The rapid pace of development in quantum computing technology has sparked a proliferation of benchmarks for assessing the performance of quantum computing hardware and software. Good benchmarks empower scientists, engineers, programmers, and users to understand a computing system's power, but bad benchmarks can misdirect research and inhibit progress. In this Perspective, we survey the science of quantum computer benchmarking. We discuss the role of benchmarks and benchmarking, and how good benchmarks can drive and measure progress towards the long-term goal of useful quantum computations, i.e., "quantum utility". We explain how different kinds of benchmark quantify the performance of different parts of a quantum computer, we survey existing benchmarks, critically discuss recent trends in benchmarking, and highlight important open research questions in this field.

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