Source-linked AI summary
Latent Space Purification via Neural Density Operators
Giacomo Torlai, Roger G. Melko
TL;DR
Laboratory quantum states may be entangled with their environment, so tomography must account for unknown mixing. The paper represents mixed states with an RBM-based neural density operator using auxiliary degrees of freedom in the latent space; on experimental photon data, it reports fidelity 0.9976 versus 0.992 for MaxLi tomography.
Problem
Laboratory quantum states are often entangled with the environment, so their purity cannot be assumed and tomography must handle unknown mixing.
Source: p. 1Method
The neural density operator uses an RBM with latent auxiliary degrees of freedom to purify a mixed state, then traces out the auxiliary system to represent its density matrix.
Source: pp. 1–2Results
On experimental photon data, NDO fidelity was 0.9976 versus 0.992 for MaxLi tomography.
Source: p. 4Takeaways & Limitations
The approach allows approximate tomography of mixed states using measurements from an arbitrary basis.
Source: p. 4
Abstract
from arXiv · showhide
Machine learning is actively being explored for its potential to design, validate, and even hybridize with near-term quantum devices. A central question is whether neural networks can provide a tractable representation of a given quantum state of interest. When true, stochastic neural networks can be employed for many unsupervised tasks, including generative modeling and state tomography. However, to be applicable for real experiments such methods must be able to encode quantum mixed states. Here, we parametrize a density matrix based on a restricted Boltzmann machine that is capable of purifying a mixed state through auxiliary degrees of freedom embedded in the latent space of its hidden units. We implement the algorithm numerically and use it to perform tomography on some typical states of entangled photons, achieving fidelities competitive with standard techniques.