When will quantum computing be a big deal?

Quantum computing has been hyped as the next revolution in computation. Is it true? Why have we not heard of huge scientific breakthroughs yet? While quantum computers do now exist, near-term quantum computers do not yet have extensive error correction and they primarily operate by applying unitary operations to a quantum state stored in the qubits. We all want to know whether we can do cutting edge science on these devices. In this talk, I will describe the types of scientific problems that are likely to lead to new scientific breakthroughs even before fault-tolerant quantum computing is available. These scientific problems can be simulated robustly even in the presence of noise and decoherence. Two problems that fall into this class are those that involve topological effects and those that involve the many-body problem in a driven and dissipative environment. I will show how both problems are robust on near-term quantum computers and what work remains to be done for them to lead to new scientific breakthroughs. Once successful, quantum computers can be employed to analyze topological properties of complex quantum systems, and we can describe the behavior of many nonequilibrium quantum systems, such as pump-probe experiments. Many of these applications are the hardest scientific problems that physicists are currently working on. In addition, I will discuss the challenges in quantum chemistry, which has been often discussed as the most likely first application of quantum computing to science. I will describe what is needed for advances in that problem as well, especially how one can use low-depth circuits (with many measurements) to solve complex problems. This talk will assume no prior expertise in quantum computing and only an undergraduate-level familiarity with quantum mechanics.