Linear Algebra for Quantum: Why Hilbert Spaces matter
Beginners often ask why we need complex numbers and Hilbert spaces. In quantum mechanics, a state is a unit vector in a complex Hilbert space H.
The transition probability between states $|psi
angleand|phi
angle$ is given by:
P=∣langlephi∣psiangle∣2
Without the inner product structure of Hilbert spaces, we wouldn't have a consistent way to define measurement probabilities.
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I've been trying to replicate the numerical results in a similar setup. My error bars are much larger—is there a specific gate decomposition you'd recommend for this?