412 research outputs found
Local spin operators for fermion simulations
Digital quantum simulation of fermionic systems is important in the context
of chemistry and physics. Simulating fermionic models on general purpose
quantum computers requires imposing a fermionic algebra on spins. The
previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two
techniques for accomplishing this task. Here we re-examine an auxiliary fermion
construction which maps fermionic operators to local operators on spins. The
local simulation is performed by relaxing the requirement that the number of
spins should match the number of fermionic modes. Instead, auxiliary modes are
introduced to enable non-consecutive fermionic couplings to be simulated with
constant low-rank tensor products on spins. We connect the auxiliary fermion
construction to other topological models and give examples of the construction
Basis set generation and optimization in the NISQ era with Quiqbox.jl
In the noisy intermediate-scale quantum era, ab initio computation of the
electronic structure problem has become one of the major benchmarks for
identifying the boundary between classical and quantum computational power. The
single-particle basis set plays a key role in the electronic structure methods
implemented on both classical and quantum devices. To investigate the
consequences of the single-particle basis set, we propose a framework for more
customizable basis set generation and basis set optimization. This framework
allows configurations of composite Gaussian-type basis functions to go beyond
typical Gaussian-type basis set frameworks such as the atomic orbitals and
floating basis sets. Such basis set generations set the stage for more flexible
variational optimization of basis set parameters. To realize this framework, we
have developed an open-source electronic structure package named ``Quiqbox'' in
the Julia programming language. Both the Hartree--Fock procedure and
Gaussian-based electronic integral computations are implemented in this
package. We compare Quiqbox with the basis set optimization package DiffiQult
and find faster convergence of the basis set optimization with lower run time.
We also demonstrate the additional customizability Quiqbox brings for more
systematic basis set research with an example of constructing and optimizing
delocalized orbitals.Comment: 15 pages, 7 figures, 5 tables, 1 listin
Machine-learning Kohn-Sham potential from dynamics in time-dependent Kohn-Sham systems
The construction of a better exchange-correlation potential in time-dependent
density functional theory (TDDFT) can improve the accuracy of TDDFT
calculations and provide more accurate predictions of the properties of
many-electron systems. Here, we propose a machine learning method to develop
the energy functional and the Kohn-Sham potential of a time-dependent Kohn-Sham
system is proposed. The method is based on the dynamics of the Kohn-Sham system
and does not require any data on the exact Kohn-Sham potential for training the
model. We demonstrate the results of our method with a 1D harmonic oscillator
example and a 1D two-electron example. We show that the machine-learned
Kohn-Sham potential matches the exact Kohn-Sham potential in the absence of
memory effect. Our method can still capture the dynamics of the Kohn-Sham
system in the presence of memory effects. The machine learning method developed
in this article provides insight into making better approximations of the
energy functional and the Kohn-Sham potential in the time-dependent Kohn-Sham
system
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