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Hands-On Quantum Machine Learning with Python

Multi-qubit Phase

Explore the concept of multi-qubit phases, including how phases shift in two-qubit systems and their representation using Bloch spheres and quantum gates. Understand the difference between global and relative phases and their impact on quantum system behavior and interference in quantum computing.

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What if we have multiple qubits? The following equation denotes the state of a two-qubit system.

∣ψ⟩=α∣00⟩+β∣01⟩+γ∣10⟩+δ∣11⟩=[αβγδ]|\psi\rangle=\alpha|00\rangle+\beta|01\rangle+\gamma|10\rangle+\delta|11\rangle=\begin{bmatrix}\alpha \\ \beta \\ \gamma \\ \delta \end{bmatrix}

The two-qubit system can be in four different states. Each state has an amplitude, too.

We’ve already specified a two-qubit system two and the Bloch spheres side by side in the lesson Two Different Qubit States. Qubit 0 is in state ∣0⟩−∣1⟩2\frac{|0\rangle-|1\rangle}{\sqrt{2}} and qubit 1 is in state −∣0⟩+∣1⟩2\frac{-|0\rangle+|1\rangle}{\sqrt{2}} ...