Within the next decade, quantum computing has the potential to provide insight to problems in physics and chemistry that would otherwise be intractable. Examples of such problems span from predicting molecular spectra to simulating field theories to probing the dynamics of spin models. Because large fault tolerant machines are still in the distant future, it will be important to design algorithms customized to current and near-term experimental hardware with a focus on NISQ (noisy-intermediate-scale quantum) devices as well as early fault tolerant machines. In order for quantum computational approaches to compete effectively with the best classical methods for simulation, it will be necessary to leverage every trick discovered in the “classical” quantum community and so we encourage the participation of those who have backgrounds in classical simulations of quantum many-body physics but might be new to quantum computation.This program will encourage exploration of both physics-based and complexity theoretic approaches to assessing which systems are most challenging for classical simulations, novel ways of using the resources provided by NISQ processors, and strategies for significantly reducing the costs of fault-tolerant quantum simulations. The program will bring together diverse communities and viewpoints at the intersection of error-correction, many-body physics, and quantum algorithms to tackle these problems.