Restricted Boltzmann machine for Quantum state tomography

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Discussion Overview

The discussion revolves around the application of restricted Boltzmann machines (RBMs) for quantum state tomography, specifically for a single-qubit system. Participants explore the methodology outlined in a referenced paper and seek clarification on the number of visible neurons required and how to determine their values based on experimental measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the number of visible neurons needed for the RBM in the context of quantum tomography.
  • Another participant questions how to determine the values of the visible neurons based on measurements taken during experiments.
  • A participant suggests that the number of visible neurons should match the number of qubits in the system to represent each possible state uniquely.
  • There is a mention of uncertainty regarding the generalization of the method to mixed states.
  • A later reply proposes that the results from experiments in a given basis can be used as input vectors for the visible layer of the RBM.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the questions raised, and multiple viewpoints regarding the methodology and its application remain. Some participants propose answers, while others express uncertainty or seek further verification.

Contextual Notes

There are unresolved questions about the generalization of the method to mixed states and the specific assumptions regarding the relationship between qubits and visible neurons.

Jufa
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TL;DR
I would like to know how one would carry out quantum tomography from a quantum state by means of the restricted Boltzmann machine. For the sake of simplicity we could choose a 1-qubit system
I'm struggling with my Final Degree Project. I would like to perform a quantum simulation and perform quantum tomography for a single-qubit using a resrticted Boltzmann machine. In order to do so I'm trying to follow the recipe in the paper "Neural Network quantum state tomography, Giacomo Torlai et al.", but I fail to understand it.
How many visible neurons are needed?
How I know which is the value of the visible neurons based on the measurments performed?
These two questions are the main ones.
Could someone please help?
Thanks a lot in advance.
 
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Anyone? I'm quite lost ans frustrated, just a little of debate would extraordinarily help.
 
Do you have a link to the paper you referenced? If so, please provide it. That makes it easier for people to respond, since they don't have to go try to find it on their own.
 
In addition I don't see how the generalisation of this method to mixed states should be performed.
 
I think I have finally come up with the two answers to the questions I made. If only someone could verify I'm right it would be very helpful:
How many visible neurons are needed?
-The answer is that we need so many visible neurons as qubits has the system. This way every possible component of the system (in a certain basis) can be reffered as a unique state of the visible neurons.
-How I know which is the value of the visible neurons based on the measurments performed?
Given a certain basis, every result of an experiment performed in that basis becomes an input vector, i.e., a certain state of the visible layer.
 

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