Quantum error correction and quantum error detection necessitate syndrome measurements to detect errors. Performing syndrome measurements for each stabilizer generator can be a significant overhead, considering the fact that the readout fidelity in the current quantum hardware is generally lower than gate fidelity. Here, by generalizing a quantum error mitigation method known as symmetry expansion, we propose a protocol called virtual quantum error detection (VQED). This method virtually allows for evaluating computation results corresponding to post-selected quantum states obtained through quantum error detection during circuit execution, without implementing syndrome measurements. Unlike conventional quantum error detection, which requires the implementation of Hadamard test circuits for each stabilizer generator, our VQED protocol can be performed with a constant depth shallow quantum circuit with an ancilla qubit, irrespective of the number of stabilizer generators. Furthermore, for some simple error models, the computation results obtained using VQED are robust against the noise that occurred during the operation of VQED, and our method is fully compatible with other error mitigation schemes, enabling further improvements in computation accuracy and facilitating high-fidelity quantum computing.
Error-mitigated quantum metrology via enhanced virtual purification
The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Institute of Quantum Information Science and Technology, The Chinese University of Hong Kong（香港量子信息科学与技术研究院，香港中文大学）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（量子信息技术与材料国家重点实验室，香港中文大学）；College of Computer and Data Science, Fuzhou University（福州大学计算机与数据科学学院）
Error Mitigation in Bosonic Systems via Virtual Distillation
Chalmers University of Technology（查尔姆斯理工大学）；École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Université libre de Bruxelles（布鲁塞尔自由大学）；International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）；University of Minho（米尼奥大学）
Virtual purification complements quantum error correction in quantum metrology
Sejong University（世宗大学）；University of Chicago（芝加哥大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Chungbuk National University（忠北国立大学）；Korea Institute for Advanced Study（韩国高等研究院）；Seoul National University（首尔大学）；Pohang University of Science and Technology (POSTECH)（浦项工科大学）
