Questions tagged [permutation]

Suppose we are given a permutation matrix (which is unitary since it corresponds to a permutation of the basis), acting on a $2^n$-dimensional Hilbert space, which can be seen as a quantum system of $n$ qubits. Is there a way to find an efficient…

Let $H$ be a Hermitian matrix of dimension $2^k$ - i.e. on a system with $k$ qubits. Let $H$ be invariant under permutations of qubits. I would like to express $H$ in the following form: $$H=\sum_{\alpha} c_{\alpha} H_{\alpha}^{\otimes k},$$ where…

Definitions $\mathcal{C}$ is the $n$-qubit Clifford group. $\mathcal{P}_C$ is the group of $n$-qubit permutation matrices in the $n$-qubit Clifford group. This group is generated by all CNOTs and Pauli $X$ strings. Note that for all $n$,…

Consider the unitary matrix $A \in \mathbb{R}^{n^2\times n^2}$ which has only the first $n$ rows explicitly defined, with the remaining rows having some flexibility. $A$ can be written in block form as $ A= \left( {\begin{array}{cccc} B\\ …