The limits of quantum circuit simulation with low precision arithmetic

TL;DR

This paper explores the potential for memory savings in quantum circuit simulations using low precision arithmetic, analyzing error accumulation and maximum effective gates through a new model and practical examples.

Contribution

It introduces a polar representation for quantum amplitudes and a normalization method to reduce rounding errors, providing explicit error bounds for low precision quantum simulations.

Findings

Memory can be significantly reduced in quantum simulations with low precision arithmetic.

The model predicts the maximum number of gates before rounding errors become dominant.

Results are demonstrated on random circuits and the quantum Fourier transform.

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.