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