Custom fermionic codes for quantum simulation
- URL: http://arxiv.org/abs/2009.11860v1
- Date: Thu, 24 Sep 2020 17:59:14 GMT
- Title: Custom fermionic codes for quantum simulation
- Authors: Riley W. Chien and James D. Whitfield
- Abstract summary: We show that locality may in fact be too strict of a condition and the size of operators can be reduced by encoding the system quasi-locally.
We give examples relevant to lattice models of condensed matter and systems relevant to quantum gravity such as SYK models.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Simulating a fermionic system on a quantum computer requires encoding the
anti-commuting fermionic variables into the operators acting on the qubit
Hilbert space. The most familiar of which, the Jordan-Wigner transformation,
encodes fermionic operators into non-local qubit operators. As non-local
operators lead to a slower quantum simulation, recent works have proposed ways
of encoding fermionic systems locally. In this work, we show that locality may
in fact be too strict of a condition and the size of operators can be reduced
by encoding the system quasi-locally. We give examples relevant to lattice
models of condensed matter and systems relevant to quantum gravity such as SYK
models. Further, we provide a general construction for designing codes to suit
the problem and resources at hand and show how one particular class of
quasi-local encodings can be thought of as arising from truncating the state
preparation circuit of a local encoding. We end with a discussion of designing
codes in the presence of device connectivity constraints.
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