发表机构
Computer Science and Engineering University at Buffalo（布法罗大学计算机科学与工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出仅需一对贝尔态的NOBOL方法，可大幅降低容错量子计算中逻辑CNOT操作的开销，适用于多种量子纠错码及架构。
AI 中文摘要
容错量子计算从根本上依赖于将逻辑量子比特编码为结构化的物理量子比特块，通常需要数十到数百个物理量子比特。作为提高容错能力的代价，逻辑门操作会带来时间和量子资源上的线性开销。例如，在单片量子计算中，对两个相距较远的逻辑量子比特执行门操作，首先需要使用线性数量的SWAP操作将逻辑量子比特移动到彼此相邻的位置；而在分布式量子计算中，执行此类操作则首先需要线性数量的辅助量子比特来形成纠缠连接（或逻辑贝尔对）。本文中，我们专注于大幅降低逻辑CNOT操作（一种基本的量子计算基本单元）的开销。我们提出了NOBOL，一种新颖的方法，仅需一对贝尔态即可对编码在任意CSS码中的两个相距较远的量子比特执行逻辑CNOT操作。更重要的是，NOBOL仅需对逻辑量子比特的逻辑X或Z算子子集执行门操作。对于许多CSS码，例如表面码，这些子集的大小远小于码本身的大小。本文中，我们描述了NOBOL的多种电路实现，包括深度最优电路，其深度相对于逻辑算子的大小呈对数级增长。最后，我们提出了有效控制误差传播的方法，且不会产生过多额外开销。由于NOBOL可有效应用于广泛的量子纠错（QEC）码，且与量子比特模态无关，适用于各种架构，包括基于单片量子处理单元（QPU）或分布式QPU的架构，因此具有广泛的应用前景。
英文摘要
Fault-tolerant quantum computation fundamentally relies on encoding a logical qubit into a structured block of physical qubits, typically in the tens to hundreds. As a trade-off for improved fault-tolerance, logical gate operations will incur a linear overhead in terms of both the amount of time and quantum resources than before. For example, in monolithic quantum computing, performing a gate operation on two distant logical qubits will first require using a linear number of SWAP operations in order to move the logical qubits next to each other; while in distributed quantum computing, doing so will first require a linear number of ancilla qubits in order to form entanglement connections (or a logical Bell pair). In this paper, we focus on significantly reducing the overhead involved in logical CNOT operations, a fundamental primitive. We propose NOBOL, a novel approach that requires only one Bell pair to perform a logical CNOT operation on two distant qubits encoded in arbitrary CSS codes. More importantly, NOBOL only requires performing gate operations on the logical X or Z operator subsets of the logical qubits. For many CSS codes, such as the surface code, these subsets are significantly smaller than the size of the code itself. In this paper, we describe various circuit realizations of NOBOL, including a depth-optimal circuit with logarithmic depth in terms of the size of the logical operators. Finally, we propose effective methods to contain error propagation without incurring much additional overhead. Since NOBOL can be effectively applied to a wide range of quantum error-correcting (QEC) codes and, in addition, is agnostic to qubit modalities and effective for various architectures, including those based on either a monolithic QPU or distributed QPUs.
