Restricted Boltzmann machine for Quantum state tomography

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SUMMARY

The discussion centers on utilizing a Restricted Boltzmann Machine (RBM) for quantum state tomography of a single qubit, referencing the paper "Neural Network Quantum State Tomography" by Giacomo Torlai et al. The participant seeks clarity on the number of visible neurons required and how to determine their values based on measurement outcomes. It is concluded that the number of visible neurons should equal the number of qubits in the system, allowing each unique state to correspond to a visible neuron. Additionally, measurement results in a given basis serve as input vectors for the visible layer.

PREREQUISITES
  • Understanding of Restricted Boltzmann Machines (RBMs)
  • Familiarity with quantum state tomography
  • Knowledge of qubit representation in quantum mechanics
  • Basic concepts of neural networks and their applications in quantum computing
NEXT STEPS
  • Read the paper "Neural Network Quantum State Tomography" by Giacomo Torlai et al.
  • Explore the implementation of Restricted Boltzmann Machines in quantum simulations
  • Investigate methods for generalizing RBMs to mixed quantum states
  • Learn about input vector formulation based on quantum measurement outcomes
USEFUL FOR

Quantum computing researchers, machine learning practitioners, and students working on quantum simulations and state tomography projects.

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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