# Can You Trust Your Quantum Simulator? MIT Physicists Report a New Quantum Phenomenon

A recent development provides a method to confirm the validity of experiments investigating the peculiar behavior of atomic-scale systems.

Physics gets weird on the atomic scale. Scientists use quantum analog simulators – laboratory experiments that involve cooling numerous atoms to low temperatures and probing them using precisely calibrated lasers and magnets – to uncover, harness and control these unusual quantum effects.

Scientists hope that any new understanding gained through quantum simulators will provide blueprints for the design of new exotic materials, smarter and more efficient electronics and practical quantum computers. But to get the insights from quantum simulators, scientists must first trust them.

That is, they must be sure that their quantum device has “high fidelity” and accurately reflects quantum behavior. For example, if a system of atoms is easily affected by external noise, researchers can assume a quantum effect where there is none. But until now there has been no reliable way to characterize the fidelity of quantum analog simulators.

In a study recently published in Nature, physicists from MIT and Caltech report a new quantum phenomenon: They found that there is a certain randomness in the quantum fluctuations of atoms and that this random behavior exhibits a universal, predictable pattern. Behavior that is random and predictable may sound like a contradiction. But the team confirmed that certain random fluctuations can indeed follow a predictable, statistical pattern.

What’s more, the researchers used this quantum randomness as a tool to characterize the fidelity of a quantum analog simulator. They showed through theory and experiments 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 determine their fidelity based on their pattern of quantum fluctuations. The protocol could help speed the development of new exotic materials and quantum computing systems.

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

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

Random evolution

The new study was motivated by a 2019 advance by Google, where researchers built a digital quantum computer called “Sycamore” that can perform a specific calculation faster than a classical computer.

While the computing units in a classical computer are “bits” that exist as either a 0 or a 1, the units in a quantum computer, known as “qubits,” can exist in a superposition of multiple states. When multiple qubits interact, they can in theory use special algorithms that solve difficult problems in much less time than any classical computers.

The Google researchers have designed a system of superconducting loops to act as 53 qubits, and have shown that the “computer” can perform a specific calculation that would normally be too tricky for even the world’s fastest supercomputer to complete. loose.

Google also happened to show that it could quantify the system’s fidelity. By randomly changing the state of individual qubits and comparing the resulting states of all 53 qubits to what the principles of quantum mechanics predict, they were able to measure the system’s accuracy.

Choi and his colleagues wondered if they could use a similar, randomized approach to determine the fidelity of quantum analog simulators. But there was one hurdle they would have to clear: Unlike Google’s digital quantum system, individual atoms and other quantum bits in analog simulators are incredibly difficult to manipulate and therefore randomly control.

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

“We found out that we don’t have to engineer this random behavior,” Choi says. “With no fine-tuning, we can only let the natural dynamics of quantum simulators evolve, and the outcome will lead to a similar pattern of randomness due to chaos.”

Build trust

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

“These 32 configurations will occur with a certain probability distribution, which people believe must be similar to predictions from statistical physics,” explains Choi. “We show they agree on average, but there are deviations and fluctuations that show a universal randomness that we did not know. And that randomness looks the same as if you ran 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 outcomes with the simulator’s actual outcomes. The closer the two are, the more accurate the quantum simulator should be.

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

Choi and colleagues also developed a numerical model to represent the experiment’s quantum dynamics, including an equation they derived to predict the universal, random fluctuations that should arise. The researchers then compared their experimental measurements to the model’s predicted outcomes and observed a very close match—strong evidence that this particular simulator can be trusted as a reflection of 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 constitutes a very basic technical tool for building increasingly larger, more precise and complex quantum systems,” says Choi. “With our tool, people can know if they are working with a reliable system.”

Reference: “Preparation of Random States and Benchmarking with Many-Body Quantum Chaos” by Joonhee Choi, Adam L. Shaw, Ivaylo S. Madjarov, Xin Xie, Ran Finkelstein, Jacob P. Covey, Jordan S. Cotler, Daniel K. Mark , Hsin-Yuan Huang, Anant Kale, Hannes Pichler, Fernando GSL Brandão, Soonwon Choi and Manuel Endres, 18 January 2023, Nature.

DOI: 10.1038/s41586-022-05442-1

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