Everything You Always Wanted to Know about Quantum Circuits

Abstract Quantum circuits are needed to realize the performance gains offered by quantum algorithms. We introduce the design and resource cost assessment of quantum circuits. We illustrate the design process through the development of quantum circuits for arithmetic computations as well as quantum datapaths for the image rotation task. This article opens by introducing physical properties unique to quantum computation. We then turn to quantum gates, quantum circuits, and how we measure the resource costs of a given quantum circuit. Resource cost measures for both NISQ computation and fault‐tolerant quantum computation are shown. We then present quantum circuits for arithmetic operations. Architectures for addition, subtraction, multiplication, and division are shown. The operation and design of each quantum arithmetic circuit are outlined. Using the arithmetic circuits presented as examples, we show how to calculate quantum circuit resource costs for both NISQ and fault‐tolerant quantum computation. This article concludes by illustrating the design of quantum datapaths for the image rotation operation.