Speaker: Ken Mochizuki (RIKEN)

Date & Time: 10am, Sep 5, 2022.

Title: Complexity transitions in non-unitary boson sampling dynamics

Abstract:

Non-Hermitian quantum mechanics have been extensively studied as an effective theory for open quantum systems exhibiting non-unitary dynamics, and various intriguing phenomena have been revealed. Non-Hermitian dynamics has been observed not only in genuinely quantum systems but also in classical systems. In that sense, it is a fundamental but largely unexplored question to what extent non-Hermitian quantum mechanics exhibits unique quantum nature distinct from classical systems. In isolated quantum systems, unique quantum nature can be discussed by its computational complexity. It is investigated in the boson sampling problem, where probability distributions of bosons can be hard to sample by classical computers.

In the seminar, we report novel transitions concerning the computational complexity in non-unitary dynamics of bosons. We find that PT-symmetry breaking, a unique phenomenon in non-Hermitian open quantum systems, is profoundly related to the computational complexity of the boson sampling problem. In the PT-broken phase, there is a dynamical transition where the probability distribution of bosons becomes approximated by that of distinguishable particles, which leads to the easiness of the boson sampling with classical computers. We discuss that the enhancement of the classical nature in terms of the easiness for sampling is ensured in the long-time regime in a wide range of non-unitary boson sampling dynamics.

Ken Mochizuki and Ryusuke Hamazaki, arXiv:2207.12624