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In collaboration with the University of Science and Technology of China, the Center for Quantum Information (CQI) at Tsinghua University demonstrated error-transparent operations on a logical qubit protected by quantum error correction (QEC). This work was recently published online in Nature Physics, s41567-020-0893-x.

Quantum computers promise to exponentially or dramatically exceed classical computers on certain problems. However, quantum information is fragile and quantum operations are not accurate enough to solve practical problems due to the inevitable environmental noise. In order to overcome these difficulties, fault-tolerant quantum computing is proposed and requires the protection of not only logical qubits that store quantum information, but also the processing of quantum information. Over recent years, QECs of quantum information have been demonstrated in various experimental platforms. However, it is still challenging to perform fault-tolerant quantum gate operations on logical qubits protected by QEC.

In standard logical qubit schemes based on architectures consisting of multiple physical qubits, transversal gates and magic-state distillation are developed theoretically for performing fault-tolerant gates on the logical qubits, but the implementations are extremely challenging. An alternative approach of fault-tolerant operations has been proposed based on the concept of error-transparent (ET) gates. However, the implementation of ET gates in the multi-qubit QEC codes also requires many-body interactions and is hard to realize experimentally. The group at CQI of Tsinghua University extends the concept of ET gates to bosonic QEC codes and experimentally demonstrates the ET phase gates on a single logical qubit that can tolerate errors occurring during the gate operations.

The hybrid quantum system that the group investigates consists of a superconducting qubit and a bosonic microwave cavity. Quantum information is encoded on superpositions of photon Fock states in the cavity with carefully chosen binomial coefficients, which can correct single photon losses, the dominant error channel of this system. In 2019, the group demonstrated QEC and universal gate set operation on this binomially encoded logical qubit (Nature Physics 15, 503–508 (2019)). In order to further tolerate the single-photon-loss error during the gate operation, ET gates require the dynamical evolutions of the logical qubit under the gate Hamiltonian are identical in both the code and error spaces. Therefore, the group developed a new technique, called photon-number-resolved ac Stark shift, to tune the frequency of each Fock state in the cavity precisely such that the ET condition is fulfilled. Their experiment demonstrated that the ET gates on the logical qubit indeed significantly outperform the regular gate with a higher gate fidelity when an error occurs during the gate operation. Furthermore, the lifetime of the logical qubit under repetitive and interleaved ET gates and QEC is longer than that with the regular gate.

This experiment of realizing ET phase gates represents important progress in QEC in recent years. The demonstrated ET gates can be readily extended to Hadamard gate and two-qubit gate for a universal ET gate set on the logical qubits. The ET gates and the bosonic QEC codes thus offer the potential for reliable quantum computation.

The corresponding authors of this work are Luyan Sun from Tsinghua University and Changling Zou from the University of Science and Technology of China. The first author is IIIS PhD candidate Yuwei Ma, and other authors include Yuan Xu, Xianghao Mu, Weizhou Cai, Ling Hu, Weiting Wang, Xiaoxuan Pan, Haiyan Wang, and Yipu Song, all from Tsinghua University. This work is supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, and the Anhui Initiative in Quantum Information Technologies.

Link:Nat. Phys. s41567-020-0893-x (2020)