Efficient Learning of Phases of Matter through Dissipative Evolution

The combination of quantum many-body and machine learning techniques has recently proved to be a fertile ground for new developments in quantum computing. Several works have shown that it is possible to classically efficiently predict the expectation values of local observables on all states within a phase of matter using a machine learning algorithm after learning from data obtained from other states in the same phase. However, existing results are restricted to phases of matter such as ground states of gapped Hamiltonians and Gibbs states that exhibit exponential decay of correlations. In this work, we drop this requirement and show how it is possible to learn local expectation values for all states in a phase, where we adopt the Lindbladian phase definition by Coser \& Pérez-García [Coser \& Pérez-García, Quantum 3, 174 (2019)], which defines states to be in the same phase if we can drive one to other rapidly with a local Lindbladian. This definition encompasses the better-known Hamiltonian definition of phase of matter for gapped ground state phases, and further applies to any family of states connected by short unitary circuits, as well as non-equilibrium phases of matter, and those stable under external dissipative interactions. Under this definition, we show thatN=O(log(n/δ)2polylog(1/ϵ)) samples suffice to learn local expectation values within a phase for a system with n qubits, to error ϵ with failure probability δ. This sample complexity is comparable to previous results on learning gapped and thermal phases, and it encompasses previous results of this nature in a unified way. Furthermore, we also show that we can learn families of states which go beyond the Lindbladian definition of phase, and we derive bounds on the sample complexity which are dependent on the mixing time between states under a Lindbladian evolution. This talk will be based on https://arxiv.org/abs/2311.07506 and is joint work with C. Rouze, J. Watson and E. Onorati.

 

BIO:
Daniel Stilck Franca is an Associate Professor at the Mathematics Department at the University of Copenhagen and the Quantum for Life Center working in quantum computing. Previous to that, he was a research scientist at INRIA and ENS Lyon. He completed his PhD in 2018 at TU Munich under the supervision of Michael Wolf, and moved to the University of Copenhagen for a postdoc after that. Lately, he is particularly interested in learning of quantum states and channels, applications of quantum Gibbs sampling and the impact of noise in quantum computation.