在色度动力学去耦中权衡电路深度与脉冲稀疏性
Trading Circuit Depth for Pulse Sparsity in Chromatic Dynamical Decoupling
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中文总结 AI 辅助
本文提出两种基于二进制和Gray矩阵的色度动力学去耦序列（CBDD和CGDD），以牺牲电路深度换取更低脉冲重复率，在IBM 127量子比特实验中验证了稀疏脉冲在短时间内的优势，并确立PRR为实用品质因数。
中文摘要 AI 辅助
随着量子比特数量迅速增加，系统地抑制大型量子比特网络中的退相干和串扰成为一个紧迫问题。一般的多量子比特动力学去耦（DD）历来基于Hadamard矩阵和正交阵列，其瞬时脉冲序列的电路深度随量子比特数量线性扩展。色度-Hadamard DD（CHaDD）通过适当对硬件图进行着色，并为每种颜色分配Hadamard矩阵的一行来改进这些方法，使得电路深度随颜色数$C$线性扩展，$C$可低至图的色数。在此，我们探讨电路深度与脉冲重复率（PRR）之间的权衡，PRR定义为量子比特被脉冲作用的时间步长平均比例，即脉冲密度的度量。我们引入了两种基于二进制和Gray矩阵的单轴序列，即色度-二进制DD（CBDD）和色度-Gray DD（CGDD），对于$C>2$，它们是非最小深度CHaDD的特例，分别实现PRR $<2/C$和PRR $=1/C$，而CHaDD的PRR高于$1/4$，代价是电路深度为$2^C$。在$C=3$的127量子比特IBM处理器上的状态保持实验中，当脉冲不鲁棒时，较稀疏的序列在短时间内优于CHaDD；这一优势在很大程度上被旨在补偿相干脉冲误差的鲁棒版本所消除，而在鲁棒序列中，CGDD在固定保护时间内使用最少脉冲。在非鲁棒的$C=3$和$C=5$调度中，固定量子比特子集上相等的PRR经验上与相似的状态保持相关。因此，当相干脉冲误差占主导时，PRR可作为色度DD的实用品质因数。
英文摘要
Suppressing decoherence and crosstalk systematically across large networks of qubits is a pressing concern as qubit counts increase rapidly. General multi-qubit dynamical decoupling (DD) has historically been based on Hadamard matrices and orthogonal arrays, with instantaneous-pulse sequences whose circuit depth scales linearly with the number of qubits. Chromatic-Hadamard DD (CHaDD) improves upon these methods by properly coloring the hardware graph and assigning to each color a row of a Hadamard matrix, resulting in a circuit depth that scales linearly with the number of colors $C$, which can be as low as the chromatic number of the graph. Here, we explore the tradeoff between circuit depth and the pulse repetition rate (PRR), the average fraction of time steps in which a qubit is pulsed, i.e., a measure of pulse density. We introduce two single-axis sequences based on binary and Gray matrices, Chromatic-Binary DD (CBDD) and Chromatic-Gray DD (CGDD), which, for $C>2$, are special cases of non-minimum-depth CHaDD and achieve PRR $<2/C$ and PRR $=1/C$, respectively, compared with a PRR above $1/4$ for CHaDD, at the price of a circuit depth of $2^C$. In state preservation experiments on a $127$-qubit IBM processor with $C=3$, the less dense sequences outperform CHaDD at short times when the pulses are not robust; this advantage is largely eliminated by robust versions designed to compensate for coherent pulse errors, and among the robust sequences, CGDD uses the fewest pulses over a fixed protection time. Across non-robust $C=3$ and $C=5$ schedules, equal PRR on a fixed qubit subset is empirically associated with similar state preservation. Thus, the PRR serves as a practical figure of merit for chromatic DD whenever coherent pulse errors dominate.
发表机构
- University of Southern California（南加州大学）
- Center for Quantum Information Science & Technology, University of Southern California（南加州大学量子信息科学与技术中心）
- Quantum Elements（量子元素）
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