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Title: Quantum simulations of excited states with active-space downfolded Hamiltonians

Abstract

Many-body techniques based on the double unitary coupled cluster ansatz (DUCC) can be used to downfold electronic Hamiltonians into low-dimensional active spaces. It can be shown that the resulting dimensionality reduced Hamiltonians are amenable for quantum computing. Recent studies performed for several benchmark systems using quantum phase estimation (QPE) algorithms demonstrated that these formulations can recover a significant portion of ground-state dynamical correlation effects that stem from the electron excitations outside of the active space. These results have also been confirmed in studies of ground-state potential energy surfaces using quantum simulators. In this letter, we study the effectiveness of the DUCC formalism in describing excited states. We also emphasize the role of the QPE formalism and its stochastic nature in discovering/identifying excited states or excited-state processes in situations when the knowledge about the true configurational structure of a sought after excited state is limited or postulated (due to the specific physics driving excited-state processes of interest). In this context, we can view the QPE algorithm as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. We illustrate these ideas onmore » examples of strongly cor- related molecular systems, characterized by small energy gaps and high density of quasi-degenerate states around the Fermi level.« less

Authors:
 [1];  [2];  [1]
  1. BATTELLE (PACIFIC NW LAB)
  2. MICROSOFT
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1581619
Report Number(s):
PNNL-SA-146959
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 23
Country of Publication:
United States
Language:
English
Subject:
quantum chemistry, quantum computing, computational chemistry, electronic structure methods

Citation Formats

Bauman, Nicholas P., Low, Guang Hao, and Kowalski, Karol. Quantum simulations of excited states with active-space downfolded Hamiltonians. United States: N. p., 2019. Web. doi:10.1063/1.5128103.
Bauman, Nicholas P., Low, Guang Hao, & Kowalski, Karol. Quantum simulations of excited states with active-space downfolded Hamiltonians. United States. doi:10.1063/1.5128103.
Bauman, Nicholas P., Low, Guang Hao, and Kowalski, Karol. Sat . "Quantum simulations of excited states with active-space downfolded Hamiltonians". United States. doi:10.1063/1.5128103.
@article{osti_1581619,
title = {Quantum simulations of excited states with active-space downfolded Hamiltonians},
author = {Bauman, Nicholas P. and Low, Guang Hao and Kowalski, Karol},
abstractNote = {Many-body techniques based on the double unitary coupled cluster ansatz (DUCC) can be used to downfold electronic Hamiltonians into low-dimensional active spaces. It can be shown that the resulting dimensionality reduced Hamiltonians are amenable for quantum computing. Recent studies performed for several benchmark systems using quantum phase estimation (QPE) algorithms demonstrated that these formulations can recover a significant portion of ground-state dynamical correlation effects that stem from the electron excitations outside of the active space. These results have also been confirmed in studies of ground-state potential energy surfaces using quantum simulators. In this letter, we study the effectiveness of the DUCC formalism in describing excited states. We also emphasize the role of the QPE formalism and its stochastic nature in discovering/identifying excited states or excited-state processes in situations when the knowledge about the true configurational structure of a sought after excited state is limited or postulated (due to the specific physics driving excited-state processes of interest). In this context, we can view the QPE algorithm as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. We illustrate these ideas on examples of strongly cor- related molecular systems, characterized by small energy gaps and high density of quasi-degenerate states around the Fermi level.},
doi = {10.1063/1.5128103},
journal = {Journal of Chemical Physics},
number = 23,
volume = 151,
place = {United States},
year = {2019},
month = {12}
}

Works referenced in this record:

Simulated Quantum Computation of Molecular Energies
journal, September 2005


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
  • DOI: 10.1038/nchem.483

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
  • DOI: 10.1063/1.4768229

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

  • Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5213

Exponentially more precise quantum simulation of fermions in second quantization
journal, March 2016


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


Elucidating reaction mechanisms on quantum computers
journal, July 2017

  • Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 29
  • DOI: 10.1073/pnas.1619152114

Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer
journal, April 2018

  • Setia, Kanav; Whitfield, James D.
  • The Journal of Chemical Physics, Vol. 148, Issue 16
  • DOI: 10.1063/1.5019371

