Encoding quantum information in
d-dimensional systems (qudits) with
d>2 offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension
d. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model
d=8 qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor
5 to
10. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition
∣+⟩L to
225~ms, compared to
19~ms under free evolution and
85~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or the motional modes of trapped ions. For example, high-dimensional systems can be used to realise `Schrödinger cat' states, superpositions of widely displaced coherent states that can also be used to illustrate quantum effects at large scales. Recent proposals have suggested encoding qubits in high-spin atomic nuclei, finite-dimensional systems that can host hardware-efficient versions of continuous-variable codes. Here we demonstrate the creation and manipulation of Schrodinger cat states using the spin-7/2 nucleus of an antimony atom embedded in a silicon nanoelectronic device. We use a multi-frequency control scheme to produce spin rotations that preserve the symmetry of the qudit, and constitute logical Pauli operations for qubits encoded in the Schrodinger cat states. Our work demonstrates the ability to prepare and control nonclassical resource states, a prerequisite for applications in quantum information processing and quantum error correction using our scalable, manufacturable semiconductor platform.
Spin precession is a textbook example of the dynamics of a quantum system that exactly mimics its classical counterpart. Here, we challenge this view by certifying the quantumness of exotic states of a nuclear spin through its uniform precession. The key to this result is measuring the positivity, instead of the expectation value, of the x -projection of the precessing spin, and using a spin >1/2 qudit that is not restricted to semi-classical spin coherent states. The experiment is performed on a single spin-7/2 123 Sb nucleus, implanted in a silicon nanoelectronic device, amenable to high-fidelity preparation, control, and projective single-shot readout. Using Schrödinger cat states and other bespoke states of the nucleus, we violate the classical bound by 18 standard deviations, proving that no classical probability distribution can explain the statistic of this spin precession and highlighting our ability to prepare quantum resource states with high fidelity in a single-atomic-scale qudit.