arXiv 2108.047262021-08quant-ph

抗长期振幅漂移的量子门

Quantum Gates Robust to Secular Amplitude Drifts

Qile David Su, Robijn Bruinsma, Wesley C. Campbell

DOI：: 10.1103/PhysRevA.104.052625

摘要：

量子门通常容易受到施加到物理量子位以驱动门的经典控制场中的缺陷的影响。减少这种误差来源的一种方法是将门分成多个部分，称为复合脉冲（CP），通常利用误差随时间的恒定性来减轻其对门保真度的影响。在这里，我们扩展这种技术来抑制长期漂移拉比频率，把它们作为幂律漂移的一阶效应的状态矢量的过度或欠旋转线性添加的总和。幂律漂移的形式为$t^p$，其中$t$为时间，常数$p$为其幂。我们表明，复合脉冲，抑制所有的幂律漂移与$p \leq n$也是高通滤波器的滤波器阶$n+1$ arXiv：1410.1624。我们提出的序列，满足我们提出的幂律幅度标准，$\text{PLA}(n)$，获得这种技术，并比较其模拟性能下的时间依赖性幅度误差的一些传统的复合脉冲序列。我们发现，有一个范围内的噪声频率的$\text{PLA}(n)$序列提供更多的误差抑制比传统的序列，但在低频率限制，非线性效应变得更重要的门保真度比频率滚降。结果，先前已知的$F_1$序列（其是$\text{PLA}(1)$准则的两个解决方案之一并且消除了线性长期漂移和一阶非线性效应两者的抑制）是比低频极限中的任何其它$\text{PLA}(n)$序列更尖锐的噪声滤波器。

英文摘要：

Quantum gates are typically vulnerable to imperfections in the classical control fields applied to physical qubits to drive the gates. One approach to reduce this source of error is to break the gate into parts, known as composite pulses (CPs), that typically leverage the constancy of the error over time to mitigate its impact on gate fidelity. Here we extend this technique to suppress secular drifts in Rabi frequency by regarding them as sums of power-law drifts whose first-order effects on over- or under-rotation of the state vector add linearly. Power-law drifts have the form $t^p$ where $t$ is time and the constant $p$ is its power. We show that composite pulses that suppress all power-law drifts with $p \leq n$ are also high-pass filters of filter order $n+1$ arXiv:1410.1624. We present sequences that satisfy our proposed power-law amplitude criteria, $\text{PLA}(n)$, obtained with this technique, and compare their simulated performance under time-dependent amplitude errors to some traditional composite pulse sequences. We find that there is a range of noise frequencies for which the $\text{PLA}(n)$ sequences provide more error suppression than the traditional sequences, but in the low frequency limit, non-linear effects become more important for gate fidelity than frequency roll-off. As a result, the previously known $F_1$ sequence, which is one of the two solutions to the $\text{PLA}(1)$ criteria and furnishes suppression of both linear secular drift and the first order nonlinear effects, is a sharper noise filter than any of the other $\text{PLA}(n)$ sequences in the low frequency limit.

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