Universal nuclear two-qubit logic operations in an exchange-coupled donor system

Scalable quantum processors require high-fidelity universal quantum logic operations, in a manufacturable physical platform, along with the capacity to couple multiple qubits together over a variable range of length scales. Nuclear spins of ion-implanted donors in silicon have demonstrated record-breaking coherence times [1], along with high fidelity (> 99%), universal 1 and 2-qubit operations [2][3], approaching the fidelity required to perform fault-tolerant quantum computation. Geometric nuclear 2-qubit controlled-Z (CZ) gates have been performed by using a single electron whose resonance frequency is conditional on the state of both nuclei [3]. This, however, requires very close spacing between the nuclei. Here we demonstrate a CZ gate between the nuclei of two widely-separate atoms, each possessing their own bound electron. The two electrons, in turn, are coupled by a weak exchange interaction J = 12 MHz, corresponding to an estimated inter-donor distance of 24 nm. Through this two-electron interaction, we are able to couple and entangle nuclei over a much larger distance than previously demonstrated. We benchmark the fidelity of these 1 and 2-qubit nuclear operations using gate set tomography (GST). Combined with the ability to perform electron 2-qubit gates between two exchange-coupled electrons [4], this work completes the toolbox for constructing a scalable spin-based quantum processor in silicon.



[1] Muhonen, J. T. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nature nanotechnology 9, 986 (2014).

[2] Pla, J.J. et al. High fidelity readout and control of a nuclear spin qubit in silicon. Nature 496, 334-338 (2013).

[3] Madzik, M. T. et al. Precision tomography of a three-qubit electron-nuclear quantum processor in silicon. Nature, 601, 348-353 (2022)

[4] Madzik, M. T. et al. Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device. Nature Communications 12, 181 (2021).