Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion

Urbanek, Miroslav; Camps, Daan; Van Beeumen, Roel; de Jong, Wibe A.

doi:10.1021/acs.jctc.0c00447

Title: Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion

Abstract

Several novel methods for performing calculations relevant to quantum chemistry on quantum computers have been proposed but not yet explored experimentally. Virtual quantum subspace expansion is one such algorithm developed for modeling complex molecules using their full orbital space and without the need for additional quantum resources. Here, we implement this method on the IBM Q platform and calculate the potential energy curves of the hydrogen and lithium dimers using only two qubits and simple classical post-processing. A comparable level of accuracy would require twenty qubits with previous approaches. We also develop an approach to minimize the impact of experimental noise on the stability of a generalized eigenvalue problem that is a crucial component of the algorithm. Our results demonstrate that virtual quantum subspace expansion works well in practice.

Authors:

^[1]; Camps, Daan ^[1];

^[1];

^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:: Fri Aug 21 00:00:00 EDT 2020

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division

OSTI Identifier:: 1766503

Grant/Contract Number:: AC02-05CH11231; AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Theory and Computation

Additional Journal Information:: Journal Volume: 16; Journal Issue: 9; Journal ID: ISSN 1549-9618

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Algorithms; Energy; Mathematical methods; Hamiltonians; Potential energy

Citation Formats


                    Urbanek, Miroslav, Camps, Daan, Van Beeumen, Roel, and de Jong, Wibe A. Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion.  United States: N. p., 2020. 
Web.  doi:10.1021/acs.jctc.0c00447.

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                    Urbanek, Miroslav, Camps, Daan, Van Beeumen, Roel, & de Jong, Wibe A. Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion.  United States.  https://doi.org/10.1021/acs.jctc.0c00447

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                    Urbanek, Miroslav, Camps, Daan, Van Beeumen, Roel, and de Jong, Wibe A. Fri .  
"Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion".  United States.  https://doi.org/10.1021/acs.jctc.0c00447.  https://www.osti.gov/servlets/purl/1766503.

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@article{osti_1766503,

  title        = {Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion},

  author       = {Urbanek, Miroslav and Camps, Daan and Van Beeumen, Roel and de Jong, Wibe A.},

  abstractNote = {Several novel methods for performing calculations relevant to quantum chemistry on quantum computers have been proposed but not yet explored experimentally. Virtual quantum subspace expansion is one such algorithm developed for modeling complex molecules using their full orbital space and without the need for additional quantum resources. Here, we implement this method on the IBM Q platform and calculate the potential energy curves of the hydrogen and lithium dimers using only two qubits and simple classical post-processing. A comparable level of accuracy would require twenty qubits with previous approaches. We also develop an approach to minimize the impact of experimental noise on the stability of a generalized eigenvalue problem that is a crucial component of the algorithm. Our results demonstrate that virtual quantum subspace expansion works well in practice.},

  doi          = {10.1021/acs.jctc.0c00447},

  journal      = {Journal of Chemical Theory and Computation},

  number       = 9,

  volume       = 16,

  place        = {United States},

  year         = {Fri Aug 21 00:00:00 EDT 2020},

  month        = {Fri Aug 21 00:00:00 EDT 2020}

}

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Fermionic partial tomography via classical shadows
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Title: Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion

Abstract

Citation Formats

Simulated Quantum Computation of Molecular Energies journal, September 2005

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability journal, June 2017

Quantum computational chemistry journal, March 2020

Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver journal, June 2019

Low-cost error mitigation by symmetry verification journal, December 2018

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

Scalar quantum field theories as a benchmark for near-term quantum computers journal, March 2019

Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents? journal, March 2020

Self-verifying variational quantum simulation of lattice models journal, May 2019

Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer journal, April 2019

Witnessing eigenstates for quantum simulation of Hamiltonian spectra journal, January 2018

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

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

Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization” journal, November 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

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal, January 1989

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

Elucidating reaction mechanisms on quantum computers journal, July 2017

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

Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization journal, December 1997

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

Cloud Quantum Computing of an Atomic Nucleus journal, May 2018

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

OpenFermion: the electronic structure package for quantum computers journal, June 2020

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

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator journal, July 2018

�ber das Paulische �quivalenzverbot journal, September 1928

Quantum Chemistry in the Age of Quantum Computing journal, August 2019

Scalable Quantum Simulation of Molecular Energies journal, July 2016

An adaptive variational algorithm for exact molecular simulations on a quantum computer journal, July 2019

Classical Optimizers for Noisy Intermediate-Scale Quantum Devices conference, October 2020

528: Optimal duration of antenatal corticosteroid (ACS) exposure and neonatal outcomes journal, January 2016

Fermionic partial tomography via classical shadows text, January 2020

Simulated Quantum Computation of Molecular Energies
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Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability
journal, June 2017

Quantum computational chemistry
journal, March 2020

Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver
journal, June 2019

Low-cost error mitigation by symmetry verification
journal, December 2018

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

Scalar quantum field theories as a benchmark for near-term quantum computers
journal, March 2019

Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?
journal, March 2020

Self-verifying variational quantum simulation of lattice models
journal, May 2019

Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer
journal, April 2019

Witnessing eigenstates for quantum simulation of Hamiltonian spectra
journal, January 2018

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

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

Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”
journal, November 2011

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

A variational eigenvalue solver on a photonic quantum processor
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Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
journal, April 2017

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

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

Elucidating reaction mechanisms on quantum computers
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Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure
journal, February 2017

Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
journal, December 1997

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

Cloud Quantum Computing of an Atomic Nucleus
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Alternative coupled-cluster ansätze II. The unitary coupled-cluster method
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journal, June 2020

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

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator
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journal, August 2019

Scalable Quantum Simulation of Molecular Energies
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