Uncomputation

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.

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.

The process is primarily motivated by the principle of implicit measurement., which states that ignoring a register during computation is physically equivalent to measuring it. Failure to uncompute garbage registers can have unintentional consequences during computation, such as wave-function collapse. For example, if we take the state ${\frac {1}{\sqrt {2}}}(|0\rangle |g_{0}\rangle +|1\rangle |g_{1}\rangle )$ where $g_{0}$ and $g_{1}$ are garbage registers depending on $|0\rangle$ and $|1\rangle$ respectively. Then if we ignore, or "drop" the $g_{i}$ registers from computation, then according to the principle of implicit measurement, we would have essentially measured it and our resulting entangled state would collapse to either $|0\rangle$ or $|1\rangle$ with 50% probability. Note that what makes this undesirable is that measurement happens before computation finishes, and thus the program may not yield the expected result.