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How to prepare an MPS circuit #218
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Hi @ACE07-Sev, I'm afraid there are no examples like this at the moment. I'm also not familiar with the paper you linked or the specific task. But some general thoughts are the following:
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I see. I am having a bit of a trouble understanding number 4. Why isn't the depth guaranteed? I thought MPS to circuit required |
Sorry I was not very clear! OK well an MPS of Want I meant to say was, there has been a fair bit of empirical work showing that in fact a circuit of depth linear in |
Did I understand what you explained accurately? Would the condition of keeping the bond dimension constant at the cost of minor infidelity sufficient for keeping the growth strictly linear? |
I was wondering, would it be possible if you could perhaps kindly have a look at the paper I sent above? I fully understand that this is for github issues, and therefore what I am asking is quite inappropriate and inconsiderate, however, I feel you would have a better idea of what I am proposing. There is also this paper, which actually does the exact same thing (to the point of using the same data, aka images), and it's only 5 or so pages. |
My goal at the moment is to simply make an algorithm which would take a state vector (a normalized list of values, with a length of If I understand correctly, you mentioned quimb does allow for MPS to circuit conversion, so I am wondering if we can pair it with tensornetwork package and do what I described. Would you be interested in assisting me with this implementation? I have a repo prepared, so I can add you there, and I would appreciate any help or guidance you can provide considering your current commitments. Again, I would like to thank you for all of your guidance and kind help thus far, it is simply more than I could ever ask for, so I do hope you can forgive my over-eagerness which I understand may sometimes come across as being inconsiderate or pushy hehe. At the moment, I am a bit lost on how to do this, so I would deeply appreciate your experience and guidance regarding this small project. |
I'm afraid I don't have time to do a deep dive into these papers or develop any research code! but I think the quote from the paper above is all consistent. If you have a To implement this MPS exactly on a quantum compute you need So with the assumption that a |
Ohh, that makes so much more sense now. I still am digesting it, but I think I am clear now. Thank you so much! May I keep this thread open? |
What is your issue?
Greetings there,
Hope all are well. I am quite new to the quimb package, and was hoping to ask if you have any existing code which would perform the following :
What this would do is approximate the initial input state through an MPS, and allow one to use that instead of the exponentially scaling exact ones like Mottonen and Shende. For your kind reference, here is the paper I am trying to implement for this :
https://arxiv.org/pdf/2311.07666.pdf
P.S : Step 1 and 2 are quite self-explanatory, and I have code for that, so basically a code which would take a state vector with an error upper bound, calculate the MPS, and then create the circuit for that MPS. Also, if you do indeed allow this (fingers crossed), I would appreciate it if you can link the reference paper you used for my learning, and to confirm if the algorithm allows you to scale the depth linearly with respect to the number of qubits, basically$O(NX^2)$ where X is the bond dimension.
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