Circuit depth scaling for quantum approximate optimization

量子位元 量子 量子电路 缩放比例 计算机科学 量子算法 量子计算机 算法 数学优化 数学 应用数学 量子纠错 量子力学 物理 几何学
作者
V. Akshay,H. Philathong,E. Campos,D. S. Rabinovich,I. Zacharov,Xiaoming Zhang,Jacob Biamonte
出处
期刊:Physical review [American Physical Society]
卷期号:106 (4) 被引量:4
标识
DOI:10.1103/physreva.106.042438
摘要

Variational quantum algorithms are the centerpiece of modern quantum programming. These algorithms involve training parametrized quantum circuits using a classical coprocessor, an approach adapted partly from classical machine learning. An important subclass of these algorithms, designed for combinatorial optimization on current quantum hardware, is the quantum approximate optimization algorithm (QAOA). Despite efforts to realize deeper circuits, experimental state-of-the-art implementations are limited to a fixed depth. However, it is known that problem density---a problem constraint to a variable ratio---induces underparametrization in fixed depth QAOA. Density-dependent performance has been reported in the literature, yet the circuit depth required to achieve fixed performance (henceforth called critical depth) remained unknown. Here, we propose a predictive model, based on a logistic saturation conjecture for critical depth scaling with respect to density. Focusing on random instances of MAX-2-SAT, we test our predictive model against simulated data with up to 15 qubits. We report the average critical depth, required to attain a success probability of 0.7, saturates at a value of 10 for densities beyond 4. We observe the predictive model to describe the simulated data within a $3\ensuremath{\sigma}$ confidence interval. Furthermore, based on the model, a linear trend for the critical depth with respect to problem size is recovered for the range of 5--15 qubits.
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