Quantum computing -- How is the relevant solution selected?

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Discussion Overview

The discussion revolves around the process of selecting a relevant solution during quantum computation, particularly in the context of algorithms like Shor's for factorizing large numbers. Participants explore how superposition and measurement play roles in this selection process.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant states that during quantum computation, all possible solutions exist in a state of superposition and questions how the relevant one is selected.
  • Another participant asserts that the selection occurs through measurement.
  • A participant compares classical and quantum computing approaches to factorization, noting that a classical computer tests pairs of numbers sequentially, while a quantum computer generates a superposition of all possible products.
  • A later reply clarifies that the quantum computer does not directly select the desired result; instead, a measurement is performed that has a high probability of yielding the correct answer, but verification is necessary.
  • One participant expresses disappointment at the complexity of the answer, indicating a desire for a simpler explanation.

Areas of Agreement / Disagreement

Participants express differing views on the clarity and simplicity of the selection process in quantum computing, with some agreeing on the role of measurement while others seek further clarification on practical implementation.

Contextual Notes

There are unresolved questions regarding the practical implementation of measurement in quantum algorithms and the conditions under which the correct result is verified.

Who May Find This Useful

Individuals interested in quantum computing, particularly those exploring the mechanics of quantum algorithms and the implications of superposition and measurement.

jeremyfiennes
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TL;DR
During a quantum computation, all possible solutions exist in a state of superposition. How is the relevant one selected?
During a quantum computation, all possible solutions exist in a state of superposition. How is the relevant one selected?
 
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I looked at it, but could not find an answer. As I understand it: when factorizing a large number, for instance, a normal computer takes pairs of numbers, multiplies them, and if the result is not the desired one, tries another pair. And so on, working sequentially.
Whereas a quantum computer generates simultaneously a superposition state of all possible products of all possible numbers, and then selects the desired one. My question is: how is this done in practice?
 
jeremyfiennes said:
I looked at it, but could not find an answer. As I understand it: when factorizing a large number, for instance, a normal computer takes pairs of numbers, multiplies them, and if the result is not the desired one, tries another pair. And so on, working sequentially.
Whereas a quantum computer generates simultaneously a superposition state of all possible products of all possible numbers, and then selects the desired one. My question is: how is this done in practice?
The quantum computer doesn't select the desired result. In the final stage of the algorithm, there is a measurement performed, and that measurement has a high probability of giving the correct answer, but the result has to be checked to make sure the right one was obtained.

https://www.quantiki.org/wiki/shors-factoring-algorithm
 
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Thanks. Dashing my hopes for a simple answer!
 

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