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Title: Quantum simulations employing connected moments expansions

Journal Article · · Physical Review Letters
DOI:https://doi.org/10.1063/5.0030688· OSTI ID:1735598

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.

Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC05-76RL01830
OSTI ID:
1735598
Report Number(s):
PNNL-SA-156136
Journal Information:
Physical Review Letters, Vol. 153, Issue 20
Country of Publication:
United States
Language:
English

References (47)

On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell‐Type Expansion Using Quantum‐Field Theoretical Methods journal December 1966
A Critical Assessment of Coupled Cluster Method in Quantum Chemistry book January 1999
A deterministic alternative to the full configuration interaction quantum Monte Carlo method journal July 2016
iCI: Iterative CI toward full CI journal January 2016
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
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
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
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
  • 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
journal January 1998
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
High Performance Emulation of Quantum Circuits
  • 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
conference November 2016
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
Über das Paulische Äquivalenzverbot book January 1993
Fermionic Quantum Computation journal May 2002
On the validity and applicability of the connected moments expansion journal March 1987
Connected moments expansion with variational Monte Carlo technique journal January 1988
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
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
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 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
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
Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations journal August 2017
Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition journal April 2019

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