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An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomenon of fragile temporal boundaries that arises during the standard logical state-preparation and measurement protocols. To address this challenge we propose a new logical state-preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure $O\left(\sqrt{n}\right)$high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard protocol in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement. Published by the American Physical Society2024 

Highly efficient air electrodes are a key component of reversible fuel cells for energy storage and conversion; however, the development of efficient electrodes that are stable against water vapor remains a grand challenge. Here we report an air–electrode, composed of double perovskite material PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) backbone coated with nanoparticles (NPs) of BaCoO 3−δ (BCO), that exhibits remarkable electrocatalytic activity for oxygen reduction reaction (ORR) while maintaining excellent tolerance to water vapor. When tested in a symmetrical cell exposed to wet air with 3 vol% H 2 O at 750 °C, the electrode shows an area specific resistance of ∼0.03 Ω cm 2 in an extended period of time. The performance enhancement is attributed mainly to the electrocatalytic activity of the BCO NPs dispersed on the surface of the porous PBCC electrode. Moreover, in situ Raman spectroscopy is used to probe reaction intermediates ( e.g. , oxygen species) on electrode surfaces, as the electrochemical properties of the electrodes are characterized under the same conditions. The direct correlation between surface chemistry and electrochemical behavior of an electrode is vital to gaining insight into the mechanisms of the electrocatalytic processes in fuel cells and electrolysers.