The limits of quantum circuit simulation with low precision arithmetic

Abstract: This is an investigation of the limits of quantum circuit simulation with Schrodinger's formulation and low precision arithmetic. The goal is to estimate how much memory can be saved in simulations that involve random, maximally entangled quantum states. An arithmetic polar representation of $B$ bits is defined for each quantum amplitude and a normalization procedure is developed to minimize rounding errors. Then a model is developed to quantify the cumulative errors on a circuit of $Q$ qubits and $G$ gates. Depending on which regime the circuit operates, the model yields explicit expressions for the maximum number of effective gates that can be simulated before rounding errors dominate the computation. The results are illustrated with random circuits and the quantum Fourier transform.