Randomness in Quantum Machines Helps Verify Their Accuracy

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In quantum computers and other experimental quantum systems, information spreads across the devices and quickly distorted like dice in a game of Boggle. This encryption process occurs when the basic units of the system called qubits (like computer bits only quantum) become entangled; entanglement is a phenomenon in quantum physics where particles connect and stay connected even though they don’t have direct contact.

These quantum devices mimic what happens in nature and allow scientists to develop new, exotic materials that may be useful in medicine, computer electronics and other fields. While full-scale quantum computers are still years away, researchers are already conducting experiments on so-called quantum simulators — quantum devices tailored to solve specific problems, such as efficiently simulating high-temperature superconductors and other quantum materials. The machines can also solve complex optimization problems, such as planning routes for autonomous vehicles to ensure they don’t collide.

A challenge in using these quantum machines is that they are very error-prone, much more so than classical computers. It is also much more difficult to identify faults in these newer systems. “For the most part, quantum computers make a lot of mistakes,” said Adam Shaw, a Caltech physics graduate student and one of two lead authors of a study in the journal Nature on a new method to verify the accuracy of quantum devices. “You can’t open the machine and look inside, and a huge amount of information is stored – too much for a classical computer to account for and verify.”

In the Nature study, Shaw and co-lead author Joonhee Choi, a former postdoctoral scientist at Caltech who is now a professor at Stanford University, demonstrate a new way to measure the accuracy of a quantum device, known as fidelity. Both researchers work in the lab of Manuel Endres, a professor of physics at Caltech and a Rosenberg scholar. The key to their new strategy is randomness. The scientists have discovered and characterized a new form of randomness that relates to the way information is encrypted in the quantum systems. But while the quantum behavior is random, universal statistical patterns can be identified in the noise.

“We’re interested in better understanding what happens when the information is encoded,” says Choi. “And by analyzing this behavior with statistics, we can look for anomalies in the patterns that indicate mistakes were made.”

“We don’t just want a result from our quantum machines, we want a verified result,” says Endres. “Because of quantum chaos, a single microscopic error leads to an entirely different macroscopic outcome, similar to the butterfly effect. This allows us to efficiently detect the error.”

The researchers demonstrated their protocol on a quantum simulator with no fewer than 25 qubits. To find out if there were any errors, they measured the system’s behavior thousands of times down to the level of a single qubit. By looking at how qubits evolved over time, the researchers were able to identify patterns in the seemingly random behavior and then look for deviations from what they expected. By finding errors, researchers eventually know how and when to fix them.

“We can trace how information moves through a system at single qubit resolution,” says Choi. “The reason we’re able to do this is that we’ve also found that this randomness, which just happens naturally, is represented at the level of just one qubit. You can see the universal random pattern in the sub-parts of the system.”

Shaw compares their work to measuring the jerkiness of waves on a lake. “When the wind comes, you get peaks and troughs on the lake, and while it might look random, you could identify a pattern in the randomness and track how the wind affects the water. We could see if the wind changes by analyzing how the pattern changes. Our new method similarly allows us to look for changes in the quantum system that would indicate errors.”

The Nature study titled “Probing random states and benchmarking with many-body quantum chaos,” is funded by the National Science Foundation through the Institute for Quantum Information and Matter, or IQIM; the Defense Advanced Research Projects Agency (DARPA); the Army Research Office, the graduate fellowship of the Eddleman Quantum Institute; the Troesh postdoctoral fellowship; the Gordon and Betty Moore Foundation; the J. Yang & Family Foundation; the Harvard Quantum Initiative (HQI) graduate fellowship; the Junior Fellowship of the Harvard Society of Fellows; the Department of Energy; and the Miller Institute for Basic Research in Science at UC Berkeley. Other authors include Ran Finkelstein, Hsin-Yuan Huang and Fernando Brandão of Caltech; Ivaylo Madjarov, Xin Xie and Jacob Covey, who conducted the research while previously at Caltech; Jordan Cotler and Anant Kale of Harvard University; Daniel Mark and Soonwon Choi from MIT; and Hannes Pichler from the University of Innsbruck in Austria.

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