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I have come across several papers that use Toffoli AND conjugate to minimize the T-depth. But since it contains a measurement, does it affect Shor's algorithm (in terms of interference, entanglement, or superposition), when used within the reversed modular multiplication circuit, such as in Vedral et al's implementation?

Toffoli AND conjugate (d), source.

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Vedral et al's modular exponentiation circuit, source: Nakahara et al's book: Quantum Computing - From Linear Algebra to Physical Realizations:

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No, it doesn't cause problems. These implementations of the operations are exactly equivalent to implementations that don't use measurement. The measurements are carefully chosen to not measure anything affecting the surrounding algorithm, and the classically controlled operations are chosen to correctly repair any kickback effects from the measurement result varying.

You can verify this in simulators. For example, here is a circuit with state displays showing that the density matrix of two qubits is correctly restored by an uncomputation procedure involving a measurement:

enter image description here

For contrast, here's an operation that's not correctly uncomputed:

enter image description here

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