Phase flip code with semiconductor spin qubits

TL;DR

This paper demonstrates the implementation of quantum error correction codes using a four-qubit germanium spin qubit array, showcasing key gates and protocols essential for scalable, fault-tolerant quantum computing.

Contribution

It introduces a practical implementation of quantum error correction with semiconductor spin qubits, including the realization of a Toffoli-like gate and phase flip codes.

Findings

Successful execution of a two-qubit phase flip code.

Implementation of a three-qubit phase flip code with a Toffoli-like gate.

Potential for co-design of hardware and software for scalable quantum computing.

Abstract

The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with standard semiconductor manufacturing. Here, we show that a quantum error correction code can be implemented using a four-qubit array in germanium. We demonstrate a resonant SWAP gate and by combining controlled-Z and controlled-$\text{S}^{-1}$ gates we construct a Toffoli-like three-qubit gate. We execute a two-qubit phase flip code and find that we can preserve the state of the data qubit by applying a refocusing pulse to the ancilla qubit. In addition, we implement a phase flip code on three qubits, making use of a Toffoli-like gate for the final correction step. Both the quality and quantity of the qubits will require significant improvement to achieve fault-tolerance. However, the capability to implement quantum error correction codes enables co-design development of quantum hardware and software, where codes tailored to the properties of spin qubits and advances in fabrication and operation can now come together to scale semiconductor quantum technology toward universal quantum computers.