# Can you trust your quantum simulator? | MIT News

At the scale of individual atoms, physics gets weird. Researchers are working to reveal, harness, and control these strange quantum effects using analog quantum simulators, laboratory experiments that involve supercooling tens to hundreds of atoms, and probing them with finely tuned lasers and magnets.

Scientists hope that any new insights gained from quantum simulators will provide blueprints for designing exotic new materials, smarter and more efficient electronic devices, and practical quantum computers. But to gain insights from quantum simulators, scientists must first trust them.

That is, they must ensure that their quantum device is “high fidelity” and accurately reflects quantum behavior. For example, if a system of atoms is easily influenced by external noise, researchers might assume a quantum effect where there is none. But there hasn’t been a reliable way to characterize the fidelity of quantum analog simulators, until now.

in a study appearing today in *Nature*, MIT and Caltech physicists report a new quantum phenomenon: They discovered that there is some randomness in the quantum fluctuations of atoms, and that this random behavior exhibits a universal and predictable pattern. Random and predictable behavior may sound like a contradiction. But the team confirmed that certain random fluctuations can follow a predictable statistical pattern.

Furthermore, researchers have used this quantum randomness as a tool to characterize the fidelity of a quantum analog simulator. They demonstrated through theory and experiment that they could determine the accuracy of a quantum simulator by analyzing its random fluctuations.

The team developed a new benchmarking protocol that can be applied to existing quantum analog simulators to measure their fidelity based on their pattern of quantum fluctuations. The protocol could help speed up the development of exotic new materials and quantum computing systems.

“This work would make it possible to characterize many existing quantum devices with very high precision,” says study co-author Soonwon Choi, an assistant professor of physics at MIT. “It also suggests that there are deeper theoretical structures behind randomness in chaotic quantum systems than we had previously thought.”

The study authors include MIT graduate student Daniel Mark and collaborators from Caltech, the University of Illinois at Urbana-Champaign, Harvard University and the University of California at Berkeley.

**random evolution**

The new study was prompted by a 2019 breakthrough by Google, where researchers had built a digital quantum computer, dubbed “Sycamore,” that could perform a specific calculation faster than a classical computer.

Google also demonstrated that it could quantify the fidelity of the system. By randomly changing the state of the individual qubits and comparing the resulting states of the 53 qubits with what the principles of quantum mechanics predict, they were able to measure the precision of the system.

Choi and his colleagues wondered if they could use a similar random approach to measure the fidelity of quantum analog simulators. But there was a hurdle they had to overcome: Unlike Google’s digital quantum system, the individual atoms and other qubits in the analog simulators are incredibly difficult to manipulate and therefore randomly control.

But through some theoretical modeling, Choi realized that the collective effect of individually manipulating the qubits in Google’s system could be reproduced in an analog quantum simulator simply by letting the qubits evolve naturally.

“We realized that we don’t have to engineer this random behavior,” says Choi. “Without fine tuning, we can let the natural dynamics of quantum simulators evolve, and the result would lead to a similar pattern of randomness due to chaos.”

**building trust**

As an extremely simplified example, imagine a system of five qubits. Each qubit can exist simultaneously as either a 0 or a 1, until a measurement is made, after which the qubits settle into one or the other state. With any measurement, the qubits can adopt one of 32 different combinations: 0-0-0-0-0, 0-0-0-0-1, etc.

“These 32 configurations will occur with a certain probability distribution, which people think should be similar to the predictions of statistical physics,” Choi explains. “We show that they agree on average, but there are deviations and fluctuations that exhibit a universal randomness that we were not aware of. And that randomness looks the same as if you were to run those random operations that Google did.”

The researchers hypothesized that if they could develop a numerical simulation that accurately represented the dynamics and universal random fluctuations of a quantum simulator, they could compare the predicted results with the actual results of the simulator. The closer the two are, the more accurate the quantum simulator needs to be.

To test this idea, Choi teamed up with Caltech experimenters, who designed a quantum analog simulator comprising 25 atoms. The physicists turned on a laser in the experiment to collectively excite the atoms, then let the qubits interact naturally and evolve over time. They measured the state of each qubit in several runs, collecting 10,000 measurements in all.

Choi and his colleagues also developed a numerical model to represent the quantum dynamics of the experiment and incorporated an equation they derived to predict the universal random fluctuations that should arise. The researchers then compared their experimental measurements with the model’s predicted results and observed a very close match: strong evidence that this particular simulator can be trusted to reflect pure quantum mechanical behavior.

More generally, the results demonstrate a new way to characterize almost any existing quantum analog simulator.

“The ability to characterize quantum devices is a very basic technical tool for building ever larger, more precise, and more complex quantum systems,” Choi says. “With our tool, people can tell if they are working with a trustworthy system.”

This research was funded, in part, by the US National Science Foundation, the Defense Advanced Research Projects Agency, the Army Office of Research, and the Department of Energy.