Hidden Variable Model for Quantum Computation with Magic States on Any Number of Qudits of Any Dimension

It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum computation with magic states on any number of qudits with any local Hilbert space dimension. This model leads to a classical simulation algorithm for universal quantum computation.Comment: 26 page