Questions tagged [linear-algebra]

For questions about vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc.

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How to write the joint action of a CP map that acts on a single qubit of a bipartite state?

The question Say I have a completely-positive (CP) map $\mathcal{A}_{ij}$ defined in terms of two projectors $\Pi_i = |i\rangle \langle i |$ and $\Pi_j = |j\rangle \langle j |$ that acts on a density ...
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Weak Schur sampling and state distinguishability

Consider the task of distinguishing between the following two $n$ qubit quantum states. $$ \rho = \frac{\mathbb{I}}{2^{n}}.$$ $$ \sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle ...
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Is decomposing high-dimensional states in terms of Pauli matrices impossible?

I've been trying to decompose a 3x3 density matrix with 3-dimensional Pauli matrices but it doesn't work for all matrices. For example, the density matrix of the state $|0\rangle + |1\rangle + |2\...
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Matrix multiplication through Block Encodings

For a project, I want to simulate a matrix multiplication on a simulated quantum circuit. Assuming that we have a matrix $A\in \mathbb{R}^{m\times n}$ stored in a quantum superposition, i.e. $$|A\...
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Encoding a block unitary matrix in a quantum circuit

My goal would be to implement the unitary matrix $M=\begin{bmatrix}U_{1} &0\\0&U_{0}\end{bmatrix}$ as a circuit for arbitrary $N \mathrm{x} N$ unitary matrices. It is trivial to show that if ...
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How to solve a linear equation of qubit operators in qiskit?

I am trying to repeat the results from Peng and Kowalski (Eq 11) which solves the analytical form of an equation consisting of powers of the Hamiltonian (moments): The $K$-th order PDS formalism is ...