Superfast encodings for fermionic quantum simulation
Abstract
Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the superfast encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree d to a qubit simulator Hamiltonian composed of Pauli operators of weight O (d ) . A system of m Fermi modes gets mapped to n =O (m d ) qubits. We propose generalized superfast encodings (GSEs) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree d ≥6 . In contrast, we prove that the original superfast encoding lacks the error correction property for d ≤6 . Second, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from O (d ) to O (logd ) . The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.
- Publication:
-
Physical Review Research
- Pub Date:
- October 2019
- DOI:
- 10.1103/PhysRevResearch.1.033033
- arXiv:
- arXiv:1810.05274
- Bibcode:
- 2019PhRvR...1c3033S
- Keywords:
-
- Quantum Physics;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 9 pages, 4 figures