Quantum software testing is an emerging research area that currently lacks systematic benchmarks to assess the effectiveness of testing techniques. Recently, some open-source benchmarks for quantum circuits and quantum software bugs have been introduced, along with some mutation analysis tools. Despite these advances, there is still little understanding of how factors such as quantum circuit characteristics (e.g., number of qubits, circuit depth), algorithms (e.g., Quantum Phase Estimation), and mutation characteristics (e.g., mutation operators) influence mutant detection in quantum circuits. Gaining a better understanding of these relations would enable the design of faulty benchmarks with diverse attributes, such as different levels of fault detection difficulty, which would help evaluate the cost-effectiveness of quantum software testing techniques more effectively. In this study, we conduct the largest empirical study to date on quantum circuit mutants, analyzing over 700,000 faulty benchmarks produced by mutating 382 real-world quantum circuits. To evaluate how easy it is to detect a mutant with certain characteristics, we defined the survival rate, a new metric that quantifies the proportion of undetected mutants in the set of mutants with those same characteristics. This empirical study provides essential insights into mutants of quantum circuits, aiming to enhance the knowledge of developers and researchers in the field. We also present a tool that recommends mutants to users based on selected characteristics, such as a specific type of quantum algorithm and the desired survival rates, along with faulty benchmarks to evaluate the cost-effectiveness of testing techniques for quantum software.