发表机构
UC Berkeley; Simons Institute for the Theory of Computing; Department of EECS, UC Berkeley; Departments of EECS & Mathematics, UC Berkeley（加州大学伯克利分校; 西蒙斯理论计算研究所; 加州大学伯克利分校电气工程和计算机科学系; 加州大学伯克利分校电气工程和计算机科学系及数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造了首个常数开销的容错量子态注入方案，通过高维超图积码实现常数深度和线性物理开销，并级联内码以应对均匀噪声。
AI 中文摘要
我们构造了首个已知的具有常数空间和时间开销的容错方案，用于将量子态注入到量子纠错码中。即，我们构造了一族常数速率的量子纠错码，对于这些码，一组裸物理量子比特可以被注入，即容错地编码，到一个码块中。类似地，一个码态可以被弹出，即容错地解码，回到裸物理量子比特。我们证明了这些注入和弹出过程在电路级局部随机噪声下成功，同时仅以很小的常数概率损坏每个量子比特，这对于裸物理量子比特是不可避免的。我们还展示了如何在局部随机噪声下执行容错纠错和码态制备。我们所有的门都可以用常数量子电路深度（即单发）实现，并且物理量子比特的数量随逻辑量子比特的数量线性增长，假设能够在旁边运行多项式大小的无噪声经典电路。我们通过取经典LDPC码的高维超图积来构造我们的量子码，而经典LDPC码又是Spielman的线性时间可编码码（STOC'95）的简化版本。由于我们得到的乘积码仅对跨量子比特具有非均匀概率的物理错误具有鲁棒性，我们随后展示了如何与各种大小的内码级联，以获得针对均匀噪声的容错性。
英文摘要
We construct the first known fault-tolerant scheme for injecting states into quantum error-correcting codes with constant space and time overhead. That is, we construct a family of constant-rate quantum error-correcting codes for which a set of bare physical qubits can be injected, i.e. fault-tolerantly encoded, into a code block. Similarly, a code state can be ejected, i.e. fault-tolerantly decoded, back into bare physical qubits. We show that these injection and ejection procedures succeed under circuit-level locally stochastic noise, while incurring just a small constant probability of corrupting each qubit, which is unavoidable for bare physical qubits. We also show how to perform fault-tolerant error correction and code-state preparation under locally stochastic noise. All of our gadgets can be implemented with constant quantum circuit depth (i.e. are single-shot), and with a number of physical qubits growing linearly with the number of logical qubits, assuming the ability to run polynomial-sized noiseless classical circuits on the side. We construct our quantum codes by taking a high-dimensional hypergraph product of classical LDPC codes, which in turn are a simplified version of Spielman's linear-time encodable codes (STOC'95). As our resulting product codes are only resilient to physical errors occurring with non-uniform probabilities across qubits, we then show how to concatenate with inner codes of various sizes to obtain fault-tolerance against uniform noise.
