Constant-depth brickwork random unitary circuits and random Pauli rotations on n qubits have constant spectral gap, independent of n and uniform over all unitary representations.
Quantum union bounds for sequential projective measurements
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abstract
We present two new quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a trigonometric representation of quantum states and should have wide application in quantum information theory for information processing tasks such as communication and state discrimination, and perhaps even in the analysis of quantum algorithms.
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2026 1verdicts
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Random unitary circuits with constant spectral gap
Constant-depth brickwork random unitary circuits and random Pauli rotations on n qubits have constant spectral gap, independent of n and uniform over all unitary representations.