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This is a common assumption in the study of quantum computation to assume that the quantum systems involved are finite-dimensional, since qubits lives in the two-dimensional Hilbert space.

According to Roman Gielerak and Marek Sawerwain, the quantum registers corresponding to a quantum computing machine with coherent pulses of light must have an infinite-dimensional character.

I am looking for arguments for and against the hypothesis that finite-dimensional structures are sufficient to study quantum computation.

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