The realization of measurement-induced quantum phases on a quantum computer with trapped ions

Trapped-ion quantum computers are quantum devices in which trapped ions vibrate together and are completely isolated from the external environment. These computers can be particularly useful for investigating and realizing various states of quantum physics.

Researchers at NIST/University of Maryland and Duke University recently used a quantum computer with trapped ions to realize two measurement-induced quantum phases, namely the pure phase and the mixed or coding phase during a purification phase transition. Their findings, published in a paper in Nature physicscontribute to the experimental understanding of many-body quantum systems.

“Our methods were based on the work of Michael Gullans and David Huse, who identified a measurement-induced purification transition in arbitrary quantum circuits,” Crystal Noel, one of the researchers who conducted the study, told Phys.org. “The main goal of our paper was to observe this critical phenomenon experimentally, using a quantum computer.”

To measure the purification phase transition first outlined by Gullans and Huse, the researchers had to average data collected across several random circuits. In addition, the measurements they collected included both unitary and projective measurements.

“By starting in a mixed state with high entropy or information, and then developing the circuits, the entropy at the end of the circuit indicates whether that information has been lost, or in other words the system has been purified,” explains Noel out. “We measured the entropy of the system after the evolution of the circuit while tuning the measurement speed across the transition.”

According to theoretical predictions, the transition from the purification phase investigated by the team should have originated on a critical point, which resembles a fault-tolerant threshold. Noel and her colleagues conducted their experiments on random circuits optimized to work well with their ion trap quantum computer. This allowed them to observe the different stages of purification with a relatively small system.

“Critical phenomena of this nature are difficult to observe because of the need for large system sizes, mid-circuit measurements, and averaging over many arbitrary circuits that take significant computation time,” Noel said. “We found a way to align the studied model with the system we had at our disposal, and show that with a minimal model, the critical phenomena can still be observed.”

Using their quantum computer with trapped ions, the team was able to investigate both the pure phase of the purification phase transition and the mixed or coding phase. In the first of these states, the system is quickly projected to a clean state, which is related to the measurement results. In the second case, the initial state of the system is partially encoded in a quantum error correcting encoding space, which retains the system memory of the original conditions for a longer period of time.

The successful realization of these two phases of the purification transition by Noel and her colleagues in their ion trap quantum computer could inspire other teams to use similar systems to investigate other quantum phases of matter. In their next work, the researchers will continue to use the same computer, now moved to the New Duke Quantum Center, to investigate other physical phenomena. Chris Monroe, the lead researcher of the recent study, is now director of this center and will lead further studies using the trapped ion quantum computer.

“We now intend to continue studying critical phenomena in arbitrary circuits using our contained ion quantum computer† We will add more qubits and mid-circuit measurements to increase hardware capabilities. We will work to find new observable and interesting transitions similar to the one observed here to understand more about quantum computing and open quantum systems in general.”

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