From the course: Quantum Computing Fundamentals

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Global and relative phase

Global and relative phase

From the course: Quantum Computing Fundamentals

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Global and relative phase

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- In the previous videos we saw how to visualize quantum states on the Bloch sphere. But a pure quantum state is represented by two complex values, alpha and beta, which each have real and imaginary components. That means four real numbers in total. So how do we go from something that should take four dimensions to represent to only three dimensions on the Bloch sphere? Short answer, some of those quantum states look the same. We've already seen the standard zero basis state shown here, represented as the vector one zero. If we measure a qubit in that state the probability of getting an outcome of zero is the absolute value of one squared, which is one. We will always measure this state as zero and we will never get an outcome of one. Now, consider what happens if we negate that state or multiply it by negative one. Now it's vector representation has a negative one in the first position and zero in the second. But if we…

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