Hamiltonian Matrix and Reduced Density Matrix Construction with Nonlinear Wave Functions

2006 ◽  
Vol 110 (28) ◽  
pp. 8880-8892 ◽  
Author(s):  
Ron Shepard
Keyword(s):  
Density Matrix ◽  
Nonlinear Wave ◽  
Wave Functions ◽  
Reduced Density Matrix ◽  
Hamiltonian Matrix ◽  
Reduced Density ◽  
Matrix Construction

scholarly journals Unrestricted treatment for the direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions

2019 ◽  
Vol 150 (16) ◽  
pp. 164106 ◽  
Author(s):  
Diego R. Alcoba ◽  
Alicia Torre ◽  
Luis Lain ◽  
Gustavo E. Massaccesi ◽  
Ofelia B. Oña ◽  
...  
Keyword(s):  
Density Matrix ◽  
Configuration Interaction ◽  
Wave Functions ◽  
Reduced Density Matrix ◽  
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.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

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