Uncomputation: Difference between revisions

Revision as of 17:30, 5 January 2025

Revision as of 17:31, 5 January 2025

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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.<ref>{{Cite journal|arxiv=quant-ph/0209060|last1=Aaronson|first1=Scott|title=Quantum Lower Bound for Recursive Fourier Sampling|journal=Quantum Information and Computation |volume=3|issue=2|pages=165–174|year=2002|doi=10.26421/QIC3.2-7 |bibcode=2002quant.ph..9060A}}</ref>

The process is primarily motivated by the principle of implicit measurement,<ref>{{cite book |last1=Nielsen, |first1=Michael; A. |last2=Chuang, |first2=Isaac L. "|title=Quantum Computationcomputation and Quantumquantum Information"information |date=2010 |publisher=Cambridge university press |___location=Cambridge |isbn=978-1107002173 |edition=10th anniversary}}</ref>{{page needed}} 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 <math></math> <math>

\frac{1}{\sqrt 2}(|0\rangle|g_0\rangle + |1\rangle|g_1\rangle)

</math> where <math>g_0</math> and <math>g_1</math> 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 <math>|0\rangle|g_0\rangle</math> or <math>|1\rangle|g_1\rangle</math> with probability <math>\frac{1}{2}</math>. What makes this undesirable is that wave-function collapse occurs before the program terminates, and thus may not yield the expected result.