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Title: Quantum simulations employing connected moments expansions

Abstract

Further advancement of quantum computing (QC) is contingent on enabling many-body models that avoid deep circuits and excessive use of CNOT gates. To this end, we develop a QC approach employing finite-order connected moment expansions (CMX) and affordable procedures for initial state preparation. We demonstrate the performance of our approach employing several quantum variants of CMX through the classical emulations on the H2 molecule potential energy surface and the Anderson model with a broad range of correlation strength. The results show that our approach is robust and flexible. Good agreements with exact solutions can be maintained even at the dissociation and strong correlation limits.

Authors:
 [1];  [1]
  1. BATTELLE (PACIFIC NW LAB)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1735598
Report Number(s):
PNNL-SA-156136
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 153; Journal Issue: 20
Country of Publication:
United States
Language:
English
Subject:
quantum computing, quantum chemistry, Electron correlation

Citation Formats

Kowalski, Karol, and Peng, Bo. Quantum simulations employing connected moments expansions. United States: N. p., 2020. Web. doi:10.1063/5.0030688.
Kowalski, Karol, & Peng, Bo. Quantum simulations employing connected moments expansions. United States. https://doi.org/10.1063/5.0030688
Kowalski, Karol, and Peng, Bo. 2020. "Quantum simulations employing connected moments expansions". United States. https://doi.org/10.1063/5.0030688.
@article{osti_1735598,
title = {Quantum simulations employing connected moments expansions},
author = {Kowalski, Karol and Peng, Bo},
abstractNote = {Further advancement of quantum computing (QC) is contingent on enabling many-body models that avoid deep circuits and excessive use of CNOT gates. To this end, we develop a QC approach employing finite-order connected moment expansions (CMX) and affordable procedures for initial state preparation. We demonstrate the performance of our approach employing several quantum variants of CMX through the classical emulations on the H2 molecule potential energy surface and the Anderson model with a broad range of correlation strength. The results show that our approach is robust and flexible. Good agreements with exact solutions can be maintained even at the dissociation and strong correlation limits.},
doi = {10.1063/5.0030688},
url = {https://www.osti.gov/biblio/1735598}, journal = {Physical Review Letters},
number = 20,
volume = 153,
place = {United States},
year = {Sat Nov 28 00:00:00 EST 2020},
month = {Sat Nov 28 00:00:00 EST 2020}
}

Works referenced in this record:

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry
book, January 1999


Coupled-cluster theory in quantum chemistry
journal, February 2007


A deterministic alternative to the full configuration interaction quantum Monte Carlo method
journal, July 2016


iCI: Iterative CI toward full CI
journal, January 2016


Density matrix formulation for quantum renormalization groups
journal, November 1992


The density-matrix renormalization group
journal, April 2005


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


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


Towards an exact description of electronic wavefunctions in real solids
journal, December 2012


Semistochastic Projector Monte Carlo Method
journal, December 2012


Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions
journal, November 2017


Communication: Approaching exact quantum chemistry by cluster analysis of full configuration interaction quantum Monte Carlo wave functions
journal, October 2018


Accelerating convergence of equation-of-motion coupled-cluster computations using the semi-stochastic CC( P ; Q ) formalism
journal, September 2020


Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit
journal, September 2017


The Ground State Electronic Energy of Benzene
journal, October 2020


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


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


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


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


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


Error mitigation extends the computational reach of a noisy quantum processor
journal, March 2019


Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm
journal, February 2018


A non-orthogonal variational quantum eigensolver
journal, July 2020


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
  • https://doi.org/10.1098/rspa.1998.0164

Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
journal, December 2006


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


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


Progress towards practical quantum variational algorithms
journal, October 2015


High Performance Emulation of Quantum Circuits
conference, November 2016

  • Haner, Thomas; Steiger, Damian S.; Smelyanskiy, Mikhail
  • SC16: International Conference for High Performance Computing, Networking, Storage and Analysis
  • https://doi.org/10.1109/SC.2016.73

Variational ansatz-based quantum simulation of imaginary time evolution
journal, September 2019


Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
journal, November 2019


Quantum inverse iteration algorithm for programmable quantum simulators
journal, January 2020


Fermionic Quantum Computation
journal, May 2002


Quantum computational chemistry
journal, March 2020


On the product of semi-groups of operators
journal, April 1959


Low-Depth Quantum Simulation of Materials
journal, March 2018


The t expansion: A nonperturbative analytic tool for Hamiltonian systems
journal, September 1984


Connected moments expansion: A new tool for quantum many-body theory
journal, January 1987


On the validity and applicability of the connected moments expansion
journal, March 1987


Methods of extrapolating the t -expansion series
journal, September 1988


t expansion and the Lipkin model
journal, May 1988


Connected moments expansion with variational Monte Carlo technique
journal, January 1988


Removal of the singularity in the moment-expansion formalism
journal, March 1995


Analytic properties of connected moments expansions
journal, April 1994


Numerical singularities in many-body moments expansions
journal, December 1997


Cumulant t -expansion for strongly correlated fermions
journal, May 2016


Exactness of Two-Body Cluster Expansions in Many-Body Quantum Theory
journal, March 2003


On the Use of Connected Moments Expansion with Coupled Cluster Reference
journal, May 2002


On the relation between the connected-moments expansion and the Lanczos variational scheme
journal, May 1994


Avoidance of singularities in moments expansions: a numerical study
journal, December 1995


A generalized moments expansion
journal, January 2006


Analytic properties of moments matrices
journal, June 2010


Upper bounds for the free energy. A generalisation of the Bogolubov inequality and the Feynman inequality
journal, February 1984


Generalized Variational Principle in Quantum Mechanics
journal, October 1995


Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms
journal, July 2020


Scalable Quantum Simulation of Molecular Energies
journal, July 2016


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


Quantum chemistry as a benchmark for near-term quantum computers
journal, November 2019


Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware
journal, April 2020


Error Mitigation for Short-Depth Quantum Circuits
journal, November 2017


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


Sub-system quantum dynamics using coupled cluster downfolding techniques
journal, June 2020


Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition
journal, April 2019