Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition which generates O((3/4)*4^n) controlled-not gates for an n-qubit input gate. The resulting circuits are up to 10 times shorter than other methods in the field. When comparing our implementation to Qubiter, we show that our implementation generates circuits with half the number of CNOT gates and a third of the total circuit length. In addition to that, it is also up to 10 times as fast. Further optimizations are proposed to take advantage of potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition.
翻译:单位分解是一种广泛使用的方法,用来将量子算法绘制成一套任意的量子门。 高效实施这一分解可以将更大的单一门转换成基本量子操作, 这是在现有的量子计算机上执行这些算法的关键。 分解可以用作整个电路的一种积极优化方法, 也可以用作量子加速器上的一种部分算法的测试。 对于分解算法的选择和实施, 假设了完美的qubits。 我们的分解技术以生成了 n-qubit 输入门的 Quantum 香农分解剖法作为基础。 由此产生的电路比实地的其他方法要短10倍。 在将我们的实施与 Qubiter 进行比较时, 我们显示我们的分解过程产生电路, 其数量为 CNOT 门的半数, 总电路长度的三分之一。 除此之外, 分解算法还高达10倍。 提议进一步优化将利用输入或中间基质轴中的潜在基础结构, 并最大限度地减少解剖时间。