On the Super-exponential Quantum Speedup of Equivariant Quantum Machine Learning Algorithms with SU($d$) Symmetry

no code implementations • 15 Jul 2022 • Han Zheng, Zimu Li, Junyu Liu, Sergii Strelchuk, Risi Kondor

We introduce a framework of the equivariant convolutional algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU($d$) symmetries.

BIG-bench Machine Learning Quantum Machine Learning

Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze

1 code implementation • 14 Dec 2021 • Han Zheng, Zimu Li, Junyu Liu, Sergii Strelchuk, Risi Kondor

We develop a theoretical framework for $S_n$-equivariant convolutional quantum circuits with SU$(d)$-symmetry, building on and significantly generalizing Jordan's Permutational Quantum Computing (PQC) formalism based on Schur-Weyl duality connecting both SU$(d)$ and $S_n$ actions on qudits.

BIG-bench Machine Learning Quantum Machine Learning

Learning hard quantum distributions with variational autoencoders

no code implementations • 2 Oct 2017 • Andrea Rocchetto, Edward Grant, Sergii Strelchuk, Giuseppe Carleo, Simone Severini

This suggests that the probability distributions associated to hard quantum states might have a compositional structure that can be exploited by layered neural networks.