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


Second-order perturbation theory with a CASSCF reference function
journal, July 1990

  • Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O.
  • The Journal of Physical Chemistry, Vol. 94, Issue 14
  • DOI: 10.1021/j100377a012

Second‐order perturbation theory with a complete active space self‐consistent field reference function
journal, January 1992

  • Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O.
  • The Journal of Chemical Physics, Vol. 96, Issue 2
  • DOI: 10.1063/1.462209

Introduction of n -electron valence states for multireference perturbation theory
journal, June 2001

  • Angeli, C.; Cimiraglia, R.; Evangelisti, S.
  • The Journal of Chemical Physics, Vol. 114, Issue 23
  • DOI: 10.1063/1.1361246

An efficient internally contracted multiconfiguration–reference configuration interaction method
journal, November 1988

  • Werner, Hans‐Joachim; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 89, Issue 9
  • DOI: 10.1063/1.455556

The equation-of-motion coupled-cluster method: Excitation energies of Be and CO
journal, December 1989


Higher-order equation-of-motion coupled-cluster methods
journal, January 2004

  • Hirata, So
  • The Journal of Chemical Physics, Vol. 121, Issue 1
  • DOI: 10.1063/1.1753556

Correlation problem in open-shell atoms and molecules: A non-perturbative linked cluster formulation
journal, December 1975

  • Mukherjee, Debashis; Moitra, Raj Kumar; Mukhopadhyay, Atri
  • Molecular Physics, Vol. 30, Issue 6
  • DOI: 10.1080/00268977500103351

Multireference coupled cluster theory in Fock space: with an application tos-tetrazine
journal, January 1991

  • Rittby, C. M. L.; Bartlett, R. J.
  • Theoretica Chimica Acta, Vol. 80, Issue 6
  • DOI: 10.1007/bf01119666

Fock-space coupled-cluster method in the intermediate Hamiltonian formulation: Model with singles and doubles
journal, June 1998

  • Meissner, Leszek
  • The Journal of Chemical Physics, Vol. 108, Issue 22
  • DOI: 10.1063/1.476377

Multireference Fock-space coupled-cluster and equation-of-motion coupled-cluster theories: The detailed interconnections
journal, October 2008

  • Musial, Monika; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 129, Issue 13
  • DOI: 10.1063/1.2982788

A coupled-cluster method for quasidegenerate states
journal, December 1988

  • Meissner, L.; Jankowski, K.; Wasilewski, J.
  • International Journal of Quantum Chemistry, Vol. 34, Issue 6
  • DOI: 10.1002/qua.560340607

A state-specific multi-reference coupled cluster formalism with molecular applications
journal, May 1998


Coupling term derivation and general implementation of state-specific multireference coupled cluster theories
journal, July 2007

  • Evangelista, Francesco A.; Allen, Wesley D.; Schaefer, Henry F.
  • The Journal of Chemical Physics, Vol. 127, Issue 2
  • DOI: 10.1063/1.2743014

Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly
journal, May 2011

  • Hanauer, Matthias; Köhn, Andreas
  • The Journal of Chemical Physics, Vol. 134, Issue 20
  • DOI: 10.1063/1.3592786

Internally contracted multireference coupled-cluster theory in a multistate framework
journal, February 2016

  • Aoto, Yuri Alexandre; Köhn, Andreas
  • The Journal of Chemical Physics, Vol. 144, Issue 7
  • DOI: 10.1063/1.4941604

State-specific multireference coupled-cluster theory: State-specific multireference coupled-cluster theory
journal, October 2012

  • Köhn, Andreas; Hanauer, Matthias; Mück, Leonie Anna
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 2
  • DOI: 10.1002/wcms.1120

Multireference Nature of Chemistry: The Coupled-Cluster View
journal, December 2011

  • Lyakh, Dmitry I.; Musiał, Monika; Lotrich, Victor F.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2001417

The Density Matrix Renormalization Group in Quantum Chemistry
journal, May 2011


Equation-of-motion coupled-cluster calculations of excitation energies. The challenge of ozone
journal, March 1999

