Method and system for decomposing single-qubit quantum circuits into a discrete basis

A quantum circuit comprising:

• a sequence of quantum gates of a universal basis set that correspond to a target quantum gate, wherein the sequence of quantum gates is made by a process comprising:
• mapping a unitary corresponding to the target quantum gate to a quaternion having a specific structure;
• factoring the quaternion into a sequence of irreducible quaternion factors;
• and
• mapping the sequence of irreducible quaternion factors into the sequence of quantum gates of the universal basis set.

A system for quantum-circuit design comprising:

• a processor;
• a computer readable storage device storing instructions, wherein the instructions, when executed by the processor, cause the processor to perform acts comprising,
• mapping a unitary corresponding to a target quantum gate to a quaternion having a specific structure;
• factoring the quaternion into a sequence of irreducible quaternion factors;
• mapping the sequence of quaternion factors into a sequence of quantum gates of a universal basis set;
• and
• storing the sequence of quantum gates into the computer-readable storage device.