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arXiv 2301.02269quant-phmath-phmath.MP
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驯服旋转波近似

Taming the Rotating Wave Approximation

Daniel Burgarth, Paolo Facchi, Robin Hillier, Marilena Ligabò

备注：
16 pages, 2 figures
发表信息：
Quantum 8, 1262 (2024)
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AI总结：

本文研究了量子拉比模型中旋转波近似（RWA）的适用边界，开发了严格的非微扰边界，发现其不仅依赖耦合强度与振荡器频率之比，还依赖初始状态平均光子数，为满足可扩展量子技术的精度需求提供了理论依据。

摘要：

光与物质的相互作用是量子力学最古老的研究领域之一，且该领域不断带来新的见解和应用。随着腔和电路量子电动力学的出现，我们现在能够实现强光物质耦合，这构成了量子技术大多数实现的基础。但量子信息处理也提出了极高的要求，需要总错误率低于百分之一才能扩展（容错）至有用的应用。由于错误也可能源于建模，这使得量子理论的关键近似之一——量子拉比模型的旋转波近似（RWA）——被推到了核心位置，该近似导出了Jaynes-Cummings哈密顿量。尽管RWA通常非常有效且对理解光物质相互作用极其有用，但越来越多的实验证据表明在某些区间它是一个糟糕的近似。在此，我们提出并回答了一个更难的问题：对于哪些实验参数，RWA虽然在定性上可能足够，但已不足以满足可扩展量子技术的需求？例如，何时错误至少为1%，何时至多为1%？为了回答这个问题，我们开发了严格的非微扰边界来驯服RWA。我们发现，这些边界不仅如预期那样依赖于耦合强度与振荡器频率的比值，还依赖于初始状态中的平均光子数。这证实了最近关于光子修饰Bloch-Siegert位移的实验。我们指出，随着实验报告了包含数百个光子的可控腔状态，以及量子纠错码探索越来越多的Fock空间，RWA的这种状态依赖性对于量子计算领域越来越重要，我们的结果为更好地理解这些实验铺平了道路。

英文摘要：

The interaction between light and matter is one of the oldest research areas of quantum mechanics, and a field that just keeps on delivering new insights and applications. With the arrival of cavity and circuit quantum electrodynamics we can now achieve strong light-matter couplings which form the basis of most implementations of quantum technology. But quantum information processing also has high demands requiring total error rates of fractions of percentage in order to be scalable (fault-tolerant) to useful applications. Since errors can also arise from modelling, this has brought into center stage one of the key approximations of quantum theory, the Rotating Wave Approximation (RWA) of the quantum Rabi model, leading to the Jaynes-Cummings Hamiltonian. While the RWA is often very good and incredibly useful to understand light-matter interactions, there is also growing experimental evidence of regimes where it is a bad approximation. Here, we ask and answer a harder question: for which experimental parameters is the RWA, although perhaps qualitatively adequate, already not good enough to match the demands of scalable quantum technology? For example, when is the error at least, and when at most, 1%? To answer this, we develop rigorous non-perturbative bounds taming the RWA. We find that these bounds not only depend, as expected, on the ratio of the coupling strength and the oscillator frequency, but also on the average number of photons in the initial state. This confirms recent experiments on photon-dressed Bloch-Siegert shifts. We argue that with experiments reporting controllable cavity states with hundreds of photons and with quantum error correcting codes exploring more and more of Fock space, this state-dependency of the RWA is increasingly relevant for the field of quantum computation, and our results pave the way towards a better understanding of those experiments.

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