Quantum computers have the capacity to change the landscape of computing. To make these devices robust to experimental imperfections, we require some form of quantum error correction. Current approaches focus on topological codes, as they appear to be in the realm of experimental capabilities. These techniques will likely lead to the first proof of principle of fault tolerance in the next 5 yr. In the long run, however, these approaches require a very large number of physical qubits to construct a fault-tolerant quantum circuit that can run interesting algorithms. As an alternative, it is proposed that quantum low-density parity-check (LDPC) codes could serve as an architecture that circumvents this problem. The best candidate class of quantum LDPC codes were discovered by Tillich and Zémor and are called hypergraph product codes. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold. With these features, they asymptotically offer a smaller overhead compared to topological codes. Here, we demonstrate how to perform Clifford gates on this class of codes using code deformation. To this end, we introduce wormhole defects on hypergraph product codes. Together with state injection, we can perform a universal set of gates within a single block of the class of hypergraph product codes.

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超图产品代码上的容错门

量子计算机具有改变计算领域的能力。为了使这些设备对实验缺陷具有鲁棒性，我们需要某种形式的量子误差校正。当前的方法集中在拓扑代码上，因为它们似乎属于实验能力领域。这些技术可能会在接下来的5年中首次产生容错原理。但是，从长远来看，这些方法需要大量的物理量子位来构建可以运行有趣算法的容错量子电路。作为替代方案，提出了量子低密度奇偶校验（LDPC）码可以用作规避此问题的体系结构。Tillich和Zémor发现了量子LDPC码的最佳候选类别，被称为超图乘积码。这些代码具有恒定的编码率，最近被证明具有恒定的容错错误阈值。具有这些功能，与拓扑代码相比，它们渐近地提供了较小的开销。在这里，我们演示如何使用代码变形在此类代码上执行Clifford门。为此，我们在超图产品代码上引入了虫洞缺陷。与状态注入一起，我们可以在超图乘积代码类的单个块内执行一组通用门。我们在超图产品代码上引入虫孔缺陷。与状态注入一起，我们可以在超图乘积代码类的单个块内执行一组通用门。我们在超图产品代码上引入虫孔缺陷。与状态注入一起，我们可以在超图乘积代码类的单个块内执行一组通用门。