Four electron spin qubits with exchange interaction

TL;DR

This paper analytically solves the exchange interaction Hamiltonian for four electron spin qubits in quantum dots, demonstrating their potential use in error correction and surface codes through a verifiable two-qubit phase gate.

Contribution

It provides an exact analytical solution for symmetric four-qubit systems and explores their application in quantum error correction circuits.

Findings

Exact solution for symmetric four-qubit exchange Hamiltonian

Implementation of a verifiable two-qubit phase gate

Analysis of error syndromes and fidelities

Abstract

Four electron spin qubits in quantum dots are studied by means of an exchange interaction Hamiltonian. The time-independent Schr\"odinger equation is exactly analytically solved for the symmetric case, that is equal qubit frequencies and equal couplings. The spin system can be used as two data-qubits and two ancillas, thereby realizing a $X$ and $Z$ stabilizing circuit exploited in error correction and surface codes. The unitary evolution of corresponding stable states is calculated and consequences for error syndromes and fidelities are assessed. It is also shown that applying the evolution operator for a prescribed duration and subsequent measurement of the ancillas lead to a `verifiable' two-qubit phase gate.