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Fermionic quantum computation

Sergey Bravyi·Alexei Kitaev
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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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Sergey Bravyi, Alexei Kitaev. 2000-04-01. Fermionic quantum computation. https://doi.org/10.1006/aphy.2002.6254

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