Method and system that produces non-stabilizer quantum states that are used in various quantum circuits and systems

A method that prepares a subject qubit in a non-stabilizer state represented by a state vector lying in the same plane as the state vector representing an initial input state of the subject qubit, the method comprising:

• initially determining a number of stages j to apply to the subject qubit in order to rotate the state vector of the subject qubit to a specified rotation angle, each stage i including a stagei control-qubit input, a stagei subject-qubit input, a stagei measurement output that outputs a measurement of an input control qubit following at least one internal two-qubit controlled-gate operation, and a stagei subject-qubit output that outputs the subject qubit following the at least one internal two-qubit controlled-gate operation;
• and
• while j is greater than 0,
• applying a next stage to the subject qubit and a control qubit,
• when a measurement value m output by the next stage is 0, indicating that the control qubit is measured by the stage to be in state |0, decrementing j, and
• when the measurement value in output by the next stage is 1, indicating that the control qubit is measured by the stage to be in state |1, incrementing j.

A single-qubit quantum circuit that carries out a unitary rotation operator U on a subject qubit input to the single-qubit quantum gate, the single-qubit quantum gate comprising:

• a source of standard-state and magic-state qubits;
• one or more quantum-circuit-subsystem resource-state factories that each produces, from two or more qubits selected from among standard-state and magic-state qubits, a control qubit;
• and
• two or more rotation quantum circuits that each applies a rotation, specified by an input control qubit, to the subject qubit;
• and
• a controller that controls the one or more quantum-circuit-subsystem resource-state factories to prepare control qubits input to the two or more rotation quantum circuits in order to apply three major rotations with respect to two non-parallel rotation axes to the subject qubit which together carry out the rotation corresponding to the unitary rotation operator U.