Complexity Transitions in Non-Unitary Boson Sampling Dynamics

• URL: http://arxiv.org/abs/2207.12624v3
• Date: Wed, 3 Aug 2022 13:52:12 GMT
• Title: Complexity Transitions in Non-Unitary Boson Sampling Dynamics
• Authors: Ken Mochizuki, Ryusuke Hamazaki
• Abstract summary: We show that parity-time ($mathcalPT$) symmetry breaking, a unique transition in non-Hermitian open systems, profoundly affects the complexity of sampling the probability distribution of bosons. In a $mathcalPT$-symmetric phase, we find only one dynamical transition, upon which the distribution of bosons ceases to be approximated by a computable one for distinguishable particles.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discover novel transitions characterized by computational complexity in non-unitary dynamics of bosons with parity-time ($\mathcal{PT}$) symmetry. We show that parity-time ($\mathcal{PT}$) symmetry breaking, a unique transition in non-Hermitian open systems, profoundly affects the complexity of sampling the probability distribution of bosons. In a $\mathcal{PT}$-symmetric phase, we find only one dynamical transition, upon which the distribution of bosons ceases to be approximated by a computable one for distinguishable particles. If the system enters a $\mathcal{PT}$-broken phase, the threshold time for the transition is suddenly prolonged. Furthermore, this phase also exhibits a notable dynamical transition on a longer time scale, at which the boson distribution again becomes computable. This transition, and hence the easiness of the boson sampling problem in long times, are true for generic postselected non-unitary quantum dynamics.

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