Early State Exclusion in 7-Qubit Spin Chains

TL;DR

This paper investigates the existence of specific Hamiltonian matrices for quantum spin chains, focusing on odd-numbered qubits, and introduces new families of matrices for 7-qubit chains with environmental effects.

Contribution

It extends the known existence results of Jacobi matrices representing quantum spin chains to the case of 7-qubit chains with environmental interactions.

Findings

Existence of 7x7 Jacobi matrices with ESE established

Infinite families of such matrices constructed for 7-qubit chains

Analysis includes environmental effects on spin chain Hamiltonians

Abstract

The existence of infinite families of $N \times N$ Jacobi matrices representing the Hamiltonians of quantum spin chains with and without early state exclusion (ESE) has been shown to exist for any even $N \geq 4$. However, their existence for odd $N \geq 7$ has remained an open problem. In Section 3, we consider a chain of qubits experiencing nearest-neighbor interactions with environmental effects and present infinite families of $7 \times 7$ Jacobi matrices with and without ESE.