Demonstrating experimentally the encoding and dynamics of a fault-tolerant logical qubit on a hyperfine-coupled nuclear spin qudit

The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Employing high-dimensional quantum systems (qudits) can offer more hardware-efficient protocols than qubit-based approaches [1-5]. Using electron-nuclear double resonance, we implement a logical qubit encoded on the four states of a I = 3/2 nuclear spin hyperfine-coupled to a S = 1/2 electron spin qubit; the encoding protects against the dominant decoherence mechanism in such systems, fluctuations of the quantizing magnetic field. We explore the dynamics of the encoded state both under a controlled application of the fluctuation and under natural decoherence processes. Our results confirm the potential of these proposals for practical, implementable, fault tolerant quantum memories [6].

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[2] Gross, Phys. Rev. Lett. 127, 010504 (2021)

[3] Chiesa et al., AIP Advances 11, 025134 (2021)

[4] Lim et al., Phys. Rev. A 108, 062403 (2023)

[5] Gross et al., Phys. Rev. Appl. 22, 014006 (2024)

[6] Lim et al., arXiv:2405.20827