A recursive parameterisation of unitary matrices

Recursive parameterisation and invariant phases of unitary matrices

We present further properties of a previously proposed recursive scheme for parameterisation of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study the invariant phases of unitary matrices. The case of four-by-four unitary matrices is investigated in detail. We also address the question of how to construct symmetric unitary matrices using the recursive approach.

Comment on "A Recursive Parametrisation of Unitary Matrices"

In this note we make a comment on the paper by Jarlskog (math-ph/0504049) in which she gave a parametrisation to unitary matrices. Namely, we show that her recursive method is essentially obtained by the canonical coordinate of the second kind in the Lie group theory, and propose a problem on constructing unitary gates in quantum computation by making use of the parametrisation.

面向n量子比特酉矩阵的可扩展量子电路

Scalable quantum circuits for $n$-qubit unitary matrices

本文提出一种基于优化的可扩展量子神经网络框架，通过新构造的Standard Recursive Block Basis参数化表示酉矩阵，以替代Pauli string basis，实现对n量子比特酉矩阵的高效近似。

来自正交群和酉辛群的特征多项式的联合矩

Joint Moments of Characteristic Polynomials from the Orthogonal and Unitary Symplectic Groups

本文建立了随机矩阵群USp(2N)和SO(2N)特征多项式联合矩的渐近公式，揭示了其与Painlevé方程的精确联系，并借此推导出联合矩的精确公式，肯定回答了Altuğ等人的问题。