dorsal/arxiv
View SchemaFermionic quantum computation
| Authors | Sergey Bravyi, Alexei Kitaev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0003137 |
| URL | https://arxiv.org/abs/quant-ph/0003137 |
| DOI | 10.1006/aphy.2002.6254 |
| Journal | Annals of Physics, Vol. 298, Iss. 1 (2002) pp.210-226 |
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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"abstract": "We define a model of quantum computation with local fermionic modes (LFMs) --\nsites which can be either empty or occupied by a fermion. With the standard\ncorrespondence between the Foch space of $m$ LFMs and the Hilbert space of $m$\nqubits, simulation of one fermionic gate takes $O(m)$ qubit gates and vice\nversa. We show that using different encodings, the simulation cost can be\nreduced to $O(\\log m)$ and a constant, respectively. Nearest-neighbors\nfermionic gates on a graph of bounded degree can be simulated at a constant\ncost. A universal set of fermionic gates is found. We also study computation\nwith Majorana fermions which are basically halves of LFMs. Some connection to\nqubit quantum codes is made.",
"arxiv_id": "quant-ph/0003137",
"authors": [
"Sergey Bravyi",
"Alexei Kitaev"
],
"categories": [
"quant-ph"
],
"doi": "10.1006/aphy.2002.6254",
"journal_ref": "Annals of Physics, Vol. 298, Iss. 1 (2002) pp.210-226",
"title": "Fermionic quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0003137"
},
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