Quantum computer error structure probed by quantum error correction syndrome measurements

With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have directly assessed the performance of superconducting devices implementing heavy-hexagon code syndrome measurements with increasing circuit sizes up to 23 qubits, against the error assumptions underpinning code threshold calculations. Data from 16 repeated syndrome measurement cycles was found to be inconsistent with a uniform depolarizing noise model, favouring instead biased and inhomogeneous noise models. Spatial-temporal correlations investigated via $Z$ stabilizer measurements revealed significant temporal correlation in detection events. These results highlight the non-trivial structure which may be present in the noise of quantum error correction circuits and support the development of noise-tailored codes and decoders to adapt

A scalable and fast artificial neural network syndrome decoder for surface codes

Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabiliser codes, surface code computations consist of a syndrome decoding step where measured stabiliser operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from a variety of noise models including depolarising errors, biased noise, and spatially inhomogeneous noise. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O($\mu$sec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.Comment: 11 pages, 6 figure

Direct observation of narrow electronic energy band formation in 2D molecular self-assembly

Surface-supported molecular overlayers have demonstrated versatility as platforms for fundamental research and a broad range of applications, from atomic-scale quantum phenomena to potential for electronic, optoelectronic and catalytic technologies. Here, we report a structural and electronic characterisation of self-assembled magnesium phthalocyanine (MgPc) mono and bilayers on the Ag(100) surface, via low-temperature scanning tunneling microscopy and spectroscopy, angle-resolved photoelectron spectroscopy (ARPES), density functional theory (DFT) and tight-binding (TB) modeling. These crystalline close-packed molecular overlayers consist of a square lattice with a basis composed of a single, flat-adsorbed MgPc molecule. Remarkably, ARPES measurements at room temperature on the monolayer reveal a momentum-resolved, two-dimensional (2D) electronic energy band, 1.27 eV below the Fermi level, with a width of ∼20 meV. This 2D band results from in-plane hybridization of highest occupied molecular orbitals of adjacent, weakly interacting MgPc's, consistent with our TB model and with DFT-derived nearest-neighbor hopping energies. This work opens the door to quantitative characterisation – as well as control and harnessing – of subtle electronic interactions between molecules in functional organic nanofilms