: 1; Journal ID: ISSN 2041-1723

Publisher:: Nature Publishing Group

Country of Publication:: United Kingdom

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Grimsley, Harper R., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J. An adaptive variational algorithm for exact molecular simulations on a quantum computer.  United Kingdom: N. p., 2019. 
Web.  doi:10.1038/s41467-019-10988-2.

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                    Grimsley, Harper R., Economou, Sophia E., Barnes, Edwin, & Mayhall, Nicholas J. An adaptive variational algorithm for exact molecular simulations on a quantum computer.  United Kingdom.  https://doi.org/10.1038/s41467-019-10988-2

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                    Grimsley, Harper R., Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J. Mon .  
"An adaptive variational algorithm for exact molecular simulations on a quantum computer".  United Kingdom.  https://doi.org/10.1038/s41467-019-10988-2.

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@article{osti_1619531,

  title        = {An adaptive variational algorithm for exact molecular simulations on a quantum computer},

  author       = {Grimsley, Harper R. and Economou, Sophia E. and Barnes, Edwin and Mayhall, Nicholas J.},

  abstractNote = {Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.},

  doi          = {10.1038/s41467-019-10988-2},

  journal      = {Nature Communications},

  number       = 1,

  volume       = 10,

  place        = {United Kingdom},

  year         = {2019},

  month        = {7}

}

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Title: An adaptive variational algorithm for exact molecular simulations on a quantum computer

Abstract

Citation Formats

Simulated Quantum Computation of Molecular Energies journal, September 2005

P si 4N um P y : An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development journal, May 2018

Approximating full configuration interaction with selected configuration interaction and perturbation theory journal, April 1991

Perturbatively selected CI as an optimal source for externally corrected CCSD journal, June 1999

An adaptive coupled-cluster theory: @CC approach journal, December 2010

Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip journal, March 2017

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

Can the Eigenstates of a Many-Body Hamiltonian Be Represented Exactly Using a General Two-Body Cluster Expansion? journal, March 2000

A sequential transformation approach to the internally contracted multireference coupled cluster method journal, May 2012

Treating large intermediate spaces in the CIPSI method through a direct selected CI algorithm journal, January 1992

Intrinsic minimal atomic basis representation of molecular electronic wavefunctions journal, October 2010

Polarized atomic orbitals for linear scaling methods journal, February 2002

Structure of the exact wave function journal, August 2000

Adaptive multiconfigurational wave functions journal, March 2014

Full Coupled-Cluster Reduction for Accurate Description of Strong Electron Correlation journal, September 2018

Simulation of electronic structure Hamiltonians using quantum computers journal, March 2011

The theory of variational hybrid quantum-classical algorithms journal, February 2016

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

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states journal, April 2017

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

Iterative CI general singles and doubles (ICIGSD) method for calculating the exact wave functions of the ground and excited states of molecules journal, May 2005

Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy journal, April 2016

Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling journal, August 2016

Polarized atomic orbitals for self-consistent field electronic structure calculations journal, December 1997

Electronic Structure Calculations and the Ising Hamiltonian journal, October 2017

Structure of the exact wave function. II. Iterative configuration interaction method journal, August 2001

Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure journal, February 2017

Computing molecular correlation energies with guaranteed precision journal, September 2013

Quantum machine learning for electronic structure calculations journal, October 2018

Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation journal, June 2018

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

Universal Quantum Simulators journal, August 1996

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

Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer journal, November 2018

Alternative coupled-cluster ansätze II. The unitary coupled-cluster method journal, February 1989

Psi4: an open-source ab initio electronic structure program : Psi4: an electronic structure program journal, October 2011

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

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

Towards quantum chemistry on a quantum computer journal, January 2010

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets journal, September 2017

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

Error analysis and improvements of coupled-cluster theory journal, January 1991

Structure of the exact wave function. V. Iterative configuration interaction method for molecular systems within finite basis journal, July 2002

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals journal, February 2004

Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer journal, September 2019

Simulated Quantum Computation of Molecular Energies
journal, September 2005

P si 4N um P y : An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development
journal, May 2018

Approximating full configuration interaction with selected configuration interaction and perturbation theory
journal, April 1991

Perturbatively selected CI as an optimal source for externally corrected CCSD
journal, June 1999

An adaptive coupled-cluster theory: @CC approach
journal, December 2010

Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
journal, March 2017

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

Can the Eigenstates of a Many-Body Hamiltonian Be Represented Exactly Using a General Two-Body Cluster Expansion?
journal, March 2000

A sequential transformation approach to the internally contracted multireference coupled cluster method
journal, May 2012

Treating large intermediate spaces in the CIPSI method through a direct selected CI algorithm
journal, January 1992

Intrinsic minimal atomic basis representation of molecular electronic wavefunctions
journal, October 2010

Polarized atomic orbitals for linear scaling methods
journal, February 2002

Structure of the exact wave function
journal, August 2000

Adaptive multiconfigurational wave functions
journal, March 2014

Full Coupled-Cluster Reduction for Accurate Description of Strong Electron Correlation
journal, September 2018

Simulation of electronic structure Hamiltonians using quantum computers
journal, March 2011

The theory of variational hybrid quantum-classical algorithms
journal, February 2016

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

Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
journal, April 2017

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

Iterative CI general singles and doubles (ICIGSD) method for calculating the exact wave functions of the ground and excited states of molecules
journal, May 2005

Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
journal, April 2016

Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling
journal, August 2016

Polarized atomic orbitals for self-consistent field electronic structure calculations
journal, December 1997

Electronic Structure Calculations and the Ising Hamiltonian
journal, October 2017

Structure of the exact wave function. II. Iterative configuration interaction method
journal, August 2001

Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure
journal, February 2017

Computing molecular correlation energies with guaranteed precision
journal, September 2013

Quantum machine learning for electronic structure calculations
journal, October 2018

Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation
journal, June 2018

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

Universal Quantum Simulators
journal, August 1996

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

Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer
journal, November 2018

Alternative coupled-cluster ansätze II. The unitary coupled-cluster method
journal, February 1989

Psi4: an open-source ab initio electronic structure program : Psi4: an electronic structure program
journal, October 2011

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

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

Towards quantum chemistry on a quantum computer
journal, January 2010

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017

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

Error analysis and improvements of coupled-cluster theory
journal, January 1991

Structure of the exact wave function. V. Iterative configuration interaction method for molecular systems within finite basis
journal, July 2002

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals
journal, February 2004

Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer
journal, September 2019