With the advance in quantum computing in recent years, quantum software becomes vital for exploring the full potential of quantum computing systems. Quantum programming is different from classical programming, for example, the state of a quantum program is probabilistic in nature, and a quantum computer is error-prone due to the instability of quantum mechanisms. Therefore, the characteristics of bugs in quantum software projects may be very different from that of classical software projects. This work aims to understand the characteristics of bugs in quantum software projects, in order to provide insights to help devise effective testing and debugging mechanisms. To achieve this goal, we conduct an empirical study on the bug reports of 125 quantum software projects. We observe that quantum software projects are more buggy than classical software projects and that quantum project bugs are more costly to fix than classical project bugs. We also identify the types of the bugs and the quantum programming components where they occurred. Our study shows that the bugs are spread across different components, but quantum-specific bugs particularly appear in the compiler, gate operation, and state preparation components. The three most occurring types of bugs are Program anomaly bugs, Configuration bugs, and Data type and structure bugs. Our study highlights some particularly challenging areas in quantum software development, such as the lack of scientific quantum computation libraries that implement comprehensive mathematical functions for quantum computing. Quantum developers also seek specialized data manipulation libraries for quantum software engineering like Numpy for quantum computing. Our findings also provide insights for future work to advance the quantum program development, testing, and debugging of quantum software, such as providing tooling support for debugging low-level circuits.