Quantum logic with spin qubits crossing the surface code threshold

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 [1, 2]. Reaching two-qubit gate fidelities above 99% has therefore been a long-standing major goal for semiconductor spin qubits. In this talk, I will discuss experimental benchmarks of spin qubits, with a particular focus on the performance of two-qubit logic. We develop a new class of randomized benchmarking protocols, namely character randomized benchmarking, to efficiently estimate the two-qubit gate fidelity and the crosstalk error between single-qubit gates [3, 4]. Then we characterize the detailed performance of a universal two-qubit gate set using self-consistent gate set tomography, and demonstrate a spin-based quantum processor in silicon with single- and two-qubit gate fidelities all above 99.5%. 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 [5]. Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault-tolerance and to possible applications in the era of noisy intermediate-scale quantum (NISQ) devices.

[1] R. Raussendorf and J. Harrington, PRL 98, 190504 (2007).

[2]  A. G. Fowler, et al., PRA 86, 032324 (2012).

[3] X. Xue, et al., PRX 9, 021011 (2019).

[4] J. Helsen, et al., npj QInfo 5, 71 (2019).

[5] X. Xue, et al., arXiv:2107.00628 (2021).