Researchers at IBM, Cornell, Harvard University, and the Weizman Institute of Science have made two major breakthroughs in the quantum computing revolution. They demonstrated an error-resistant implementation of universal quantum gates and demonstrated the power of a topological quantum computer in solving hard problems that conventional computers couldn’t manage. The researchers demonstrated the ability to encode information by braiding Fibonacci string net condensate (Fib SNC) anyons in two-dimensional space, which is crucial for being fault tolerant and resistant to error. The researchers demonstrated the power of their method on a known hard problem, chromatic polynomials, which originated from a counting problem of graphs with different colored nodes and a few simple rules. The protocol used, sampling the chromatic polynomials for a set of different graphs where the number of colors is the golden ratio, is scalable, so other researchers with quantum computers can duplicate it at a larger scale. Studying topologically ordered many-body quantum systems presents tremendous challenges for quantum researchers. The researchers at IBM were critical in understanding the theory of the topological state and designing a protocol to implement it on a quantum computer. Their other colleagues made essential contributions with the hardware simulations, connecting theory to experiment and determining their strategy. The research was supported by the National Science Foundation, the U.S. Department of Energy, and the Alfred P. Sloan Foundation.