Magic state factory constructions for producing CCZ and T states

A quantum computing device comprising:

• a register of qubits comprising multiple target qubits, multiple ancilla qubits, and multiple stabilizer qubits each prepared in a respective initial state;
• a plurality of control lines coupled to the register of qubits;
• a plurality of control devices coupled to the plurality of control lines;
• and
• one or more classical processors;
• wherein the quantum computing device is configured to:
• prepare a register of qubits in a zero state, the register comprising a plurality of target qubits, a plurality of ancilla qubits and a plurality of stabilizer qubits;
• perform, for each stabilizer qubit, an X gate on i) multiple ancilla qubits, or ii) multiple ancilla qubits and one of the target qubits using the stabilizer qubit as a control;
• measure the stabilizer qubits to determine respective stabilizer qubit states;
• performing, on each of the ancilla qubits, a Z1/4 quantum gate and a Hadamard quantum gate;
• measure each of the ancilla qubits to determine respective ancilla qubit states;
• perform, conditioned on each determined ancilla qubit state, i) a NOT operation on a selected stabilizer qubit, or ii) a NOT operation on the selected stabilizer qubit and a Z gate on one or more respective target qubits;
• perform, on each target qubit and conditioned on a determined state of a respective stabilizer qubit, a Z gate on the target qubit;
• and
• perform an X gate on each of the target qubits to obtain the CCZ state.

A method for transforming a CCZ state into three output T states, the method comprising:

• obtaining i) three target qubits prepared in a CCZ state, ii) a first ancilla qubit in a T state, iii) a multiple additional ancilla qubits prepared in a zero state, and iv) multiple stabilizer qubits prepared in a zero state;
• performing an X gate on a target qubit and an additional ancilla qubit using a first stabilizer qubit as a control and measuring the first stabilizer qubit to determine a state of the first stabilizer qubit;
• performing an X gate on multiple target qubits and an additional ancilla qubit using a second stabilizer qubit as a control and measuring the second stabilizer qubit to determine a state of the second stabilizer qubit;
• performing a X1/2 gate on an additional ancilla qubit;
• performing a Z gate on multiple target qubits and the first ancilla qubit using a third stabilizer qubit as a control;
• performing a Hadamard gate on the first ancilla qubit and measuring the first ancilla qubit, an additional ancilla qubit and a third stabilizer qubit to determine respective qubit states;
• performing a X1/2 gate on an additional ancilla qubit;
• performing a Z gate on a target qubit and an additional ancilla qubit using a fourth stabilizer qubit as a control;
• performing a Hadamard gate on an additional ancilla qubit and measuring the additional ancilla qubit and the fourth stabilizer qubit to determine respective qubit states;
• performing a NOT operation on a stabilizer qubit using an additional ancilla qubit as a control, and two NOT operations on the additional ancilla qubit and the stabilizer qubit using a different stabilizer qubit as a control;
• performing a Z gate on multiple target qubits and an additional ancilla qubit using two stabilizer qubits as a control;
• performing a Hadamard gate on an additional ancilla qubit and measuring the additional ancilla qubit and a stabilizer qubit to determine respective qubit states;
• and
• performing multiple classically controlled Pauli operators on the three target qubits conditioned on the determined states of the ancilla qubits.