On Rounding Errors in the Simulation of Quantum Circuits

Jonas Klamroth, Bernhard Beckert

Abstract: The realm of quantum computing is inherently tied to real numbers. However, quantum simulators nearly always rely on floating-point arithmetic and thus may introduce rounding errors in their calculations. In this work, we show how we can nevertheless trust the computations of simulators under certain conditions where we can rule out that floating-point errors disturb the obtained measurement results. We derive theoretical bounds for the errors of floating-point computations in quantum simulations and use these bounds to extend the implementation of an existing verification tool to show the soundness of the tool’s analysis for a number of well-established quantum algorithms.