Physics & Astronomy Quantum Nano Seminar - Kanav Setia, Dartmouth College

Title: "Superfast Encoding and Error Correction"

October 25, 2018
4 pm - 5 pm
Location
Wilder 202
Sponsored by
Physics & Astronomy Department
Audience
Public
More information
Tressena Manning
603-646-2854

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 Bravyi-Kitaev Superfast (BKSF) encoding, here on referred to as Superfast encoding. 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(md) qubits. We propose Generalized Superfast Encodings (GSE) which require the same number of qubits as the original one but have more favorable properties. 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. Although, superfast encoding can correct single qubit errors with the introduction of Auxiliary modes. Further, 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.

Location
Wilder 202
Sponsored by
Physics & Astronomy Department
Audience
Public
More information
Tressena Manning
603-646-2854