Rigorous approach quantifies and verifies almost all quantum states

Quantum information systems, that is, systems that process, store or transmit information by taking advantage of the effects of quantum mechanics, could, in principle, outperform classical systems in certain optimization, calculation, 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 correspond to desired (i.e. target) states.

Conventional protocols for verifying quantum states rely on experimentally demanding deep quantum circuits or exponential numbers 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 the California Institute of Technology recently developed a more scalable approach that could be used to quantify and verify almost any quantum state. This newly introduced protocol, presented in an article published in Natural physicsrelies on far fewer measurements and calculations on a single qubit than previously proposed approaches.

“Our initial motivation came from the need to verify neural network representations of quantum states,” Hsin-Yuan (Robert) Huang, author of the paper, told Phys.org. “Neural networks have proven remarkably powerful at representing various quantum states, including those with extremely high entanglement. However, as in everyday generative AI models, such as ChatGPT, these models can hallucinate patterns that are not present in real data.”

Once a deep learning algorithm is trained on experimental measurements of a quantum state, it can sometimes learn “false” correlations instead of true quantum features; a phenomenon called “hallucination”. If it learns these false correlations, the model in question will no longer be able to reliably represent a quantum state or offer information that could help draw scientific conclusions about the quantum system being measured.

“Our main goal was to develop a rigorous approach to verify that the neural network model accurately represents the state in the laboratory, ensuring that scientists can confidently use these models for quantum research,” Huang said.

The new protocol developed by Huang and his colleagues is surprisingly simple, but it has so far proven very effective. Essentially, the approach works by randomly selecting a qubit in the quantum system under examination and measuring a randomly selected Pauli operator in that qubit (i.e. one of three key observable quantum 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 effectively checks whether the target state matches the laboratory state,” Huang explained. “The main advantage is that this only requires single-qubit measurements. No advanced quantum computing capabilities or entanglement 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 maximum entanglement.”

The researchers showed that measuring individual qubits in this random way allowed them to determine whether a multi-qubit system was close to its target quantum state. Their article suggests in particular that their approach could be applicable to the verification of almost all quantum states.

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

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

“We are now exploring the broader implications of this surprising fact that measurements on a single qubit are sufficient to discover a highly nonlocal entanglement structure,” Huang added.

“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 also want to understand the fundamental limits of what can be learned from local measurements and develop efficient quantum learning algorithms that exploit this information.”

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