Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix

2002 ◽  
Vol 65 (6) ◽  
Author(s):  
David A. Mazziotti
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Reduced Density Matrix ◽  
Variational Minimization ◽  
Molecular Ground State ◽  
Reduced Density ◽  
Ground State Energies

Variational reduced-density-matrix method for ground-state nuclear motion

2007 ◽  
Vol 75 (1) ◽  
Author(s):  
Eugene Kamarchik ◽  
David A. Mazziotti
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Matrix Method ◽  
Reduced Density Matrix ◽  
Nuclear Motion ◽  
Reduced Density

scholarly journals The electronic ground-state energy problem: A new reduced density matrix approach

2006 ◽  
Vol 125 (6) ◽  
pp. 064101 ◽  
Author(s):  
Eric Cancès ◽  
Gabriel Stoltz ◽  
Mathieu Lewin
Keyword(s):  
Density Matrix ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Electronic Ground State ◽  
Reduced Density Matrix ◽  
Matrix Approach ◽  
Energy Problem ◽  
Reduced Density ◽  
Electronic Ground

Extraction of ionization energies from the ground-state two-particle reduced density matrix

2004 ◽  
Vol 400 (1-3) ◽  
pp. 90-93 ◽  
Author(s):  
John D. Farnum ◽  
David A. Mazziotti
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Reduced Density Matrix ◽  
Ionization Energies ◽  
Reduced Density

scholarly journals Quantum simulation of molecules without fermionic encoding of the wave function

2021 ◽  
Vol 23 (11) ◽  
pp. 113037
Author(s):  
David A Mazziotti ◽  
Scott E Smart ◽  
Alexander R Mazziotti
Keyword(s):  
Wave Function ◽  
Density Matrix ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Molecular Simulations ◽  
Wave Functions ◽  
Reduced Density Matrix ◽  
Particle Wave Function ◽  
Reduced Density

Abstract Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N-qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H4 is presented.

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