[论文解读] Entanglement and Quantum Error Correction with Superconducting Qubits

Matthew Reed|arXiv (Cornell University)|Nov 26, 2013

Quantum Information and Cryptography参考文献 160被引用 25

一句话总结

本论文展示了在电路量子电动力学（cQED）架构中，利用超导transmon量子比特实现确定性纠缠制备与量子误差纠正。通过将量子比特耦合至共享微波谐振器，作者实现了两量子比特受控相位门，以制备贝尔态与GHZ态，并利用三量子比特Toffoli门实现量子重复码，从而在退相干导致保真度受限的情况下，实现对比特翻转与相位翻转错误的自主纠正。

ABSTRACT

A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.

研究动机与目标

• 在cQED平台上开发并展示可扩展的量子误差纠正技术。
• 通过谐振器介导的相互作用，实现确定性的两量子比特与三量子比特纠缠。
• 利用三量子比特Toffoli门实现量子重复码，以实现自主误差纠正。
• 通过将一维传输线谐振器替换为三维盒式谐振器，提升相干时间。
• 实现原位量子比特频率调谐，以实现精确的哈密顿量控制与系统表征。

提出的方法

• 在cQED架构中，通过共享微波传输线谐振器介导的虚光子交换实现量子比特纠缠。
• 向谐振器施加校准的微波脉冲，在transmon量子比特上执行单量子比特与双量子比特门操作。
• 通过谐振器与量子比特的混合化，增强测量信号放大与保真度。
• 通过实现三量子比特Toffoli门，将逻辑量子比特编码于三量子比特GHZ态中，以实现误差纠正。
• 将一维谐振器替换为三维微波腔体，使量子比特相干时间提高一个数量级。
• 集成控制线路以实现原位量子比特频率调谐，并完成系统哈密顿量的完整表征。

实验结果

研究问题

• RQ1 在cQED系统中，能否通过谐振器介导的相互作用可靠地生成确定性的两量子比特纠缠？
• RQ2 能否以高保真度制备三量子比特GHZ态，作为量子误差纠正的基础？
• RQ3 能否利用三量子比特Toffoli门实现量子重复码，并自主纠正比特翻转或相位翻转错误？
• RQ4 将一维传输线谐振器替换为三维盒式谐振器，对量子比特相干性与错误率有何影响？
• RQ5 能否通过原位量子比特频率控制改善系统校准，并实现精确的哈密顿量工程？

主要发现

• 作者成功利用谐振器介导的受控相位门生成了两量子比特贝尔态与三量子比特GHZ态。
• 利用三量子比特GHZ态作为逻辑量子比特，通过Toffoli门演示了对比特翻转与相位翻转错误的自主纠正。
• 尽管观察到正确的误差纠正行为，但整体保真度仍较低，主要受退相干效应影响。
• 将一维谐振器替换为三维盒式谐振器后，量子比特相干时间提高了约一个数量级。
• 通过控制线路实现了原位量子比特频率控制，使系统哈密顿量的完整表征与调谐成为可能。
• 量子重复码的实现已从原则上得到验证，但受限于实验噪声与退相干效应。