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Ipsilateral axillary adenopathy post-COVID mRNA vaccine has been widely reported and guidelines for management have been established. Isolated changes of axillary tail trabecular thickening without associated adenopathy in the breast present a diagnostic dilemma and no official guidelines have thus far been reported. This finding has been reported after COVID mRNA vaccine and has never been reported with any other vaccine. We report on a patient with such changes on screening mammography 1.5 months after the fifth dose of a COVID-mRNA vaccine and 1 week after RSV vaccine. This raises the possibility that such changes can be seen with vaccines other than the COVID mRNA series of vaccines. The main differential diagnosis includes mastitis and inflammatory breast cancer. The transient nature of this finding with spontaneous resolution at diagnostic mammography and the vaccination history helps to establish the diagnosis and exclude breast cancer.

It is well understood that a two-dimensional grid of locally interacting qubits is a promising platform for achieving fault-tolerant quantum computing. However in the near future, it may prove less challenging to develop lower-dimensional structures. In this paper, we show that such constrained architectures can also support fault tolerance; specifically we explore a 2×N array of qubits where the interactions between non-neighboring qubits are enabled by shuttling the logical information along the rows of the array. Despite the apparent constraints of this setup, we demonstrate that error correction is possible and identify the classes of codes that are naturally suited to this platform. Focusing on silicon spin qubits as a practical example of qubits believed to meet our requirements, we provide a protocol for achieving full universal quantum computation with the surface code, while also addressing the additional constraints that are specific to a silicon spin-qubit device. Through numerical simulations, we evaluate the performance of this architecture using a realistic noise model, demonstrating that both surface code and more complex quantum low-density parity-check codes efficiently suppress gate and shuttling noise to a level that allows for the execution of quantum algorithms within the classically intractable regime. This work thus brings us one step closer to the execution of quantum algorithms that outperform classical machines.

Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may correspond to individual qubits or to clusters and could potentially disrupt the code sufficiently to generate logical errors. In this paper, we explore a novel $adaptive$ approach for surface code quantum error correction on a defective lattice. We show that combining an appropriate defect detection algorithm and a quarantine of the identified zone allows one to preserve the advantage of quantum error correction at finite code sizes, at the cost of a qubit overhead that scales with the size of the defect. Our numerics indicate that the code's threshold need not be significantly affected; for example, for a certain scenario where small defects repeatedly arise in each logical qubit, the noise threshold is $2.7\%$ (versus the defect-free case of $2.9\%$). These results pave the way to the experimental implementation of large-scale quantum computers where defects will be inevitable.

Many quantum computing platforms are based on a two-dimensional (2D) physical layout. Here we explore a concept called looped pipelines, which permits one to obtain many of the advantages of a three-dimensional (3D) lattice while operating a strictly 2D device. The concept leverages qubit shuttling, a well-established feature in platforms like semiconductor spin qubits and trapped-ion qubits. The looped-pipeline architecture has similar hardware requirements to other shuttling approaches, but can process a stack of qubit arrays instead of just one. Even a stack of limited height is enabling for diverse schemes ranging from NISQ-era error mitigation through to fault-tolerant codes. For the former, protocols involving multiple states can be implemented with a space-time resource cost comparable to preparing one noisy copy. For the latter, one can realize a far broader variety of code structures; as an example we consider layered 2D codes within which transversal cnots are available. Under reasonable assumptions this approach can reduce the space-time cost of magic state distillation by 2 orders of magnitude. Numerical modeling using experimentally motivated noise models verifies that the architecture provides this benefit without significant reduction to the code’s threshold.