Fermionic quantum computation

2000/03/31 by Sergey Bravyi, Alexei Kitaev · 7 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1006/aphy.2002.6254

published as Annals of Physics, Vol. 298, Iss. 1 (2002) pp.210-226 · 18 pages, Latex; one reference added

arxiv created 2000/04/01 · arxiv updated 2009/12/01

Abstract

We define a model of quantum computation with local fermionic modes (LFMs) -- sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest-neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.

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