PIRSA:22120025

Quantum Error Mitigation and Error Correction: a Mathematical Approach

Cao, N. (2022). Quantum Error Mitigation and Error Correction: a Mathematical Approach . Perimeter Institute. https://pirsa.org/22120025

Cao, Ningping. Quantum Error Mitigation and Error Correction: a Mathematical Approach . Perimeter Institute, Dec. 05, 2022, https://pirsa.org/22120025 

          @misc{ pirsa_PIRSA:22120025,
            doi = {10.48660/22120025},
            url = {https://pirsa.org/22120025},
            author = {Cao, Ningping},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum Error Mitigation and Error Correction: a Mathematical Approach },
            publisher = {Perimeter Institute},
            year = {2022},
            month = {dec},
            note = {PIRSA:22120025 see, \url{https://pirsa.org}}
          }

Ningping Cao

University of Waterloo

Talk number
PIRSA:22120025
Collection
Talk Type
Subject
Abstract

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, has a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). We examine the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace-preserving while the commonly-used MoorePenrose pseudoinverse may not be. Finally, we study the consequences of having imperfect knowledge about system noise and derive conditions when noise can be reduced using QEM.

Zoom link:  https://pitp.zoom.us/j/91543402893?pwd=b09IS3VWNk5KZi8ya3gzSmRKRFJidz09