Noisy Intermediate-Scale Quantum Algorithms: Opportunities, Limitations, and Lessons

Noisy intermediate-scale quantum (NISQ) devices represent the first generation of programmable quantum hardware capable of exploring regimes beyond classical simulation, yet they operate without full error correction and under severe noise and resource constraints. In this talk, I will review the core ideas underlying NISQ-era quantum algorithms, focusing on variational and hybrid quantum classical approaches and their applications across quantum chemistry, optimization, and many-body physics. I will discuss what these algorithms can and fundamentally cannot achieve in the presence of noise, limited circuit depth, and finite sampling, highlighting key theoretical insights and experimental lessons that have shaped the field over the past decade.

Beyond the physics, I will share the narrative behind the writing of our Reviews of Modern Physics article, including how we identified unifying themes in a rapidly evolving literature, balanced optimism with rigor, and structured a review intended to be accessible to non-specialists while remaining useful to experts. I will conclude with my perspective on open challenges and promising future directions for NISQ algorithms, as well as reflections on how comprehensive reviews can help guide fast-moving areas of modern physics.