Improved Bounds for Rounding Errors in Quantum Circuit Simulators

Simulators play a crucial role in the development of quantum software, yet they differ from actual quantum devices in that their computations are carried out using floating-point arithmetic rather than real arithmetic. In [7], we introduced bounds on the errors that may arise due to these discrepancies. In the present work, we extend and refine these bounds, demonstrating that we can achieve tighter estimates that scale more efficiently with the number of gates in a quantum circuit. Furthermore, the newly derived bounds can be computed with minimal relaxation, making them practically applicable. We show that these improved bounds are effective in excluding significant errors across a wide range of quantum circuits, thus providing a more reliable framework for simulating quantum systems.