Parameter-Shift Rule | Exact Quantum Analytical Gradients
Quick Technical Answer:
The Parameter-Shift Rule is a technique for computing the exact analytical gradient of a parameterized quantum expectation value ⟨H⟩(θ) by evaluating the quantum circuit at two shifted parameter points (θ + π/2 and θ - π/2).
Formula / Unitary:
\frac{\partial \langle H \rangle}{\partial \theta} = \frac{\langle H \rangle\left(\theta + \frac{\pi}{2}\right) - \langle H \rangle\left(\theta - \frac{\pi}{2}\right)}{2}
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Frequently Asked Questions
Why does the parameter-shift rule outperform finite difference on quantum hardware?
Finite differences require tiny shifts Δθ that are drowned out by hardware shot noise. The parameter-shift rule uses macroscopic shifts of π/2 that are resilient to statistical measurement noise.