Bounding Rounding Errors in the Simulation of Quantum Circuits

Quantum simulators are a ubiquitous part of quantum software development. This is especially true for the current NISQ-era but will probably remain true for a long time as error-free controlled testing is hardly possible on real devices. However, quantum simulators are implemented in classical languages and thus fall prey to rounding errors. We present bounds on these errors based on the number of gates and qubits alone. This can be crucial to rule out rounding errors prior to executing the circuit. Additionally, we show that these theoretical bounds are sufficient to essentially rule out relevant rounding errors for the simulation of small to medium-sized circuits and even for larger circuits under the assumption that only 1- and 2-qubit gates are used.