Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter ansatz. We find that in combinatorial optimization problems, since the solutions are described by bit strings, one can trade the expressiveness of the ansatz for high trainability. To be specific, by focusing on the max-cut problem we introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA). The quantum circuits are comprised with single-qubit rotation gates implementing on each qubit. The rotation angles of the gates can be trained free of barren plateaus. Thus, the approximate solution of the max-cut problem can be obtained with probability close to 1. To illustrate the effectiveness of QQRA, we compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.
翻译:优化参数化量子电路将保证高效使用短期量子计算机以实现潜在的量子优势。 但是, 参数 antaz 的可容性和可训练性之间有一个臭名昭著的权衡。 我们发现, 在组合优化问题上,由于解决方案被比特字符描述, 人们可以将 ansatz 的表达性换成高可训练性。 具体地说, 我们引入了一个简单而高效的算法, 名为 Quantum Qubit Rotoriation Algorithm ( ⁇ RA ) 。 量子电路由每个qubit 执行的单位旋转门组成。 门的旋转角度可以被训练为没有贫瘠的高原。 因此, 最大量问题的大致解决办法可以接近于 1. 的可能性获得 。 为了说明“ RA ” 的有效性, 我们把它与已知的量子精度优化算法和古典的Goemans- Williamson 算法进行比较 。