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Quantum information systems, systems that process, store or transmit information leveraging quantum mechanical effects, could, in principle, outperform classical systems in some optimization, computational, sensing, and learning tasks. An important aspect of quantum information science is the reliable quantification of quantum states in a system, to verify that they match desired (i.e., target) states.

Conventional protocols to verify quantum states rely on experimentally challenging deep quantum circuits or an exponential number of single-qubit measurements. This makes them impractical for real-world applications, particularly for quantifying highly entangled states in larger quantum information systems.

Researchers at California Institute of Technology recently developed a more scalable approach that could be used to quantify and verify almost all quantum states. This newly introduced protocol, presented in a paper in Nature Â鶹ÒùÔºics, relies on significantly fewer single-qubit measurements and computations than previously proposed approaches.

"Our initial motivation stemmed from the need to verify neural network representations of quantum states," Hsin-Yuan (Robert) Huang, an author of the paper, told Â鶹ÒùÔº. "Neural networks have proven remarkably powerful at representing diverse quantum states, including those with extremely high entanglement. However, like in everyday generative AI models, such as ChatGPT, these models can hallucinate patterns that aren't present in the actual data."

After a deep learning algorithm is trained on experimental measurements of a quantum state, it can sometimes learn "false" correlations instead of genuine quantum features; a phenomenon referred to as "hallucination." If it learns these fake correlations, the model in question will no longer be able to reliably represent a quantum state or offer insight that could help to draw scientific conclusions about the quantum system that was measured.

"Our main objective was to develop a rigorous approach to verify that the neural network model faithfully represents the laboratory state, ensuring scientists can confidently use these models for quantum research," said Huang.

The new protocol developed by Huang and his colleagues is surprisingly simple, yet it has so far proved to be highly effective. Essentially, the approach works by randomly selecting one qubit from the quantum system that is being examined and measuring a randomly selected Pauli operator in this qubit (i.e., one of three key quantum observable features), while measuring all other qubits on a standard basis.

"By repeating this procedure a polynomial number of times, we prove that the measurement data efficiently verifies whether the target state matches the laboratory state," explained Huang. "The key advantage is that this requires only single-qubit measurements. No advanced quantum computing capabilities or entangling operations are needed to implement our protocol. Furthermore, we prove that these simple single-qubit measurements work for almost all target states, even those with exponentially high circuit complexity and maximal entanglement."

The researchers showed that measuring individual qubits in this random fashion allowed them to determine if a many-qubit system is close to its target quantum state. Notably, their paper suggests that their approach could be applicable to the verification of almost all quantum states.

"This means local single-qubit measurements can reveal the intricate entanglement and quantum correlations spanning the entire system," said Huang. "Prior to this work, the prevailing understanding was that such local measurements could only probe local correlations but not global quantum properties like highly nonlocal entanglement across the entire many-body system. Our results fundamentally change this perspective, showing that simple local measurements contain far more information about global quantum structure than previously recognized."

The new protocol introduced by Huang and his colleagues could soon be validated further in tests involving various lab-created quantum systems. Other research teams could also use this approach or devise similar ones to quantify the quantum states that emerge in the systems they are developing.

"We are now exploring the broader implications of this surprising fact that single-qubit measurements suffice to uncover highly nonlocal entanglement structure," added Huang.

"This will involve developing improved protocols for benchmarking quantum devices, verifying neural network models of quantum states, and extending certification to other quantum objects such as quantum dynamics and quantum channels. We're also interested in understanding the fundamental limits of what can be learned from local measurements and developing efficient quantum learning algorithms that leverage these insights."

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