[论文解读] Computational Role of Collective Tunneling in a Quantum Annealer

Sergio Boixo, Vadim Smelyanskiy+8 more|arXiv (Cornell University)|Nov 14, 2014

Quantum Computing Algorithms and Architecture参考文献 1被引用 23

一句话总结

该论文首次提供了在可编程量子退火机中，多量子比特量子隧穿增强优化性能的实验证据。通过基于NIBA的量子主方程模型，作者证明了集体隧穿——在临界演化阶段被抑制，但可通过耗散促进——使D-Wave Two设备在16和200量子比特问题中优于经典热跃迁，尤其在这些情况下表现出更强的性能。

ABSTRACT

Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We develop a theoretical model based on a NIBA Quantum Master Equation to describe the multiqubit dissipative tunneling effects under the complex noise characteristics of such quantum devices. We start by considering a computational primitive, an optimization problem consisting of just one global and one false minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the "critical" phase during the evolution where quantum tunneling "decides" the right path to solution. In a later stage dissipation facilitates the multiqubit tunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-Wave Two quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specifically, we provide an analysis of an optimization problem with sixteen qubits, demonstrating eight qubit tunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

研究动机与目标

• 为可编程量子退火机中多量子比特量子隧穿作为计算资源提供实验证据。
• 在超导量子器件的真实噪声条件下，对耗散性多量子比特隧穿进行建模。
• 证明在受挫量子比特簇中，量子隧穿比经典热跃迁能更快收敛至全局最小值。
• 通过与美国宇航局 Ames 实验室获取的 D-Wave Two 量子退火机实验数据对比，验证理论模型。
• 量化成功概率的温度依赖性，揭示量子路径与经典路径的相反趋势。

提出的方法

• 开发了非绝热主方程（NIBA）模型，以描述噪声量子器件中多量子比特耗散隧穿行为。
• 使用一个具有全局最小值和一个虚假最小值的计算原语，通过强簇内耦合的受挫量子比特簇实现。
• 对量子环境的集体效应进行建模，显示在临界阶段被抑制，而在后期阶段被促进。
• 引入χ探测模型以拟合D-Wave设备的串扰效应，通过公式(117)和(118)调整耦合项和局部场。
• 在15 mK的算法温度下执行12.5万至12.8万次随机路径积分蒙特卡罗（SVMC）模拟，以与D-Wave实验数据对比。
• 将χ探测参数校准为0.0025，使SVMC与实验成功概率之间的残差误差最小化。

实验结果

研究问题

• RQ1 能否在可编程量子退火机中实验观测到多量子比特量子隧穿作为计算资源？
• RQ2 耗散与集体隧穿之间的相互作用如何影响量子退火中的成功概率？
• RQ3 量子隧穿与经典热跃迁的成功概率温度依赖性有何不同？
• RQ4 基于NIBA的量子主方程模型在多大程度上能准确描述D-Wave Two设备的实验数据？
• RQ5 通过χ建模的串扰效应在真实设备中如何影响量子退火性能？

主要发现

• NIBA量子主方程模型能准确描述D-Wave Two量子退火机的实验成功概率。
• 在16量子比特问题中，多量子比特隧穿提高了成功概率，证实了八量子比特集体隧穿效应。
• 在最大达200量子比特的大规模问题中，由于隧穿效应，成功概率仍高于经典热跃迁。
• 成功概率的温度依赖性在量子隧穿与经典热跃迁中表现出相反趋势：量子模型中成功率随温度升高而增加，而经典模型中则随温度升高而降低。
• χ = 0.0025的χ探测模型最符合实验数据，显著降低了SVMC模拟中的残差误差。
• SVMC模拟中χ = 0.0025时的成功概率高于无χ的情况，证实有效铁磁性可降低势垒并增强隧穿效应。