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michael_nielsen's profile
michael_nielsen
michael_nielsen
michael_nielsen
@michael_nielsen

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michael_nielsen

@michael_nielsen

Searching for the numinous. Co-purveyor of https://quantum.country/ 

San Francisco, CA
michaelnielsen.org
Joined July 2008

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    1. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      Trying to understand the ground state of the AKLT model, and having trouble parsing the paper. Here's how it's described in the famous AKLT paper, and the corresponding Hamiltonian:pic.twitter.com/wv9iEBF1k5

      1 reply 0 retweets 23 likes
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    2. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      A few tidbits: the model is spin s=1. The s=1 spins in the chain are modelled as the symmetric subspace of 2 spin 1/2 particles, i.e., the space spanned by ^^, vv, and ^v+v^, in an obvious notation.

      1 reply 0 retweets 3 likes
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    3. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      It seems that we should think of the bonds between dots in the image as being like spin 1/2 singlets, ^v-v^. So this wld be s'thing like: *(^v-v^)(^v-v^)*, where the two * states are to be specified. But I don't see how to choose the *s so these are in the right sym. subspacespic.twitter.com/TJQXWnai06

      3 replies 0 retweets 4 likes
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    4. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      Anyone understand the ground state of AKLT / what I'm missing? @tobiasosborne @AndrewDohertyQu @andrewmchilds @dabacon?

      3 replies 0 retweets 1 like
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    5. dabacon‏ @dabacon 28 Sep 2018
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      Replying to @michael_nielsen @tobiasosborne and

      Wow all of those people are way more qualified than I am (esp @AndrewDohertyQu but he's in stealth startup land and won't answer my DMs!) The ground state is simply take spin 1/2 singlets and then project ends of neighboring singlets onto S=1 states?

      1 reply 0 retweets 3 likes
    6. michael_nielsen‏ @michael_nielsen 28 Sep 2018
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      Replying to @dabacon @tobiasosborne and

      michael_nielsen Retweeted michael_nielsen

      This, I guess?https://twitter.com/michael_nielsen/status/1045863881292242945 …

      michael_nielsen added,

      michael_nielsen @michael_nielsen
      Replying to @MStoudenmire
      I'm afraid I found that unclear. Is it saying that you construct the product of the spin singlet states, and then project onto the symmetric subspace of the paired spin 1/2's?
      1 reply 0 retweets 0 likes
    7. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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      Replying to @michael_nielsen @dabacon and

      Sprung!! Sorry Dave about the no reply situation. Mike you are correct about this account of the AKLT state

      2 replies 0 retweets 1 like
    8. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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      Replying to @AndrewDohertyQu @michael_nielsen and

      Mike if you want some other refs to subsequent work would recommend Werner and others CMP paper, Gross and others on the correlation space picture. And the whole literature in “SPT” phases which explains the near degeneracies on the line that you were discussing with Miles

      2 replies 0 retweets 1 like
    9. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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      Replying to @AndrewDohertyQu @michael_nielsen and

      Fact that linear cluster state Hamiltonian has, essentially, the same physics is not an accident. It’s in same phase as AKLT

      1 reply 0 retweets 1 like
    10. michael_nielsen‏ @michael_nielsen 3 Oct 2018
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      Replying to @AndrewDohertyQu @dabacon and

      Curious if "same phase" implies "if one be used as a substrate for QC the other can too" (and vice versa)?

      1 reply 0 retweets 0 likes
      michael_nielsen‏ @michael_nielsen 3 Oct 2018
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      Replying to @michael_nielsen @AndrewDohertyQu and

      (I know that some AKLT states can be used as a substrate for QC. But wondering in general what statements can be made.)

      9:12 PM - 3 Oct 2018
      1 reply 0 retweets 0 likes
        1. Andrew Doherty‏ @AndrewDohertyQu 3 Oct 2018
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          Replying to @michael_nielsen @dabacon and

          For linear states like this you might hope for 1 qubit MBQC with pretty much any state “in the phase.” it is lucky that Dominic Else is cleverer than those lightweights Bartlett and Doherty https://arxiv.org/pdf/1201.4877  ! State of the art, I think: https://arxiv.org/abs/1803.00095 

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