Sparse non-orthogonal wave function expansions from the extension of the generalized Pauli constraints to the two-electron reduced density matrix

2019 ◽  
Vol 150 (14) ◽  
pp. 144102 ◽  
Author(s):  
Jan-Niklas Boyn ◽  
David A. Mazziotti
Keyword(s):  
Wave Function ◽  
Density Matrix ◽  
Reduced Density Matrix ◽  
Reduced Density

scholarly journals Decoherence in Pre-Big-Bang Cosmology

1997 ◽  
Vol 12 (09) ◽  
pp. 597-612 ◽  
Author(s):  
André Lukas ◽  
Rudolf Poppe
Keyword(s):  
Wave Function ◽  
Density Matrix ◽  
Quantum Cosmology ◽  
Big Bang ◽  
Reduced Density Matrix ◽  
Wave Number ◽  
Exit Problem ◽  
Specific Choice ◽  
Big Bang Model ◽  
Reduced Density

We analyze the quantum cosmology of the simplest pre-big-bang model without dilaton potential. In addition to the minisuperspace variables we include inhomogeneous dilaton fluctuations and determine their wave function on a semiclassical background. This wave function is used to calculate the reduced density matrix and to find criteria for the loss of decoherence. It is shown that coherence between different backgrounds can always be achieved by a specific choice of vacua. Their exact expressions as functions of the wave number and the background quantities are given. Generically, however, decoherence can be expected. In particular, we discuss the implications of these results on the "exit problem" of pre-big-bang cosmology.

scholarly journals Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation

Computation ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 135
Author(s):  
Carmelo Naim ◽  
Claudio Amovilli
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Density Matrix ◽  
Quantum Monte Carlo ◽  
Valence Bond ◽  
Reduced Density Matrix ◽  
Electronic Density ◽  
Complete Active Space ◽  
Energy Functionals ◽  
Reduced Density

In this work, we present a method to build a first order reduced density matrix (1-RDM) of a molecule from variational Quantum Monte Carlo (VMC) computations by means of a given correlated mapping wave function. Such a wave function is modeled on a Generalized Valence Bond plus Complete Active Space Self Configuration Interaction form and fits at best the density resulting from the Slater-Jastrow wave function of VMC. The accuracy of the method proposed has been proved by comparing the resulting kinetic energy with the corresponding VMC value. This 1-RDM is used to analyze the amount of correlation eventually captured in Kohn-Sham calculations performed in an unrestricted approach (UKS-DFT) and with different energy functionals. We performed test calculations on a selected set of molecules that show a significant multireference character. In this analysis, we compared both local and global indicators of nondynamic and dynamic correlation. Moreover, following the natural orbital decomposition of the 1-RDM, we also compared the effective temperatures of the corresponding Fermi-like distributions. Although there is a general agreement between UKS-DFT and VMC, we found the best match with the functional LC-BLYP.

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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