Non-unitary free boson dynamics and the boson sampling problem
- URL: http://arxiv.org/abs/2110.12230v1
- Date: Sat, 23 Oct 2021 14:27:07 GMT
- Title: Non-unitary free boson dynamics and the boson sampling problem
- Authors: Xiao Chen
- Abstract summary: We show that each boson is performing a non-unitary quantum walk in real space.
We numerically show that in the one dimensional system, when the measurement strength is finite, the system is in the frozen phase.
- Score: 6.723539428281127
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We explore the free boson unitary dynamics subject to repeated random forced
measurement. The input state is chosen as a Fock state in real space with the
particle number conserved in the entire dynamics. We show that each boson is
performing a non-unitary quantum walk in real space and its dynamics can be
mapped to directed polymers in a random medium with complex amplitude. We
numerically show that in the one dimensional system, when the measurement
strength is finite, the system is in the frozen phase with all the bosons
localized in the real space. Furthermore, these single particle wave functions
take the same probability distribution in real space after long time evolution.
Due to this property, the boson sampling for the output state becomes easy to
solve. We further investigate circuit with non-local unitary dynamics and
numerically demonstrate that there could exist a phase transition from a
localized phase to a delocalized phase by varying the measurement strength.
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