Fault-tolerant qubit encoding using a spin-7/2 qudit

Abstract

The implementation of error correction protocols is a central challenge in the development of practical quantum information technologies. Recently, multi-level quantum resources such as harmonic oscillators and qudits have attracted interest in this context because they offer the possibility of additional Hilbert space dimensions in a spatially compact way. Here we propose a quantum memory, implemented on a spin-7/2 nucleus hyperfine-coupled to an electron spin-1/2 qubit, which provides first order $X$, $Y$ and $Z$ error correction using significantly fewer quantum resources than the equivalently effective qubit-based protocols. Our encoding may be efficiently implemented in existing experimentally realised molecular electron-nuclear quantum spin systems. The strategy can be extended to higher-order error protection on higher-spin nuclei.

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Cited by in corpus (9)

• Schrödinger cat states of a nuclear spin qudit in silicon
• Fault-Tolerant Computing with Single Qudit Encoding
• Qutrit and Qubit Circuits for Three-Flavor Collective Neutrino Oscillations
• Demonstrating experimentally the encoding and dynamics of an error-correctable logical qubit on a hyperfine-coupled nuclear spin qudit
• Designing quantum error correction codes for practical spin qudit
• Dissipative phase transition: from qubits to qudits
• Dynamical decoupling of interacting spins through group factorization
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• Fault-Tolerant Encoding of Logical Qudits in Spin Systems