Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class—number-phase codes—which includes the well-known cat and binomial codes, among many others. The entangling gate in our scheme is code-agnostic and can be used to interface different rotation-symmetric encodings. In addition to a universal set of operations, we propose a teleportation-based error correction scheme that allows recoveries to be tracked entirely in software. Focusing on cat and binomial codes as examples, we compute average gate fidelities for error correction under simultaneous loss and dephasing noise and show numerically that the error-correction scheme is close to optimal for error-free ancillae and ideal measurements. Finally, we present a scheme for fault-tolerant, universal quantum computing based on concatenation of number-phase codes and Bacon-Shor subsystem codes.

中文翻译：

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旋转对称的玻色子代码的量子计算

这里介绍的Bosonic旋转码是基于相空间旋转对称性的一类广泛的Bosonic纠错码。我们提出了适用于此类子集的通用量子计算方案-数相代码-其中包括众所周知的cat码和二项式代码以及许多其他代码。我们方案中的纠缠门是与代码无关的，可用于接口不同的旋转对称编码。除了通用的操作集外，我们还提出了一种基于隐形传态的纠错方案，该方案允许完全在软件中跟踪恢复。以猫和二项式代码为例，我们计算了在同时损失和移相噪声的情况下进行纠错的平均门保真度，并通过数字显示了纠错方案接近于无误差辅助和理想测量的最优值。最后，我们提出了一种基于数相代码和Bacon-Shor子系统代码的串联的容错通用量子计算方案。