Many-body variational state preparation in the age of machine learning and quantum computing
In this seminar I will discuss several approaches to the fundamental problem of efficiently preparing many-body quantum states. I will present both classical and quantum algorithms for this task, focusing on the respective advantages and limitations.
In the context of quantum algorithms, I will consider variational states based on parameterised quantum circuits.
I will introduce the concept of Quantum Natural Gradient  and its efficient implementation  using the Simultaneous Perturbation Stochastic Approximation.
I will also discuss an efficient variational quantum algorithm named “projected – Variational Quantum Dynamics” (p-VQD) realizing an iterative, global projection of the exact time evolution onto the parameterized manifold .
In the context of classical algorithms, I will show instead how variational parameterisations based on neural network quantum states  can be used to simulate NISQ-scale quantum computers, and show the example of QAOA .
 James Stokes, Josh Izaac, Nathan Killoran, and Giuseppe Carleo, Quantum 4, 269 (2020)
 Julien Gacon, Christa Zoufal, Giuseppe Carleo, and Stefan Woerner, arXiv:2103.09232 (2021)
 Stefano Barison, Filippo Vicentini, and Giuseppe Carleo, arXiv:2101.04579 (2021)
 Giuseppe Carleo, and Matthias Troyer, Science 355, 602 (2017)
 Matija Medvidović, and Giuseppe Carleo, npj Quantum Inf 7, 101 (2021)
The Laboratory for Theoretical and Computational Physics