Deutsch's Algorithm

Deutsch’s algorithm implementation

In our last example, we asked the oracle whether the function is constant or balanced. And this is what we get as an answer. Not more, not less.

The following code shows a function that embeds a discrete oracle in a quantum circuit.

This circuit includes a measurement of the first qubit. Therefore, our QuantumCircuit contains a QuantumRegister with two qubits (line 11) and a ClassicalRegister with one bit (line 12) to hold the measurement.

By default, both qubits are initialized in the state $|0\rangle$. We put the second qubit into the state $|1\rangle$ by applying the X-gate in line 18. Then, we apply the Hadamard gate to both qubits in lines 20-21. We send the two qubits through the oracle in line 24 that we take as a parameter of this function in line 5.

We apply another Hadamard gate on the first qubit we received as an output of the oracle in line 27. We measure it and store it in the ClassicalRegister in line 30. We use the qasm_simulator in line 33 because it supports multiple executions (in this case, it supports up to 1,000 executions in line 36) of a quantum circuit that includes a measurement (see the lesson Hands-on introduction to quantum entanglement).

Even though our algorithm around the oracle treats it as a black box, we need a corresponding implementation when we want to run the oracle for a specific function.