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Quantum computation is a continuously growing research area which is based onnature and resources of quantum mechanics, as superposition and entanglement.In its quantum circuits version, the use of convenient and appropriate gates isessential. But while those gates adopt convenient forms for computationalalgorithms, their design depends on specific quantum systems and stu? beingused. These gates need manage quantum systems based on physical interactionsruled by quantum Hamiltonians. With this, gates design is restricted toproperties and limitations of interactions and physical elements beinginvolved. This work shows how anisotropic Ising interactions, written in a nonlocal basis, lets reproduce elementary operations in terms of which unitaryprocesses can be factorized. In this sense, gates could be written as asequence of pulses ruled by that interaction driven by magnetic fields, statingalternative results in quantum gates design for magnetic systems.

Factorization of unitary matrices induced by 3D anisotropic Ising interaction