Computing with spin qubits at the surface code error threshold

Abstract

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault-tolerance, the ability to correct errors faster than they occur. The central requirement for fault-tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the ~1% error threshold of the well-known surface code. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are well positioned for scaling as they can leverage advanced semiconductor technology. Here we report a spin-based quantum processor in silicon with single- and two-qubit gate fidelities all above 99.5%, extracted from gate set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighboring qubit. Utilizing this high-fidelity gate set, we execute the demanding task of calculating molecular ground state energies using a variational quantum eigensolver algorithm. Now that the 99% barrier for the two-qubit gate fidelity has been surpassed, semiconductor qubits have gained credibility as a leading platform, not only for scaling but also for high-fidelity control.

19 pages, 11 figures

References in corpus (7)

• Surface codes: Towards practical large-scale quantum computation
• Single-shot read-out of an individual electron spin in a quantum dot
• Fault-tolerant quantum computation with high threshold in two dimensions
• Electrically driven single electron spin resonance in a slanting Zeeman field
• Scalable gate architecture for densely packed semiconductor spin qubits
• Precision tomography of a three-qubit donor quantum processor in silicon
• Rapid high-fidelity gate-based spin read-out in silicon

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