This interdisciplinary program seeks to bridge quantum error correction and many-body physics paradigms and is stimulated by recent demonstrations of early quantum error correction and fault tolerance in programmable quantum computing platforms. A promising perspective on robustness against noise, such as the threshold theorem for fault tolerant quantum computation, is through the viewpoint of stable “dynamical phases” in which quantum information remains protected for sufficiently weak noise due to active error correction. Following the recent experimental advances, it is timely to extend the classification to noise-robust dynamical phases and to address several central questions including:

• What is the emergent statistical mechanics and universal many-body physics of fault-tolerant systems below threshold and near their critical point?
• How can we characterize and classify distinct phases of matter based on their ability to store and process encoded quantum information?
• How do we manipulate, describe, and decode the dynamics of encoded quantum information during noisy computation?
• Can we classify fault-tolerant algorithms as a phase of a quantum process?