# Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit

## TL;DR

This paper demonstrates a silicon-based encoded three-spin qubit with low error rates, using a novel benchmarking protocol to quantify both computational and leakage errors, advancing scalable quantum computing.

## Contribution

It introduces a silicon triple-dot qubit encoded in a subsystem, employing a modified benchmarking protocol to measure errors, including leakage, with only voltage-controlled exchange interactions.

## Key findings

- Total error rate of 0.35% for unitary operations
- Leakage driven by substrate nuclear spins at 0.17%
- Operational benefits of encoded subsystems demonstrated

## Abstract

Quantum computation requires qubits that satisfy often-conflicting criteria, including scalable control and long-lasting coherence. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Though such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes and can also allow logical control with a single type of entangling interaction while maintaining favorable features of the underlying physical system. Here we demonstrate a qubit encoded in a subsystem of three coupled electron spins confined in gated, isotopically enhanced silicon quantum dots. Using a modified "blind" randomized benchmarking protocol that determines both computational and leakage errors, we show that unitary operations have an average total error of 0.35%, with 0.17% of that coming from leakage driven by interactions with substrate nuclear spins. This demonstration utilizes only the voltage-controlled exchange interaction for qubit manipulation and highlights the operational benefits of encoded subsystems, heralding the realization of high-quality encoded multi-qubit operations.