Quantum algorithm design and quantum control are both key elements of quantum computing research. They represent two complementary yet historically distinct domains at the heart of quantum information science, and provide new paradigms for understanding many-body physics, non- equilibrium physics, and quantum matter. Quantum algorithms focus on designing continuous or discrete operations that can outperform classical computation, where computational power and complexity are intimately linked to complex phases of many-body systems. As a realization of quantum algorithms, quantum circuits can be viewed as dynamical processes that direct a many-body quantum system out of equilibrium. Quantum control, on the other hand, seeks to manipulate physical systems and quantum dynamics with precision and robustness. And, within these non-equilibrium dynamics, a new emerging concept is feedback control. Such feedback-controlled systems will have distinct dynamics, phase transitions, critical behavior and universality that is yet to be discovered.

As quantum computers and devices approach scales where control imperfections, noise, and limited resources become the main bottlenecks, the interplay between quantum algorithms and quantum control has emerged as a critical frontier to enable practical realizations of quantum error correction. A deeper integration of algorithmic and control perspectives, including mid-circuit measurement and feedforward, with many-body and non-equilibrium physics could reshape how we design, optimize, and implement quantum computation, enabling more efficient use of both near-term hardware and scalable fault-tolerant quantum computers. As their physical counterparts, novel quantum error correction and fault-tolerance concepts can inspire new discoveries of quantum matter in regimes that have not been experimented with before.