Effect on ion-trap quantum computers from the quantum nature of the driving field

Abstract

In this study, we evaluate the effect on ion-trap quantum computers (QCs) from the quantum nature of the driving field, and propose a theoretical limit for ion-trap QCs that may impact the design of quantum algorithms and realization of practical QCs. We obtain, for the first time, the permitted depth of logical operation for fault-tolerant ion-trap QCs. Physically, we provide an exact (full-quantum) description of the QC system, and present for the first time its time evolution after gate operations; mathematically, we solve problems such as certain summations of trigonometric series with any given precision. Comparing the actual state after CNOT gates driven by a quantized field with the expected state, we obtain the failure probability and estimate that the numberof CNOT gates on the same pair of physical qubits is notmore than $10^2$ in one error-correction period, which is a physical limit that cannot be easily overcome. The conclusion can help determine the number of CNOT operations between coding and decoding in one error-correction period and can be used as a reference for quantum algorithm design.