The pace and unpredictability of evolution are critically relevant in a variety of modern challenges: combating drug resistance in pathogens and cancer, understanding how species respond to environmental perturbations like climate change, and developing artificial selection approaches for agriculture. Great progress has been made in quantitative modeling of evolution using fitness landscapes, allowing a degree of prediction for future evolutionary histories. Yet fine-grained control of the speed and the distributions of these trajectories remains elusive. We propose an approach to achieve this using ideas originally developed in a completely different context -counterdiabatic driving to control the behavior of quantum states for applications like quantum computing and manipulating ultra-cold atoms. Implementing these ideas for the first time in a biological context, we show how a set of external control parameters (i.e. varying drug concentrations / types, temperature, nutrients) can guide the probability distribution of genotypes in a population along a specified path and time interval. This level of control, allowing empirical optimization of evolutionary speed and trajectories, has myriad potential applications, from enhancing adaptive therapies for diseases, to the development of thermotolerant crops in preparation for climate change, to accelerating bioengineering methods built on evolutionary models, like directed evolution of biomolecules.The quest to control evolutionary processes in areas like agriculture and medicine predates our understanding of evolution itself. Recent years have seen growing research efforts toward this goal, driven by rapid progress in quantifying genetic changes across a population 1-3 as well as a global rise in challenging problems like therapeutic drug resistance 4-6 . New approaches that have arisen in response include prospective therapies that steer evolution of pathogens toward maximized drug sensitivity 7, 8 , typically requiring multiple rounds of selective pressures and subsequent evolution under them. Since we cannot predict the exact progression of mutations that occur in the course of the treatment, the best we can hope for is to achieve control over probability distributions of evolutionary outcomes. However, our lack of precise control over the timing of these outcomes poses a major practical impediment to engineering the course of evolution. This naturally raises a question: Rather than being at the mercy of evolution's unpredictability and pace, what if we could simultaneously control the speed and the distribution of genotypes over time?Controlling an inherently stochastic process like evolution has close parallels to problems in other disciplines.Quantum information protocols crucially depend on coherent control over the time evolution of quantum states under external driving 9, 10 , in many cases requiring that a system remain in an instantaneous ground state of a time-varying Hamiltonian in applications like cold atom transport 11 and quantum adiabatic computat...