The Quafu cloud quantum computing platform (CQCP) serves as a bridge connecting quantum computing technology development with algorithmic applications. It holds unique value in promoting the practical implementation of quantum computing technology and fostering the growth of the quantum computing application ecosystem. Since its launch in 2023 by the Beijing Academy of Quantum Information Sciences (BAQIS), Quafu has consistently adhered to principles of openness, stability, and high quality, providing free, high-performance cloud quantum computing services to users worldwide, earning widespread recognition from users around the world. In 2024, BAQIS further enhanced the platform by deploying several quantum cloud systems with scales exceeding 100 qubits, providing users with more diverse and efficient services. Since its inception, Quafu has successfully completed over 5 million quantum computing tasks and has contributed to numerous research achievements. To date, more than 20 scientific papers utilizing the Quafu CQCP have been published.

Recently, a collaborative research team from Shenzhen University and The Chinese University of Hong Kong utilized the ScQ-136 (named as Baiwang) superconducting quantum chip on the Quafu CQCP of BAQIS to experimentally verify the tradeoff relationship for simultaneous measurement of any finite number of incompatible observables. On October 6, 2024, the corresponding results were published in npj Quantum Information entitled “Simultaneous measurement of multiple incompatible observables and tradeoff in multiparameter quantum estimation.”

Non-commutativity is a significant feature that distinguishes quantum theory from the classical one. For incompatible (non-commuting) observables, Heisenberg's uncertainty principle dictates that their simultaneous precise measurement is impossible, requiring approximations in practical scenarios. A central question in understanding and harnessing the full potential of quantum systems is determining how accurately multiple incompatible observables can be captured in a single measurement. The uncertainty relations describing the approximation of non-commuting observables in a single measurement are known as measurement uncertainty relations. Most existing researches have focused on the approximation of two observables in a single measurement. However, many practical applications involve multiple observables, where the errors associated with their simultaneous approximation remain largely unexplored. In this work, the researchers proposed two methods for deriving error-tradeoff relations in the simultaneous measurement of an arbitrary number of observables. The first method provided an analytical tradeoff relation for any number of observables. The second method used semidefinite programming to establish tighter bounds. By combining these two approaches, the research team derived a more stringent analytical equilibrium relationship for two observables than any existing equilibrium relationship. The team further applied these methods to quantum metrology, deriving tighter tradeoff relations for simultaneous multi-parameter estimation, a core topic in modern quantum parameter estimation research.

Furthermore, the researchers experimentally validated their theoretical results using the superconducting quantum chip ScQ-136 (Baiwang) available on the Quafu CQCP of BAQIS. This superconducting chip features a 136-qubit two-dimensional square lattice structure (Figure 1). In this work, specific qubits from the chip were utilized, with qubit fidelities reaching as high as 99%. The “three-state method” was employed to calculate the root mean square (RMS) error (Figure 2a). Experimental results, both for pure and mixed states, were consistent with theoretical predictions, successfully verifying the proposed error-tradeoff relations (Figures 2b and 2c). These findings provided strong experimental support for the theoretical framework.

The first and corresponding author of this work is Hongzhen Chen, assistant professor of Shenzhen University. The primary corresponding author is Haidong Yuan from The Chinese University of Hong Kong, and another corresponding author is Lingna Wang. This research was supported by the funding from the Ministry of Science and Technology, the Research Grants Council of Hong Kong, and the Guangdong Quantum Science Strategic Program. The Quafu CQCP bridged the gap between theoretical derivations and practical experiments, empowering new research efforts and advancing fundamental studies in quantum metrology using cloud-based quantum hardware. The research team expressed their gratitude for the platform’s contribution.

Article link: https://www.nature.com/articles/s41534-024-00894-x

Figure 1: Architecture of the quantum processor “ScQ-P136”.

Figure 2: (a) Scheme diagram for evaluating the mean squared error using the “3-state method”. (b) Error-tradeoff relations for the simultaneous measurement of three spin operators on a pure state. (c) Error-tradeoff relations for the simultaneous measurement of three spin operators on a mixed state.