Yaroslav Herasymenko - Efficient learning of quantum states prepared with few fermionic non-Gaussian gates

Fri, 04 Oct 2024 00:00:00 +0000

Efficient learning of quantum states prepared with few fermionic non-Gaussian gates

Ce séminaire, donné par Yaroslav Herasymenko, aura lieu le 04 October 2024, à 12:0. Il aura lieu en salle 26-00/534.

Vous trouverez un plan du campus ici.

Résumé

The aim of quantum state tomography is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard; and only a few classes of states are currently known to be efficiently learnable. In this talk, I would like to present an efficient algorithm for learning states on n fermion modes prepared by any number of Gaussian and at most t non-Gaussian gates. By Jordan-Wigner mapping, it extends to n-qubit states produced by nearest-neighbor matchgate circuits with at most t SWAP-gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of the algorithm is poly(n,2^t); thus if t=O(log(n)), it is efficient. I will detail why this performance is optimal, under the common cryptographic assumption of LWE hardness. Finally, I will present our property testing algorithm, and explain why our tomography algorithm is efficient for some target states arising in many-body physics.

Yaroslav Herasymenko | LIP6 - Équipe QI

Yaroslav Herasymenko - Efficient learning of quantum states prepared with few fermionic non-Gaussian gates

Efficient learning of quantum states prepared with few fermionic non-Gaussian gates

Résumé