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Fault-Tolerant Quantum Computation with Higher-Dimensional Systems

Daniel Gottesman
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Abstract

Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to d-dimensional systems, and I will discuss the theory of fault-tolerant computation using such codes. I prove that universal fault-tolerant computation is possible with any higher-dimensional stabilizer code for prime d.

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Daniel Gottesman. 1998-02-02. Fault-Tolerant Quantum Computation with Higher-Dimensional Systems. https://doi.org/10.1016/s0960-0779(98)00218-5

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