论文标题
绘制最佳近似量子编译问题
Sketching the Best Approximate Quantum Compiling Problem
论文作者
论文摘要
本文通过固定CNOT和旋转门的电路结构，然后在旋转角度优化量子的结构，从优化的角度考虑量子汇编问题。我们经典地解决优化问题，并考虑算法工具将其扩展到更高数量的Qubits。我们研究了随机梯度下降和两个草图和解决算法。对于所有三种算法，我们使用矩阵向量而不是矩阵 - 矩阵计算有效地计算梯度。允许在一小时内进行运行时，我们使用任何草图和解决算法的实现都可以编译9个Qubit，27个CNOT电路； 12个Qubit，24个CNOT电路；和15个Qubit，15个CNOT电路。没有我们的算法工具，标准优化将不会超过9个Qubit，9个CNOT电路，除此之外，从理论上讲，贫瘠的高原在理论上主导了。
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and consider algorithmic tools to scale it to higher numbers of qubits. We investigate stochastic gradient descent and two sketch-and-solve algorithms. For all three algorithms, we compute the gradient efficiently using matrix-vector instead of matrix-matrix computations. Allowing for a runtime on the order of one hour, our implementation using either sketch-and-solve algorithm is able to compile 9 qubit, 27 CNOT circuits; 12 qubit, 24 CNOT circuits; and 15 qubit, 15 CNOT circuits. Without our algorithmic tools, standard optimization does not scale beyond 9 qubit, 9 CNOT circuits, and, beyond that, is theoretically dominated by barren plateaus.
