Two-qubit Amplification

Learn about two-qubit amplification.

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Let’s continue with the circuit with two qubits and four possible states.

Again, we start with an equal superposition of all states. With four states, each state has an amplitude of 0.50.5 and a resulting measurement probability of 0.250.25.

Equal superposition of four states

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from qiskit import QuantumCircuit, Aer, execute
from qiskit.visualization import plot_histogram, plot_bloch_multivector, plot_state_qsphere
qc = QuantumCircuit(2)
qc.h(0)
qc.h(1)
# execute the qc
results = execute(qc,Aer.get_backend('statevector_simulator')).result()
plot_histogram(results.get_counts())

In the next step, we need to implement the oracle. Its purpose is to flip the amplitude of the favorable state. For example, let’s say it is in state 10|10\rangle. Remember thatwe read the qubits from the right (qubit at position 0) to the left (qubit at position 1).

The controlled ZZ-gate (CZCZ ...