Daily Papers

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of Λ = 2.14 pm 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% pm 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 pm 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 μs at distance-5 up to a million cycles, with a cycle time of 1.1 μs. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 times 10^9 cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.

Preparing high-fidelity logical magic states is crucial for fault-tolerant quantum computation. Among prior attempts to reduce the substantial cost of magic state preparation, magic state cultivation (MSC), a recently proposed protocol for preparing T states without magic state distillation, achieves state-of-the-art efficiency. Inspired by this work, we propose a new MSC procedure that would produce a logical T state on a rotated surface code at a further reduced cost. For our MSC protocol, we define a new code family, the RP^2 code, by putting the rotated surface code on RP^2 (a two-dimensional manifold), as well as two self-dual CSS codes named SRP-3 and SRP-5 respectively. Small RP^2 codes are used to hold logical information and checked by syndrome extraction (SE) circuits. We design fast morphing circuits that enable switching between a distance 3 (5) RP^2 code and an SRP-3 (SRP-5) code on which we can efficiently check the correctness of the logical state. To preserve the high accuracy of the cultivated logical T state, we design an efficient and easy-to-decode expansion stage that grows a small RP^2 code to a large rotated surface code in one round. Our MSC protocol utilizes non-local connectivity, available on both neutral atom array and ion trap platforms. According to our Monte Carlo sampling results, our MSC protocol requires about an order of magnitude smaller space-time volume to reach a target logical error rate around 10^{-9} compared to the original MSC protocol.

An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by their different distributions, which has not been taken into account, thus leading to unreasonable distance measurement. Therefore, we propose a cluster-customized distance metric for categorical data clustering, which can competitively update distances based on different distributions of attributes in each cluster. In addition, we extend the proposed distance metric to the mixed data that contains both numerical and categorical attributes. Experiments demonstrate the efficacy of the proposed method, i.e., achieving an average ranking of around first in fourteen datasets. The source code is available at https://anonymous.4open.science/r/CADM-47D8