论文标题
通过测量在稳定器代码上实施克利福德大门
Implementing Clifford Gates on Stabilizer Codes via Measurement
论文作者
论文摘要
我们描述了一种使用测量和校正操作的方法，以便在稳定器代码中实现Clifford组，从而将[Bombin，2011]的结果概括为拓扑子系统颜色代码。在距离的子系统稳定器中，距离至少$ 3 $可以实现故障。特别是，这提供了一种方法，可以通过测量和纠正三个可观察结果，在15 Quibit Reed-Muller量子代码中实现逻辑HADAMARD型门。这是[Paetznick and Reichardt，2013]提出的方法生成一组门的一种替代方法，该门是通用该代码的量子计算的通用。该构建的灵感来自[Colladay and Mueller，2018]的代码重新布线的描述。 受[Colladay和Mueller，2018]的代码重新布线策略的启发，我们描述了一种使用测量和校正操作的方法，以便在任何稳定器代码的代码空间中实现Clifford组，并在整个稳定器代码的代码空间中实现了一套足够的条件。特别地，这提供了一种方法，可以通过测量和纠正两个可观察到的逻辑HADAMARD型门在15 Quibit Reed-Muller量子代码中实现逻辑，从而提供了两个可观察到的物品，从而提供了通用性所需的唯一非转换门。此外，此方法适用于复曲面代码和量子LDPC代码
We describe a method to use measurements and correction operations in order to implement the Clifford group in a stabilizer code, generalising a result from [Bombin,2011] for topological subsystem colour codes. In subsystem stabilizer codes of distance at least $3$ the process can be implemented fault-tolerantly. In particular this provides a method to implement a logical Hadamard-type gate within the 15-qubit Reed-Muller quantum code by measuring and correcting only three observables. This is an alternative to the method proposed by [Paetznick and Reichardt, 2013] to generate a set of gates which is universal for quantum computing for this code. The construction is inspired by the description of code rewiring from [Colladay and Mueller, 2018]. Inspired by the code rewiring strategy of [Colladay and Mueller, 2018], we describe a method to use measurements and correction operations in order to implement the Clifford group in the code space of any stabilizer code, and we specify a sufficient set of conditions under which the distance of the code is preserved throughout. In particular this provides a method to implement a logical Hadamard-type gate within the 15-qubit Reed-Muller quantum code by measuring and correcting only two observables, providing the only non-transversal gate required for universality. Furthermore this approach is applicable to the toric code and quantum LDPC code
