Bulletin of the American Physical Society
2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session B47: Quantum Algorithms and Complexity
11:30 AM–2:30 PM,
Monday, March 6, 2023
Room: Room 313
Sponsoring
Unit:
DQI
Chair: Nic Ezzell, University of Southern California
Abstract: B47.00008 : Equivalence between fermion-to-qubit mappings in two spatial dimensions*
12:54 PM–1:06 PM
Presenter:
Yu-An Chen
(University of Maryland, College Park)
Authors:
Yu-An Chen
(University of Maryland, College Park)
Yijia Xu
(University of Maryland, College Park)
In particular, we discover a new super-compact encoding using 1.25 qubits per fermion on the square lattice. We prove the existence of finite-depth quantum circuits to obtain fermion-to-qubit mappings with qubit-fermion ratios $r=1+ frac{1}{2k}$ for positive integers $k$, utilizing the trivialness of quantum cellular automata (QCA) in two spatial dimensions. Also, we provide direct constructions of fermion-to-qubit mappings with ratios arbitrarily close to 1. When the ratio reaches 1, the fermion-to-qubit mapping reduces to the 1d Jordan-Wigner transformation along a certain path in the two-dimensional lattice.
Finally, we explicitly demonstrate that the Bravyi-Kitaev superfast simulation, the Verstraete-Cirac auxiliary method, Kitaev’s exactly solved model, the Majorana loop stabilizer codes, and the compact fermion-to-qubit mapping can all be obtained from the exact bosonization.
*Y.-A.C is supported by the JQI fellowship at the University of Maryland.Y.X. is supported by ARO W911NF-15-1-0397, National Science Foundation QLCI grant OMA-2120757, AFOSR-MURI FA9550-19-1-0399, Department of Energy QSA program.
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