Equation 8 · Variational Evolution: How Quantum Computers Learn Their Answers
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The result, now known throughout the field as the barren-plateau problem, is precise and unwelcome. For a parametrized circuit that forms an approximate unitary 2-design — informally, a circuit random enough, or deep enough, that its output statistics resemble those of a genuinely random unitary — the variance of the gradient of the cost function with respect to almost any parameter shrinks exponentially as the number of qubits n grows:
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