Neural networks accurately quantize quantum entanglement

A new study shows that neural networks can estimate the degree of entanglement in quantum systems more efficiently than traditional techniques.

The research was published as a cover article in Science Advances on July 19 under the title "Deep learning of quantum entanglement from incomplete measurements".

Quantifying entanglement is crucial in large-scale quantum technology, but a comprehensive characterization of quantum states is not realistic due to resource constraints.

Entanglement is at the heart of quantum mechanics, and entanglement is the idea that multiple particles share a common wavefunction, so interfering with one particle affects all the others. Measuring the degree of entanglement in a system is therefore part of understanding how "quantum" it is, said Miroslav Ježek, a co-author of the study and a physicist at Palacky University in the Czech Republic. "Starting with simple two-particle systems that discuss the fundamentals of quantum physics, you can observe this behavior." On the other hand, there is a direct link between entanglement changes and phase transitions in macroscopic matter.

The degree of entanglement of any two particles in a system can be quantified by a number. Obtaining an exact value for this number requires reconstructing the wavefunction, but measuring quantum states destroys the wavefunction; therefore, multiple copies of the same state must be measured over and over again - this is quantum tomography, which is analogous to classical tomography, in which a series of two-dimensional images are used to construct a three-dimensional image, an unavoidable consequence of quantum theory.

Ana Predojević, a physicist at Stockholm University in Sweden and a member of the research team, says, "If it were possible to understand the quantum state through a single measurement, then a quantum bit would not be a quantum bit: it would just be a bit, and there would be no quantum communication."

The problem is that the uncertainties inherent in quantum measurements make it extremely difficult to measure the entanglement between quantum bits in a quantum processor because, for each quantum bit, one must perform a complete multi-quantum bit wavefunction tomography image - which can take days even for small processors.

As a result, Predojević says, "You can't just make one measurement and say whether there is entanglement or not." It's like when people take CAT (computed axial tomography) scans of the spine, which need to be in a tube for 45 minutes so they can get a full image: it's not possible to know if there's a problem with this or that vertebrae from a five-minute scan.

While calculating entanglement with 100% accuracy requires a full quantum state tomography, there are several algorithms that can guess the quantum state from partial information, Ježek explains, and the problem with this approach is that "there is no mathematical evidence that entanglement can be accounted for with a certain accuracy by a certain number of finite measurements".

In the new study, Ježek, Predojević, and their colleagues took a different approach, abandoning the notion of reconfiguration of quantum states altogether in favor of focusing solely on the degree of entanglement. To do this, they designed deep neural networks to study entangled quantum states and trained them on numerically generated data.Ježek says, "We know the output of the network after we randomly choose the quantum state and generate the state: because we know the amount of entanglement in the system; but we can also simulate the data we get when we measure different numbers of copies from different directions ...... These simulated data are the inputs to the network."

The network used this data to teach itself to make better and better estimates of the entanglement with a given set of measurements. The researchers then checked the accuracy of the algorithm using a second set of simulated data; they found that the algorithm's error was about a factor of 10 lower than conventional quantum tomography estimation algorithms.

Schematic of the three methods for inferring quantum correlations

Finally, the researchers measured two real entangled systems in their experiment: a resonantly pumped semiconductor quantum dot and a spontaneous parametric downconversion two-photon source. "We measured the complete quantum state layer imaging ...... From this we know everything about the quantum state." Ježek said, "Then we omitted some of those measurements."

As more and more measurements were omitted, they compared the prediction errors of the deep neural network to those of the same conventional algorithm: the neural network's errors were significantly lower.

Performance of MaxLik and DNN-based methods on experimental datasets

In a recent interview, Ryan Glasser, a quantum optics expert at Tulane University in Louisiana, who has previously used machine learning to estimate quantum states, also hailed the new work as "significant".

One of the problems with quantum technology right now is that we've gotten to the point where we can scale things up to bigger systems," Glasser said. ...... we want to be able to fully understand quantum systems. Quantum systems are notoriously subtle and difficult to measure and fully characterize ...... This time, the researchers have shown that they can quantize the amount of entanglement in the system very accurately, which will be very useful for us to study larger and larger quantum systems: because nobody wants a two-qubit quantum computer."

The team now plans to extend its research to even larger quantum systems. Ježek is also interested in the reverse problem, for example: "Suppose we need to measure the amount of entanglement in a quantum system with an accuracy of, say, 1%; what is the minimum level of measurement we need to get an estimate of entanglement at that level?"

Reference link:

[1] https://www.science.org/doi/10.1126/sciadv.add7131

[2]https://physicsworld.com/a/neural-networks-speed-up-quantum-state-measurements/

[3]https://www.su.se/english/news/unlocking-the-quantum-enigma-deep-learning-to-quantify-entanglement-from-incomplete-measurements -1.663721