Hamiltonian Model for Fault Tolerant Singlet-Like Excitation: First Principles Approach

Abstract

Deriving quantum error correction and quantum control from the Schrödinger equation for a unified qubit-environment Hamiltonian will give insights into how microscopic degrees of freedom affect the capability to control and correct quantum information beyond that of phenomenological theory. Here, we investigate the asymptotic reduced state of two qubits coupled to each other solely via a common heat bath of linear harmonic oscillators and search for evidence of fault-tolerant excited qubit states. We vary the Hamiltonian parameters, including the qubit-qubit and qubit-bath detuning, the bath spectral density, and whether or not we use the Markov approximation in the calculation of our dynamics. In proximity to special values of these parameters, we identify these states as asymptotic reduced states that are arbitrarily pure, excited, unique, and have high singlet fidelity. We emphasize the central role of the Lamb-shift as an agent responsible for fault tolerant excitations. To learn how these parameters relate to performance, we discuss numerical studies on fidelity and error recovery time.