An Upper Bound to the Number of Gates on Single Qubit within One Error-Correction Period of Quantum Computation

TL;DR

This paper establishes an upper bound on the number of logical operations on a single qubit within one error-correction cycle, highlighting fundamental limits for fault-tolerant quantum computing.

Contribution

It introduces a parameter based on quantum Rabi oscillation amplitude to estimate the maximum logical operations per qubit per error-correction period and assesses its decoherence limit.

Findings

The upper bound is constrained by the amplitude behavior of quantum Rabi oscillation.

Even with standard error thresholds, the maximum number of reliable gates per qubit is very small.

Implementing complex fault-tolerant gates like Toffoli within one cycle is highly challenging.

Abstract

Based on the amplitude behavior of quantum Rabi oscillation driven by a coherent field we show that there exists an upper bound to the number of logical operation performed on any single qubit within one error-correction period of a quantum computation. We introduce a parameter to depict the maximum of this number and estimate its decoherence limit. The analysis shows that a generally accepted error-rate threshold of quantum logic gates limits the parameter to so small a number that even a double of fault-tolerant Toffoli gates can hardly be implemented reliably within one error-correction period. This result suggests that the design of feasible fault-tolerant quantum circuits is still an arduous task.