Quantum information science a research field of physics and computer science that studies the fundamental properties of quantum systems and how they can be used in information processing tasks, including quantum cryptography, quantum computing, and quantum metrology.
Quantum computing, one of the most important areas in the field, is believed to outperform its classical counterpart in certain tasks. Based on the principles of quantum mechanics, quantum computers use qubits instead of binary bits to store and process information. The qubits have the remarkable property of superposition, allowing them to exist in multiple states at once and perform certain computations faster and more efficiently than classical computers. This leads to exponential speed-ups in tasks such as factoring large numbers and simulating quantum systems. As such, quantum computing is widely regarded as one of the most essential directions in the post-Moore era.
In reality, with the scaling up of quantum devices, the increasing hardware noises may limit the performances of quantum computing and impede the realization of quantum advantages. Fast and reliably characterizing device errors are essential for high-precision large-scale quantum computers. Randomized benchmarking was proposed to estimate the average fidelity of a quantum process. However, conventional randomized benchmarking methods are limited to the Clifford gate set, which are not universal gate set, and suffer from complicated implementations of numerous multi-qubit twirling gates in practice. How to efficiently and reliably estimate the fidelity of a large-scale quantum process from a universal gate set remains an open problem.
To address the problems, a joint research group led by Prof. Xiongfeng Ma from Tsinghua University reported and numerically demonstrated two practical protocols, character-cycle benchmarking (CCB) protocol and a character-average benchmarking (CAB) protocol, with more efficiency and reliability for quantum operation characterizations.
The proposed proposals make use of local twirling gates to estimate the process fidelity of an individual multi-qubit operation. The relevant research results were published in Photonics Research, Volume 11, No. 1, 2023 (Yihong Zhang,Wenjun Yu, Pei Zeng, Guoding Liu, and Xiongfeng Ma, Scalable fast benchmarking for individual quantum gates with local twirling, Photonics Research, 2023, 11(1): 81).
The schematic circuit of the CCB and CAB protocols are shown in Fig.1, where the target quantum operation to be characterized is twirled by the local gates. The main difference between the CAB and CCB protocols is the additional local Clifford gates at the beginning and end of the circuit, which can largely decrease the sampling complexity for gate characterization.
Fig. 1. Illustrations of circuit and procedures used in (a) CCB and (b) CAB protocols. The orange boxes represent the target gate U and its inverse gate U^-1. The blue and green boxes represent the random Pauli gate and random local Clifford gate. The yellow boxes denote the inverse gate for the m inner gate layers in the light blue box.
It is worth noting that our protocols have the ability to characterize a large class of quantum gates including and beyond the Clifford group via the local gauge transformation, which forms a universal gate set for quantum computing. Such extension can be seen as a significant improvement over standard randomized benchmarking methods.
As concrete examples, we numerically demonstrate our protocols for a non-Clifford gate, controlled-(TX), and a five-qubit quantum error-correcting encoding circuit. The simulation results show that our protocols can estimate the fidelity of individual quantum operations reliably and efficiently. Furthermore, we compare with another advanced method called cross-entropy benchmarking proposed by the Google team and show that the CAB protocol achieves three orders of magnitude improvements in terms of the sampling complexity, as shown in Fig. 2.
Fig. 2. Simulation results for the 5-qubit quantum error correcting encoding circuit with a noise channel. The theoretical process fidelity is 94.70%. (a) Box plot of the CAB fidelities. (b) Box plots of the CAB and XEB fidelities. The green dashed line represents the theoretical process fidelity.
Our protocols preserve the simplicity and robustness of conventional randomized benchmarking methods. As Prof. Xiongfeng Ma said 'we are confident that our protocols will drive the progress of universal fault-tolerant quantum computing.' Additionally, exploring the possibility of extending our randomization and estimation methods to characterize other properties such as unitarity and coherence would be a valuable direction for future research.
