Simulation of three-spin evolution under XX Hamiltonian on quantum processor of IBM-Quantum Experience

TL;DR

This paper simulates three-spin chain evolution under the XX Hamiltonian on IBM's quantum processor, addressing discrepancies between theoretical and experimental state transfer probabilities and proposing a universal correction method.

Contribution

It introduces a method to reduce differences between simulated and theoretical results for three-node XX Hamiltonian evolution on quantum hardware.

Findings

Significant difference observed between calculated and theoretical transfer probabilities.

Proposed two-parameter transformation effectively reduces this difference.

Transformation is universal for three-node systems governed by the XX Hamiltonian.

Abstract

We simulate the evolution of three-node spin chain on the quantum processor of IBM Quantum Experience using the diagonalization of $XX$-Hamiltonian and representing the evolution operator in terms of CNOT operations and one-qubit rotations. We study the single excitation transfer from the first to the third node and show the significant difference between calculated and theoretical values of state transfer probability. Then we propose a method reducing this difference by applying the two-parameter transformation including the shift and scale of the calculated probabilities. { We demonstrate the universality of this transformation inside of the class of three-node evolutionary systems governed by the $XX$-Hamiltonian.