measure(q,c) job = execute(circuit, backend, shots = 1000 ) job_monitor(job) counts = job. lish testable conditions for correctability in OAQEC.
The first step is to initialise a 3 qubit register. z(q) #Add this to simulate a phase flip error circuit. Thus, for a non-degenerate quantum stabilizer code, linearly independent correctable errors will have unequal error syndromes. We show that the theory of operator quantum error correction can be naturally generalized by. Step 1: Initialise the quantum and classical registers. get_backend( 'ibmq_qasm_simulator' ) q = QuantumRegister( 3, 'q' ) c = ClassicalRegister( 1, 'c' ) circuit = QuantumCircuit(q,c) circuit. get_provider(hub = 'ibm-q' ) backend = provider. enable_account( 'ENTER API KEY HERE' ) provider = IBMQ. See our previous tutorial on correcting bit flip errors: Implementationįrom qiskit import QuantumRegister from qiskit import QuantumRegister, ClassicalRegister from qiskit import QuantumCircuit, execute,IBMQ from import job_monitor print ( ' \n Phase Flip Code' ) print ( '-' ) IBMQ. Because this has altered the computational state of the qubit we can correct this using CNOT gates and a Toffoli gate where the main qubit is the target and the control qubits are the ancillary qubits.Ĭheck out our tutorial on the Z-gate to learn more about phase flips: However because the main qubits phase was changed it will not be in its previous state but flipped from 1 to 0 or vice versa. After this a Hadamard gate is applied to all qubits again which will take them out of superposition since two Hadamard gates applied leave the state of the qubits unchanged. Next all qubits are put in to superposition using a Hadamard gate.Īfter this a phase flip error will occur on the main qubit which will effect its phase.
#Correctable error quantum error correction code
The phase flip code works identically to the bit flip code in that it first transfers the state of the main qubit to the ancillary qubits using CNOT gates. However as said before it can be corrected using the phase flip code. 14.2 Quantum Error Reduction by Symmetrization Classical computers can be made more reliable through the use of redundancy. This exact criterion for whether error sets are correctable provides a rigorous. In essence this error is equivalent to a Z-gate. In this chapter we will review some approaches to quantum error correction and explain how entanglement is both the problem, and solution. 3 Quantum Error Correction, the Stabilizer Formalism, and Fault Toler. A phase flip error is a type of error that effects the phase of the qubit. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code.