论文标题
通过cartan分解的近乎最佳的量子电路结构
Near-optimal quantum circuit construction via Cartan decomposition
论文作者
论文摘要
我们显示了Lie代数对量子电路的cartan分解的适用性。这种方法可用于合成可以有效实施任何所需统一操作的电路。我们的方法找到了相关谎言代数的代数发生器的明确量子电路表示，允许在量子计算机上直接实施cartan分解。该构造是递归的，使我们能够将任何电路扩展到发电机和单个Qubit上的旋转矩阵，通过我们的递归算法，我们发现发电机本身可以用受控的不（CNOT）和交换门来明确表示。我们的方法独立于标准的CNOT实现，并且可以轻松地适应其他跨量电路元素。除了它的多功能性外，我们在使用CNOT门时还达到了近乎最佳的计数，实现了$ \ frac {21} {21} {16} {16} 4^n $的渐近CNOT成本。
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum circuit representations of the algebraic generators of the relevant Lie algebras allowing the direct implementation of a Cartan decomposition on a quantum computer. The construction is recursive and allows us to expand any circuit down to generators and rotation matrices on individual qubits, where through our recursive algorithm we find that the generators themselves can be expressed with controlled-not (CNOT) and SWAP gates explicitly. Our approach is independent of the standard CNOT implementation and can be easily adapted to other cross-qubit circuit elements. In addition to its versatility, we also achieve near-optimal counts when working with CNOT gates, achieving an asymptotic cnot cost of $\frac{21}{16}4^n$ for $n$ qubits.
