Creating a logical conjunction of the five controls out of Toffoli gates and ancilla bits. Uncomputation is used to restore the ancilla bits to their original states before finishing.

Uncomputation is a technique, used in reversible circuits, for cleaning up temporary effects on ancilla bits so that they can be re-used.^[1]

Uncomputation is a fundamental step in quantum computing algorithms. Whether or not intermediate effects have been uncomputed affects how states interfere with each other when measuring results.^[2]

The process is primarily motivated by the principle of implicit measurement.^[3], which states that discarding a register during computation is physically equivalent to measuring it. Failure to uncompute garbage registers can have unintentional consequences. For example, if we take the state ${\displaystyle }$ ${\displaystyle {\frac {1}{\sqrt {2}}}(|0\rangle |g_{0}\rangle +|1\rangle |g_{1}\rangle )}$ where ${\displaystyle g_{0}}$ and ${\displaystyle g_{1}}$ are garbage registers. Then, if we do not apply any further operations to those registers, according to the principle of implicit measurement, the entangled state has been measured, resulting in a collapse to either ${\displaystyle |0\rangle |g_{0}\rangle }$ or ${\displaystyle |1\rangle |g_{1}\rangle }$ with probability ${\displaystyle {\frac {1}{2}}}$. What makes this undesirable is that wave-function collapse occurs before the program terminates, and thus may not yield the expected result.

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