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Please predict whether this patent is acceptable.PATENT ABSTRACT: Quantum circuits are synthesized based on a projective gate set derived from a set of single-qubit gates, typically a basis set such as the Clifford+T gates or the V-gates. An initial projective gate set is used to determine at least one characteristic of a quaternion algebra, and the quaternion algebra is used to define a new projective gate set. Exactly synthesizable unitaries are identified, and a circuit approximating a target unitary is defined in the single-qubit gate set by mapping from the new projective gate set.