Simple Circuits for Exact Elimination of Leakage in a Qubit Embedded in a Three-level System

TL;DR

This paper introduces a novel method using finite rotation gates to exactly eliminate leakage errors in a three-level quantum system, exemplified by a charge quadrupole qubit, improving qubit fidelity without extra pulses.

Contribution

It presents a new exact leakage elimination strategy based on su(2) subalgebra, applicable to three-level systems, reducing experimental complexity and error sensitivity.

Findings

Exact leakage elimination achieved without additional pulses

Universal single-qubit gates generated by two or three Hamiltonian propagators

Method applicable to charge quadrupole qubits in triple quantum dots

Abstract

Leakage errors damage a qubit by coupling it to other levels. Over the years, several theoretical approaches to dealing with such errors have been developed based on perturbation arguments. Here we propose a different strategy: we use a sequence of finite rotation gates to exactly eliminate leakage errors. The strategy is illustrated by the recently proposed charge quadrupole qubit in a triple quantum dot, where there are two logical states to support the qubit and one leakage state. We have found an su(2) subalgebra in the three-level system, and by using the subalgebra we show that ideal Pauli x and z rotations, which are universal for single-qubit gates, can be generated by two or three propagators of experimentally-available Hamiltonians. The proposed strategy does not require additional pulses, is independent of error magnitude, and potentially reduces experimental overheads. In addition, the magnitude of detuning fluctuation can be estimated based on the exact solution.