Asymmetric quantum error correction efficiently tackles application-specific noise effects

Abstract

Noise is a major challenge for current quantum computers. It can be broadly categorized into bit-flip and phase-flip errors. These two types do not necessarily affect the executed algorithm, thus also the application, in the same way. We illustrate this general effect for the example of the quantum approximate optimization algorithm (QAOA) applied to a small instance of the flight-gate assignment (FGA) problem. We compare bit-flip and phase-flip Pauli noise under both layer-level and gate-level noise models, using two circuit decompositions of the same ideal QAOA unitary: a CNOT-based decomposition and a native-$R_{ZZ}$ decomposition. In the simulations, bit-flip noise produces the larger degradation in the performance of the quantum optimization. The asymmetry is most visible in the layer-level and native-$R_{ZZ}$ simulations. We explain this by how the errors affect mixing, final measurements, and how they propagate inside the circuit. We then exploit these insights to tackle noise particularly efficiently using asymmetric error-correcting codes. As an illustration, we use the quantum parity code (QPC), a generalization of the 9-qubit Shor code, and show that a smaller asymmetric code can achieve nearly the same improvement as a larger symmetric choice. This demonstrates that error-correction resources should be assigned not only according to physical error rates, but also according to how strongly each error channel affects the application. As a result, asymmetric quantum error correction proves useful even in cases where the noise model is symmetric. Finally, we discuss how information about the noise obtained through calibration can be exploited in our approach.