A Fast Quantum Mechanical Algorithm for Database Search Lov K. Grover

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 A Fast Quantum Mechanical Algorithm for Database Search 1996 STOC / arXiv 10.1145/237814.237866 quant-ph/9605043 grover1996-search grover1996-search.txt, the project's staged copy aa23555d7edc8d51c2c15e954290d916f7478750 arxiv-open quantum-computing

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 0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them about this quote: THE FORMULA IS GARBLED IN THE EXTRACTED TEXT: 'O (~~' stands for the paper's O(√N), so the bracket it opens never closes in this copy; the rest of the sentence is quoted as printed. Quotation withheld because this record is not cleared for redistribution. Quotation withheld because this record is not cleared for redistribution. mathematical-proof Quotation withheld because this record is not cleared for redistribution. THE PROBLEM'S WHOLE COST MODEL RESTS ON ONE STIPULATION ABOUT VERIFICATION, STATED IN A SINGLE SENTENCE: Quotation withheld Checking is free and finding is expensive - and the separation between the two is what makes `search` a measurable quantity at all. The stipulation is not defended; it defines the object about this quote: THE STAGED TEXT OF THIS PAPER IS A TWO-COLUMN SCRAMBLE (damage shape 5), which has no detector: every token in a reordered sentence is a real word. This span was verified BY READING that it is continuous English, after a token test had reduced 140 sentences to 55 and reading reduced 55 to 4. Neighbouring text is interleaved and must not be quoted without the same check. Quotation withheld because this record is not cleared for redistribution. A RESULT IS CALLED IMPORTANT AND UNSURPRISING IN THE SAME BREATH, WITH THE REASON DRAWN FROM PHYSICS RATHER THAN FROM COMPUTATION: quantum mechanical computers were shown to be at least as powerful as classical computers - AN IMPORTANT BUT NOT SURPRISING RESULT, SINCE CLASSICAL COMPUTERS, AT THE DEEPEST LEVEL, ULTIMATELY FOLLOW THE LAWS OF QUANTUM MECHANICS. The surprisingness of a theorem is assessed by an argument from what the machines are made of about this quote: THE STAGED TEXT OF THIS PAPER IS A TWO-COLUMN SCRAMBLE (damage shape 5), which has no detector: every token in a reordered sentence is a real word. This span was verified BY READING that it is continuous English, after a token test had reduced 140 sentences to 55 and reading reduced 55 to 4. Neighbouring text is interleaved and must not be quoted without the same check. Quotation withheld because this record is not cleared for redistribution. A FORMALISATION IS DATED, ATTRIBUTED, AND ITS SUPERIORITY CLAIM IS SCOPED IN THE SAME SENTENCE: THE DESCRIPTION OF QUANTUM MECHANICAL COMPUTERS WAS FORMALIZED IN THE LATE 80s AND EARLY 90s and they were shown to be more powerful than classical computers ON VARIOUS SPECIALIZED PROBLEMS. The word `formalized` is given a date and four citations, and the advantage is restricted to a class of problems rather than asserted in general about this quote: THE STAGED TEXT OF THIS PAPER IS A TWO-COLUMN SCRAMBLE (damage shape 5), which has no detector: every token in a reordered sentence is a real word. This span was verified BY READING that it is continuous English, after a token test had reduced 140 sentences to 55 and reading reduced 55 to 4. Neighbouring text is interleaved and must not be quoted without the same check. Quotation withheld because this record is not cleared for redistribution. OPTIMALITY IS CLAIMED BY CITING SOMEONE ELSE'S LOWER BOUND, AND THE BOUND'S OWN CONDITION IS QUOTED WITH IT: THERE IS A MATCHING LOWER BOUND on how fast the desired item can be identified - another paper shows what is needed IN ORDER TO IDENTIFY THE DESIRED ELEMENT, WITHOUT ANY INFORMATION ABOUT THE STRUCTURE OF THE DATABASE. The optimality claim carries its own condition - an absence of structure - and the condition travels with the claim in the same sentence rather than being left to a reader about this quote: THE STAGED TEXT OF THIS PAPER IS A TWO-COLUMN SCRAMBLE (damage shape 5), which has no detector: every token in a reordered sentence is a real word. This span was verified BY READING that it is continuous English, after a token test had reduced 140 sentences to 55 and reading reduced 55 to 4. Neighbouring text is interleaved and must not be quoted without the same check. Quotation withheld because this record is not cleared for redistribution. what this limits: any expectation of further speedup: THERE IS A MATCHING LOWER BOUND ON HOW FAST THE DESIRED ITEM CAN BE IDENTIFIED Quotation withheld because this record is not cleared for redistribution. what this limits: the generality claim, and note our staged text is damaged here: THE ALGORITHM THIS PAPER DOES NOT USE ANY IMOWLEDGE OF PROBLEM [OCR for 'knowledge'] - no problem structure is exploited Quotation withheld because this record is not cleared for redistribution. what this limits: the single-solution presentation: the algorithm as given assumes exactly one state satisfies the condition, and the multiple-solution case needs separate treatment Quotation withheld because this record is not cleared for redistribution. what this limits: the strongest reading of the speedup: IF IT WERE POSSIBLE TO REDUCE THE NUMBER OF STEPS TO A FINITE POWER OF O(log N) (INSTEAD OF O(sqrt N) AS IN THIS PAPER), FOR NP-COMPLETE PROBLEMS IT WOULD YIELD A POLYNOMIAL TIME ALGORITHM - and it does not Quotation withheld because this record is not cleared for redistribution. about this quote: THE FORMULA IS GARBLED IN THE EXTRACTED TEXT: 'Cl ( ~~' stands for the paper's Ω(√N), so the bracket it opens never closes in this copy; the rest of the sentence is quoted as printed. Quotation withheld because this record is not cleared for redistribution.

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