Optimal control with flag qubits

TL;DR

This paper introduces Flag-GRAPE, a novel optimal control method using flag ancillas to actively reduce decoherence in quantum systems, improving fidelity and compatibility with error correction.

Contribution

The paper presents a new control framework with flag ancillas and the Flag-GRAPE algorithm that actively tailors noise structure and integrates post-selection, surpassing traditional methods.

Findings

Achieves 51% reduction in infidelity in superconducting circuits

Enhances robustness across broad noise regimes

Improves logical state preparation when combined with quantum error correction

Abstract

High-fidelity quantum operations are the cornerstone of fault-tolerant quantum computation. In open quantum systems, traditional optimal control only passively resists decoherence, leaving environment-induced uncertainty as a fundamental performance bottleneck. To overcome this, we propose a new optimal control framework with flag ancillas and the Flag-GRAPE algorithm, which can actively tailor the system's noise structure. Through embedding post-selection directly into the objective function, Flag-GRAPE correlates decoherence errors with the ancilla's unexpected state. Subsequent measurement and post-selection effectively expel this uncertainty, circumventing the fidelity bounds of traditional control. Numerical simulations in a superconducting quantum circuit demonstrate a $51\%$ reduction in infidelity compared to traditional closed-system pulses and also show that such enhancement is robust across broad noise regimes. Furthermore, by actively converting unstructured decoherence into heralded erasure errors, Flag-GRAPE is inherently compatible with quantum error correction. We demonstrate this by initializing a logical cat-code state, showing that the combination between Flag-GRAPE and QEC yields immediate state preparation enhancements. This new framework can reduce hardware overhead for fault-tolerant architectures and open up a practical path toward logical state preparation gain in near-term experiments.