For Clifford angle assignments in single-layer variational circuits, the probability of a nonzero Pauli expectation value is exactly 1/4 in some observable/wiring combinations and decays like 1/2^{n/2} in others, with intermediate mixtures fitted by an empirical exponent.
Understanding the difficulty of training deep feedforward neural networks
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The Stabilizer Bootstrap of Quantum Machine Learning with up to 10000 qubits
For Clifford angle assignments in single-layer variational circuits, the probability of a nonzero Pauli expectation value is exactly 1/4 in some observable/wiring combinations and decays like 1/2^{n/2} in others, with intermediate mixtures fitted by an empirical exponent.