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ngrunenberg

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- TL;DR Summary
- Scott Aaronson talked about how quantum computers work by "choreographing amplitudes"; what exactly did he mean by that? Do we need to know most of the answer before a quantum computer is of any use?

Apologies in advance if this is a stupid question, I'm not the brightest. I recently listened to Scott Aaronson's conversation with Lex Fridman, and an interview he did for Scientific American, regarding quantum computing (QC from now on) and have a question regarding how a QC finds a solution.

This is an excerpt from the interview:

"In particular, if an event can happen one way with a positive amplitude, and another way with a negative amplitude, those two amplitudes can “interfere destructively” and cancel each other out, so that the event never happens at all. The goal, in quantum computing, is always to choreograph things so that for each wrong answer, some of the paths leading there have positive amplitudes and others have negative amplitudes, so they cancel each other out, while the paths leading to the right answer reinforce."¹

My question(s) is the following:

I) When he talks about choreographing amplitudes, is he essentially saying that we take a problem with a vast solution space, of which we know a large subset of true and false solutions, and try to "collapse" the correct wave function by cancelling out what we assume to be false values and reinforcing amplitudes that converge toward the correct answer; then hope the final measurement "collapsed" the correct solutions' wave function?

II) If that is the case, do we square the amplitude of that solution, as we do in physics, to get a probability? If so, does that mean we only get a value for the probability of that particular solution being the right one?

III) If we have to know so much about the solution in the first place and the challenge is programming an algorithm to get the correct solution, would it be impossible to have novel solutions to problems in which we have no epistemological priors about the possible solution space? Apologies again if this is a silly question and thank you in advance for taking the time to answer it.

This is an excerpt from the interview:

"In particular, if an event can happen one way with a positive amplitude, and another way with a negative amplitude, those two amplitudes can “interfere destructively” and cancel each other out, so that the event never happens at all. The goal, in quantum computing, is always to choreograph things so that for each wrong answer, some of the paths leading there have positive amplitudes and others have negative amplitudes, so they cancel each other out, while the paths leading to the right answer reinforce."¹

My question(s) is the following:

I) When he talks about choreographing amplitudes, is he essentially saying that we take a problem with a vast solution space, of which we know a large subset of true and false solutions, and try to "collapse" the correct wave function by cancelling out what we assume to be false values and reinforcing amplitudes that converge toward the correct answer; then hope the final measurement "collapsed" the correct solutions' wave function?

II) If that is the case, do we square the amplitude of that solution, as we do in physics, to get a probability? If so, does that mean we only get a value for the probability of that particular solution being the right one?

III) If we have to know so much about the solution in the first place and the challenge is programming an algorithm to get the correct solution, would it be impossible to have novel solutions to problems in which we have no epistemological priors about the possible solution space? Apologies again if this is a silly question and thank you in advance for taking the time to answer it.