Simulation of quantum many-body physics, such as looking for ground state properties and real time dynamics, plays an important role in the study of condensed matter physics and quantum computation. With recent advancement of machine learning, new methods have been proposed to enhance quantum many-body physics simulation. In the first half of this talk, I will present a new class of wave functions, neural network backflow (NNB). NNB directly dresses mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. It produces the anti-symmetry property of fermionic wave function and generalizes the standard backflow to arbitrary lattice. We benchmark NNB on a Hubbard model at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals. In the second half of the talk, I will present an exact probabilistic formulation of quantum dynamics through positive value-operator measurements (POVM). In this formulation, unitary dynamics and quantum channels are represented by quasi-stochastic matrices acting on true probability distributions which specify the quantum state univocally. Using the POVM formalism, we have developed a practical algorithm for the probabilistic simulation of quantum circuits with the Transformer, a powerful ansatz responsible for the most recent breakthroughs in the natural language processing research. The method is applied to state preparation of GHZ state and Linear Graph state up to 60 qubits, as well as variational quantum circuit preparation of the ground state of the Transverse Field Ising Model.
Contact: Lei Wang, 9853