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Universal computation with quantum fields

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Abstract

We explore a way of universal quantum computation with particles which cannot occupy the same position simultaneously and are symmetric under exchange of particle labels. Therefore the associated creation and annihilation operators are neither bosonic nor fermionic. In this work we first show universality of our method and numerically address several examples. We demonstrate dynamics of a Bloch electron system from a viewpoint of adiabatic quantum computation. In addition we provide a novel Majorana fermion system and analyze phase transitions with spin-coherent states and the time average of the out-of-time-order correlator (OTOC). We report that a first-order phase transition is avoided when it evolves in a non-stoquastic manner and the time average of the OTOC diagnoses the phase transitions successfully.

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Notes

  1. \([a_i,a^\dagger _j]=\delta _{ij}, [a_i,a_j]=[a^\dagger _i,a^\dagger _j]=0\) for bosons.

  2. \(\{a_i,a^\dagger _j\}=\delta _{ij}, \{a_i,a_j\}=\{a^\dagger _i,a^\dagger _j\}=0\) for fermions.

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Acknowledgements

I am grateful to Katsuya Hashino, Viktor Jahnke and Kin-ya Oda for stimulating discussion and useful comments on the draft. The author was partly supported by Grant-in-Aid for JSPS Research Fellow, No. 19J11073.

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  1. Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Kazuki Ikeda

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  1. Kazuki Ikeda
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Correspondence to Kazuki Ikeda.

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Ikeda, K. Universal computation with quantum fields. Quantum Inf Process 19, 331 (2020). https://doi.org/10.1007/s11128-020-02811-5

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