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arXiv 2403.14647quant-phcond-mat.other
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使用里德堡-超导量子比特混合系统执行非局域相位估计

Performing Non-Local Phase Estimation with a Rydberg-Superconducting Qubit Hybrid

Juan Carlos Boschero

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98 pages
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AI总结：

本研究通过数值模拟在超导-谐振器-原子混合系统中执行分布式相位估计算法，利用量子最优控制（GRAPE）算法优化门构建保真度，发现C-shunt因子能降低磁通量子比特噪声，使相位估计准确率超过90%。

摘要：

分布式量子计算是 NISQ 时代实现高容量计算的关键。本研究通过数值模拟在一种拟议的新型超导-谐振器-原子混合系统中执行分布式相位估计算法，探讨了构建量子网络所需的关键要素。相位估计算法用于估计给定酉算子的相位或特征值，并且是许多其他已知量子算法（如 Shor's algorithm 和量子计数算法）的子过程。分布式相位估计算法利用两个量子比特之间的纠缠门，称为 E2 门，它提供了将量子信息从一台量子计算机传输到另一台的可能性，数值模拟显示其构建时间为 17ns，保真度为 93%。本研究解析推导了每个系统的哈密顿动力学及噪声源，并利用量子最优控制（QOC），即梯度上升脉冲工程（GRAPE）算法，以最小化相应系统门构建中的保真度误差。GRAPE 算法展示了对里德堡原子单量子比特和多量子比特门非常精确的工程实现，保真度高于 90%，而磁通量子比特受噪声影响严重，多量子比特门保真度低于 90%。结果表明，C-shunt 因子能够降低磁通量子比特的噪声，进而提高了使用 4 个计数量子比特准确估计相位的概率。在低 C-shunt 因子 $0<ζ<1000$ 时，观察到下降/上升过程中的时间步数与优化中运行的 GRAPE 迭代次数之间存在权衡。对于 $ζ= 1000$，GRAPE 算法在大量时间步数和大量 GRAPE 迭代下表现出有效性，估计准确率超过 90%。

英文摘要：

Distributed quantum computation is the key to high volume computation in the NISQ era. This investigation explores the key aspects necessary for the construction of a quantum network by numerically simulating the execution of the distributed phase estimation algorithm in a proposed novel superconducting-resonator-atom hybrid system. The phase estimation algorithm is used to estimate the phase or eigenvalue of a given unitary operator and is a sub-process of many other known quantum algorithms such as Shor's algorithm and the quantum counting algorithm . An entangling gate between two qubits is utilised in the distributed phase estimation algorithm, called an E2 gate which provides the possibility to transfer quantum information from one quantum computer to another, which was numerically shown to have a construction time of 17ns at a fidelity of 93%. This investigation analytically derives the Hamiltonian dynamics as well as the noise sources of each system and utilizes quantum optimal control (QOC), namely the gradient ascent pulse engineering (GRAPE) algorithm, to minimize fidelity error in the corresponding systems gate construction. The GRAPE algorithm showed very accurate engineering of Rydberg atom single and multi-qubit gates with fidelities higher than 90% while the flux qubit suffered greatly from noise with multi-qubit gate fidelities lower than 90%. The C-shunt factor was shown to decrease the noise of the flux qubit which in turn increased the probability of accurately estimating the phase using 4 counting qubits. A trade off was observed between the number of time steps in the descent/ascent and the number of GRAPE iterations ran on the optimisation for low C-shunt factors $0<ζ<1000$. For $ζ= 1000$, the GRAPE algorithm showed effectiveness for a large number of time steps and large amount of GRAPE iterations by reaching estimation accuracies greater than 90%.

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