Trapped-ion processor demonstrates verifiable quantum random sampling

One of the key goals within the field of quantum computing is to achieve what is known as a quantum advantage. This term essentially describes the point after which a quantum computer can outperform a classical computer on a specific task or solve a problem that is beyond the reach of classical computers.

One task that could be used to demonstrate a quantum advantage, known as quantum random sampling, entails the generation of samples from a probability distribution. This task is very difficult for classical computers to perform, but it could theoretically be completed by quantum computers.

While past studies have successfully tackled random sampling tasks using quantum computers, actually verifying that a system effectively performs these tasks has proved challenging. This is because many existing verification techniques based on classical data are either too computationally demanding or difficult to apply to larger quantum systems.

Researchers at Universität Innsbruck, Freie Universität Berlin and other institutes have introduced a new protocol to verify quantum random sampling, which draws from the measurement-based model of quantum computation (MBQC). This protocol, outlined in a paper published in Nature Communications, was successfully demonstrated on a trapped-ion quantum processor.

“Originally, we were inspired by questions on what computational tasks could be solved on a quantum computer that could not be solved on a classical computer efficiently,” Jens Eisert, co-author of the paper, told Phys.org.

“At that time, the first ideas of what are now called ‘quantum advantages’ came up, referring to problems for which there is strong evidence that a quantum computer could outperform classical supercomputers.”

Random sampling problems, the tasks that the researchers focused on in their paper, entail taking raw data from a quantum experiment and trying to classically sample it from a distribution close to the correct quantum distribution. The successful implementation of these schemes could help to generate outputs that would be very difficult to predict using classical computers.

“Surprising as this may sound, this is something quantum computers are good at,” explained Eisert, “We started out from work in the group that was aimed at finding the simplest possible such prescription. This amounted to preparing a simple product state arranged in an array, performing one layer of quantum circuits and performing local simple measurements.”

While conducting their previous research, the researchers were surprised to discover that a set of simple schemes could give rise to sampling problems. They then decided to try to apply these schemes in an experimental setting, using a trapped-ion quantum processor.

“We thought to ourselves, ‘Hey, if such a simple setting can give rise to a quantum advantage, then can we transform this into an experimentally feasible setting that works for a trapped ion-settings and that recycles the ions?'” said Eisert. “We were intrigued.”

When they started conducting their experiments, the team soon realized that the random sampling scheme they identified was efficiently verifiable. Given its lower computational demands compared to previous approaches to verify quantum random sampling, it could also be easier to apply to larger quantum computers.

“A key challenge for random sampling schemes is that one cannot efficiently verify their correctness based on classical data alone,” explained Eisert.

“Yet if one has some trust in the quantum measurement apparatus, one can do this. We efficiently verify the correctness of the scheme, even though the classical sampling from a close to the quantum distribution is hard and would not be possible for a larger scheme of the same type.”

This study could contribute to the study of classical and quantum computers, helping researchers to understand the limits of classical systems and where an algorithmic quantum advantage sets in. This knowledge could in turn help to build increasingly larger and better performing quantum computers.

To demonstrate their protocol, the researchers applied it to a quantum processor comprised of trapped single ions that can be precisely manipulated in their quantum state. Within this processor, they prepared a so-called cluster state, which is a state known to play a key role in measurement-based quantum computing.

“The experiment samples from measurement outcomes obtained from measuring a 4×4 cluster state, involving 16 qubits, where some of the qubits could be recycled,” said Thomas Monz and Martin Ringbauer, the team leads of the experimental team in Innsbruck.

“The cute aspect is that we could verify the correctness of the state preparation and sampling by estimating the state fidelity and have compared this with more conventional approaches such as cross-entropy benchmarking.”

Using their protocol, the researchers were able to reliably estimate the fidelity of the cluster state in their quantum processor. Notably, they found that the samples produced by the processor were very close to those they had predicted.

“We think that our work has various key contributions, the first of which is a technological one,” said Eisert, “The trapped ion platform that makes use of single trapped ions more than once constitutes an advancement.

“In addition, its conceptual advancement is that it provides an understanding that the correctness of sampling experiments is efficiently possible even if one cannot efficiently classically sample from almost the right distribution. This is intriguing, as one can say some experiment has been correctly performed even if one cannot make predictions about it.”

With many research teams worldwide working to improve the performance of quantum computers, Eisert and his colleagues hope that their efforts will help to understand where their quantum advantage sets (i.e., on what tasks they could perform better than classical computers).

In the future, the scheme they devised could be used by other teams to test the performance of their quantum computing systems on random sampling tasks.

“We see this as an important step towards devising more sophisticated quantum computing platforms,” added Eisert.

“These days, for example, there are substantial steps taken towards making quantum schemes more resilient against errors. We see these efforts as contributing to the bigger research scheme of building quantum computers. There is also a meta-message coming out of this: technological progress is only ensured if theoretical and experimental considerations come together.”

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