Surface code computations using Auto-CCZ quantum states

A quantum computation system comprising:

• a plurality of data qubits;
• a plurality of routing qubits;
• and
• a plurality of control devices configured to operate the plurality of data qubits and the plurality of routing qubits;
• wherein the quantum computation system is configured to perform operations comprising:
• applying a first Hadamard gate to a first routing qubit and applying a second Hadamard gate to a second routing qubit, wherein the first routing qubit is prepared in a magic state and interacts with a first data qubit and the second routing qubit is prepared in a magic state and interacts with a second data qubit;
• measuring the first routing qubit using a Z basis measurement to obtain a second classical bit
• measuring the second routing qubit using a Z basis measurement to obtain a third classical bit;
• and
• performing classically controlled fix up operations on the first data qubit and second data qubit using the second classical bit and the third classical bit.

A method for implementing an auto corrected CCZ operation on a first, second and third data qubit using a quantum computer, the method comprising:

• measuring a fourth routing qubit to obtain a fourth classical bit that represents an on state, wherein the fourth routing qubit is prepared in a magic state and interacts with the second data qubit;
• measuring a seventh routing qubit to obtain a seventh classical bit that represents an on state, wherein the seventh routing qubit is prepared in a magic state and interacts with the third data qubit;
• applying a first Hadamard gate to a fifth routing qubit prepared in a magic state and applying a second Hadamard gate to a sixth routing qubit prepared in a magic state;
• measuring the fifth routing qubit using a Z basis measurement to obtain a fifth classical bit and measuring the sixth routing qubit using a Z basis measurement to obtain a sixth classical bit;
• applying a third Hadamard gate to an eighth routing qubit prepared in a magic state and applying a fourth Hadamard gate to a ninth routing qubit prepared in a magic state;
• measuring the eighth routing qubit using a Z basis measurement to obtain an eighth classical bit and measuring the ninth routing qubit using a Z basis measurement to obtain a ninth classical bit;
• applying a fifth Hadamard gate to a second routing qubit prepared in a magic state and applying a sixth Hadamard gate to a third routing qubit prepared in a magic state;
• measuring the second routing qubit using a Z basis measurement to obtain a second classical bit and measuring the third routing qubit using a Z basis measurement to obtain a third classical bit;
• and
• performing classically controlled fix up operations on the first, second and third data qubits using each of the classical bits.

A quantum computation system comprising:

• a plurality of data qubits;
• a plurality of routing qubits;
• and
• a plurality of control devices configured to operate the plurality of data qubits and the plurality of routing qubits;
• wherein the quantum computation system is configured to perform operations comprising:
• measuring a fourth routing qubit to obtain a fourth classical bit that represents an on state, wherein the fourth routing qubit is prepared in a magic state and interacts with a second data qubit;
• measuring a seventh routing qubit to obtain a seventh classical bit that represents an on state, wherein the seventh routing qubit is prepared in a magic state and interacts with a third data qubit;
• applying a first Hadamard gate to a fifth routing qubit prepared in a magic state and applying a second Hadamard gate to a sixth routing qubit prepared in a magic state;
• measuring the fifth routing qubit using a Z basis measurement to obtain a fifth classical bit and measuring the sixth routing qubit using a Z basis measurement to obtain a sixth classical bit;
• applying a third Hadamard gate to an eighth routing qubit prepared in a magic state and applying a fourth Hadamard gate to a ninth routing qubit prepared in a magic state;
• measuring the eighth routing qubit using a Z basis measurement to obtain an eighth classical bit and measuring the ninth routing qubit using a Z basis measurement to obtain a ninth classical bit;
• applying a fifth Hadamard gate to a second routing qubit prepared in a magic state and applying a sixth Hadamard gate to a third routing qubit prepared in a magic state;
• measuring the second routing qubit using a Z basis measurement to obtain a second classical bit and measuring the third routing qubit using a Z basis measurement to obtain a third classical bit;
• and
• performing classically controlled fix up operations on the second and third data qubits using each of the classical bits.