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

This seminar, given by Yaroslav Herasymenko, will happend on 04 October 2024, at 12:0. It will take place in Room 26-00/534.

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Abstract

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 - QI Team

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

Abstract