Fermionic Quantum Computation

✍ Scribed by Sergey B. Bravyi; Alexei Yu. Kitaev

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 153 KB
• Volume: 298
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2002.6254

✦ Synopsis

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.