Physics & Astronomy - Virtual PhD Thesis Defense - Kanav Setia, Dartmouth

Title: "Fermionic Quantum Simulation"

July 24, 2020
2 pm - 5 pm
Location
Zoom: https://dartmouth.zoom.us/j/92691743413?pwd=VzVOeWErQ0lONnJZQXpkYmdFTXNkUT09
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. In this thesis, we explore number of topics aimed at making quantum simulation close to realization. We present two encodings, Bravyi-Kitaev superfast encoding (BKSF) and the generalized superfast encoding (GSE). These encoding map 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 $M$ Fermionic modes gets mapped to $n=O(Md)$ qubits. We show that both these encodings have inherent quantum error correction properties. We prove that the BKSF encoding in general, cannot correct all the single qubit errors. In certain systems, auxiliary Fermionic modes could introduced to guarantee single qubit error correction. In contrast, if the degree of the interaction graph is greater than equal to six, the GSE guarantees single qubit error correction without any auxiliary Fermionic modes. Further, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O(d)$ to $O(\log d)$. In the last chapter of this thesis, we present different techniques to use the point group symmetries in the molecules to reduce the number of qubits required for quantum simulation.  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.

Location
Zoom: https://dartmouth.zoom.us/j/92691743413?pwd=VzVOeWErQ0lONnJZQXpkYmdFTXNkUT09
Sponsored by
Physics & Astronomy Department
Audience
Public
More information
Tressena Manning
603-646-2854