From the course: Quantum Computing Fundamentals

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Represent qubits on the Bloch sphere

Represent qubits on the Bloch sphere

From the course: Quantum Computing Fundamentals

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Represent qubits on the Bloch sphere

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- In the previous video, we visualized a quantum state vector on a two-dimensional graph that simplified things to explain the concepts, but it overlooked the fact that we're actually working with complex numbers. Our probability amplitudes, alpha and beta, are both complex numbers, which means they each have real and imaginary components indicated here with the Re and Im notation. That means to fully represent this quantum state, consisting of two complex numbers, we'll actually need four real-valued coefficients. Trying to visualize something in four dimensions is kind of hard. - Fortunately, we don't need to. We can use a representation called the Bloch sphere, which lets us visualize a pure quantum state in three-dimensional space as a point on the surface of a sphere. - Hold up. How do we just go from needing four dimensions to only three? - We'll get to that soon in another video. For now, just know there…

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