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Control and Representation of n-qubit Quantum Systems

W. E. Baylis·R. Cabrera·C. Rangan
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Abstract

Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any other by a compact unitary transformation with 2^(n+1)-1 real angles, 2^n of which are azimuthal-like and the rest polar-like. The results follow from a modeling of the Hilbert space of n-qubits by a minimal left ideal of an associative algebra. This representation is expected to be useful in the design of new compact control techniques or more efficient algorithms in quantum computing.

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W. E. Baylis, R. Cabrera, C. Rangan. 2006-07-06. Control and Representation of n-qubit Quantum Systems. https://arxiv.org/abs/quant-ph/0606019

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