Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation.
The detection of gravitational waves from a neutron star merger, GW170817, marked the dawn of a new era in time-domain astronomy. Monitoring of the radio emission produced by the merger, including high-resolution radio imaging, enabled measurements of merger properties including the energetics and inclination angle. In this work we compare the capabilities of current and future gravitational wave facilities to the sensitivity of radio facilities to quantify the prospects for detecting the radio afterglows of gravitational wave events. We consider three observing strategies to identify future mergers – widefield follow-up, targeting galaxies within the merger localisation and deep monitoring of known counterparts. We find that while planned radio facilities like the Square Kilometre Array will be capable of detecting mergers at gigaparsec distances, no facilities are sufficiently sensitive to detect mergers at the range of proposed third-generation gravitational wave detectors that would operate starting in the 2030s.
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