Quantum State Tomography with Neural Networks

The code implement neural-network quantum state tomography (QST), i.e. the recontruction reconstruction of an unknown quantum state from a set of measurements. It relies on the parametrization of the quantum state with a restricted Boltzmann Machine (RBM). The reconstruction is performed using standard unsupervised machine learning.

Requirements

The code is writted in C++11, with the only requirement being Eigen3, a header-only library for linear algebra.

Compiling

g++ main.cpp -O2 -I PATH_TO_EIGEN3 -std=c++11 -o run.x

Running

./run.x -PARAMETER1 par1 -PARAMETER2 par2 ...

The parametrs are:

• -nv: Number of visible units
• -nh: Number of hidden units
• -w : Width of initial weights distribution
• -nc: Numer of sampling chains
• -cd: Number of Gibbs updates in Contrastive Divergence
• -lr: Learning rate
• -l2: L2 regularization constant
• -bs: Batch size
• -ns: Numer of training samples
• -ep: Number of training iterations
• -basis: Set of measurements bases

Features

Current features

• RBM for binary Hilbert spaces.
• RBM-state for positive wavefunctions.
• QST of positive wavefunctions through minimization of the KL divergence.
• RBM-state for complex wavefunctions.
• QST of complex wavefunctions through minimization of a generalized KL divergence

Under testing

• RBM-state for density matrices.

Upcoming features

• QST of mixed states.
• RBM for multinomial Hilbert spaces.
• RBM-state for real non-positive wavefunctions.
• MPI support.
• Code documentation.

Tutorials (coming soon)

• 1d quantum Ising model.
• Entangled photonic pure states.