  • Watts, John D.; Bartlett, Rodney J.
  • Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Vol. 55, Issue 3
  • DOI: 10.1016/s1386-1425(98)00258-3

The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt
journal, July 2001

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 115, Issue 2
  • DOI: 10.1063/1.1378323

Coupled-cluster theory for excited electronic states: The full equation-of-motion coupled-cluster single, double, and triple excitation method
journal, November 2001

  • Kucharski, Stanisław A.; Włoch, Marta; Musiał, Monika
  • The Journal of Chemical Physics, Vol. 115, Issue 18
  • DOI: 10.1063/1.1416173

Note: Excited state studies of ozone using state-specific multireference coupled cluster methods
journal, December 2012

  • Bhaskaran-Nair, Kiran; Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 137, Issue 21
  • DOI: 10.1063/1.4769775

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
journal, January 2009

  • Booth, George H.; Thom, Alex J. W.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 131, Issue 5
  • DOI: 10.1063/1.3193710

Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo
journal, January 2010

  • Cleland, Deidre; Booth, George H.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 132, Issue 4
  • DOI: 10.1063/1.3302277

Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations
journal, March 2019

  • Deustua, J. Emiliano; Yuwono, Stephen H.; Shen, Jun
  • The Journal of Chemical Physics, Vol. 150, Issue 11
  • DOI: 10.1063/1.5090346

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
  • DOI: 10.1088/2058-9565/aad3e4

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


Optimum phase-shift estimation and the quantum description of the phase difference
journal, November 1996


Quantum algorithms revisited
journal, January 1998

  • Cleve, R.; Ekert, A.; Macchiavello, C.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969
  • DOI: 10.1098/rspa.1998.0164

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
journal, December 2006

  • Berry, Dominic W.; Ahokas, Graeme; Cleve, Richard
  • Communications in Mathematical Physics, Vol. 270, Issue 2
  • DOI: 10.1007/s00220-006-0150-x

On the Relationship Between Continuous- and Discrete-Time Quantum Walk
journal, October 2009


Quantum Algorithm for Spectral Measurement with a Lower Gate Count
journal, July 2018


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
  • DOI: 10.1039/b804804e

Variational Quantum Computation of Excited States
journal, July 2019


Hamiltonian Simulation by Qubitization
journal, July 2019


Applicability of coupled-pair theories to quasidegenerate electronic states: A model study
journal, November 1980

  • Jankowski, K.; Paldus, J.
  • International Journal of Quantum Chemistry, Vol. 18, Issue 5
  • DOI: 10.1002/qua.560180511

Diradical Character View of Singlet Fission
journal, December 2011

  • Minami, Takuya; Nakano, Masayoshi
  • The Journal of Physical Chemistry Letters, Vol. 3, Issue 2
  • DOI: 10.1021/jz2015346

Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
journal, July 2019

  • Bauman, Nicholas P.; Bylaska, Eric J.; Krishnamoorthy, Sriram
  • The Journal of Chemical Physics, Vol. 151, Issue 1
  • DOI: 10.1063/1.5094643

Properties of coupled-cluster equations originating in excitation sub-algebras
journal, March 2018

  • Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 148, Issue 9
  • DOI: 10.1063/1.5010693

A state‐selective multireference coupled‐cluster theory employing the single‐reference formalism
journal, August 1993

  • Piecuch, Piotr; Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 99, Issue 3
  • DOI: 10.1063/1.466179

Active-space coupled-cluster methods
journal, November 2010


Multireference coupled‐cluster method using a single‐reference formalism
journal, January 1991

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 94, Issue 2
  • DOI: 10.1063/1.460031

The implementation of the multireference coupled‐cluster method based on the single‐reference formalism
journal, March 1992

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 96, Issue 5
  • DOI: 10.1063/1.461878

NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010

  • Valiev, M.; Bylaska, E. J.; Govind, N.
  • Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489
  • DOI: 10.1016/j.cpc.2010.04.018

Improved techniques for preparing eigenstates of fermionic Hamiltonians
journal, May 2018

  • Berry, Dominic W.; Kieferová, Mária; Scherer, Artur
  • npj Quantum Information, Vol. 4, Issue 1
  • DOI: 10.1038/s41534-018-0071-5

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

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153