Abstract: This application concerns methods, apparatus, and systems for performing quantum circuit synthesis and/or for implementing the synthesis results in a quantum computer system. In certain example embodiments: a universal gate set, a target unitary described by a target angle, and target precision is received (input); a corresponding quaternion approximation of the target unitary is determined; and a quantum circuit corresponding to the quaternion approximation is synthesized, the quantum circuit being over a single qubit gate set, the single qubit gate set being realizable by the given universal gate set for the target quantum computer architecture.

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.

Abstract: This application concerns methods, apparatus, and systems for performing quantum circuit synthesis and/or for implementing the synthesis results in a quantum computer system. In certain example embodiments: a universal gate set, a target unitary described by a target angle, and target precision is received (input); a corresponding quaternion approximation of the target unitary is determined; and a quantum circuit corresponding to the quaternion approximation is synthesized, the quantum circuit being over a single qubit gate set, the single qubit gate set being realizable by the given universal gate set for the target quantum computer architecture.

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.