Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator.
Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator.
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DOI：
10.1073/pnas.2006373117
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发表时间：
2020-10-13
影响因子：
11.1
通讯作者：
Monroe C
中科院分区：
文献类型：
--
作者：
Pagano G;Bapat A;Becker P;Collins KS;De A;Hess PW;Kaplan HB;Kyprianidis A;Tan WL;Baldwin C;Brady LT;Deshpande A;Liu F;Jordan S;Gorshkov AV;Monroe C
变分量子算法将量子资源与经典优化方法相结合，为解决量子多体和经典优化问题提供了一种有前景的方法。一个关键问题是变分算法如何作为量子比特数的函数来执行。在这里，我们通过应用变分量子算法 (QAOA) 来近似计算长程 Ising 模型（量子模型和经典模型）的基态能量，并研究在最多 40 个量子位的俘获离子量子模拟器上的算法性能，从而解决这个问题。作为量子位数量的函数，观察到可以忽略不计的性能下降和几乎恒定的运行时间缩放。通过对误差源进行建模，我们解释了实验性能，为更普遍地实现混合量子经典算法奠定了基础。量子计算机和模拟器可能比传统计算机和模拟器具有显着的优势，提供对量子多体系统的深入了解，并可能提高解决指数级困难问题的性能，例如优化和可满足性。在这里，我们报告使用模拟量子模拟器实现低深度量子近似优化算法（QAOA）。我们估计了具有可调谐范围的长程相互作用的横向场伊辛模型的基态能量，并通过使用高保真、单次、单独的量子位测量对 QAOA 输出进行采样来优化相应的组合经典问题。我们通过详尽的搜索和变分参数的闭环优化来执行该算法，用多达 40 个捕获离子量子位来近似基态能量。我们使用引导启发式方法对实验进行基准测试，该方法随系统规模进行多项式缩放。我们观察到，与数值一致，当我们扩大系统规模时，QAOA 性能不会显着下降，并且运行时间大致独立于量子位的数量。最后，我们对系统中发生的错误进行了全面分析，这是将 QAOA 应用于更一般问题实例的关键一步。
Variational quantum algorithms combine quantum resources with classical optimization methods, providing a promising approach to solve both quantum many-body and classical optimization problems. A crucial question is how variational algorithms perform as a function of qubit number. Here, we address this question by applying a variational quantum algorithm (QAOA) to approximate the ground-state energy of a long-range Ising model, both quantum and classical, and investigating the algorithm performance on a trapped-ion quantum simulator with up to 40 qubits. A negligible performance degradation and almost constant runtime scaling is observed as a function of the number of qubits. By modeling the error sources, we explain the experimental performance, marking a stepping stone toward more general realizations of hybrid quantum–classical algorithms. Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.
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影响因子：
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作者：
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通讯作者：
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