PIRSA:26010069

Complexity in approximate quantum error correction

Yi, J. (2026). Complexity in approximate quantum error correction. Perimeter Institute. https://pirsa.org/26010069

Yi, Jinmin. Complexity in approximate quantum error correction. Perimeter Institute, Jan. 05, 2026, https://pirsa.org/26010069 

          @misc{ pirsa_PIRSA:26010069,
            doi = {10.48660/26010069},
            url = {https://pirsa.org/26010069},
            author = {Yi, Jinmin},
            keywords = {Other},
            language = {en},
            title = {Complexity in approximate quantum error correction},
            publisher = {Perimeter Institute},
            year = {2026},
            month = {jan},
            note = {PIRSA:26010069 see, \url{https://pirsa.org}}
          }

Jinmin Yi Perimeter Institute for Theoretical Physics

Talk numberPIRSA:26010069
DOI10.48660/26010069
Collection
Talk Type Scientific Series
Subject

Abstract

Quantum codes achieving approximate quantum error correction (AQEC) are useful, and often fundamentally important, from both practical and physical perspectives, yet still lack a systematic understanding. In this talk, we connect AQEC capability to quantum circuit complexity in both all-to-all and geometric settings. We introduce subsystem variance, a parameter closely tied to optimal AQEC precision, and show: (i) if subsystem variance is below an O(k/n) threshold, then every code state obeys circuit-complexity lower bounds; (ii) if two code states admit circuit-complexity upper bounds, then subsystem variance must be Ω(1). Together, these results yield a complete “phase diagram” of AQEC codes. Our theory of AQEC provides a versatile framework for understanding the quantum complexity and order of many-body quantum systems. Applications include complexity constraints for (approximate) QEC codes with transversal logical gates and W-state preparation, as well as new perspectives on topological order, criticality, and Lieb–Schultz–Mattis–type constraints. Ref: arXiv:2310.04710, 2510.04453.