Non-traditional Approach to Quantum Computing
Ion I. Geru · Applied Magnetic Resonance · 2014
The N-qubit system characterized by an effective spin $$S = 2^{N - 1} - {1/2}$$ is carried out in the representation of two coupled harmonic oscillators. It is shown that quantum computing results obtained with spinor algebra can be obtained also using the algebra of two coupled harmonic oscillators which is a convenient formalism, especially in the case of large number of qubits. In this formalism the non-abelian and abelian groups of the order of 16 related to one- and two-qubit systems were found. The structure of Cayley tables of those groups is different due to different commutation (anticommutation) relations for operators forming each group.