Abstract We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model, dynamical quantum phase transition in cavity QED arrays, Markovian dynamics for interacting two-level systems, and the non-Markovian dynamics of the pure-dephasing spin-boson model. These examples will be useful for undergraduate and graduate students with a medium or high-level background in MATLAB, and also for researchers interested in numerical studies applied to quantum optics and condensed matter systems.
Nowadays, quantum computers have been proven to solve the complex problem more efficient and process data more security than classical computer.However, the effect of noises and unwanted environments make the needs of quantum error correction code to build the practical quantum information system.Since the quantum computation algorithms need to be verified in classical computer before implement in quantum computers, the novel framework for verification in classical computer has been become essentially and importantly.In this discussion, a novel framework for quantum information system simulation is proposed which is based on MATLAB environment.First, we analysis the basic notation and elementary elements of a quantum system via mathematical model.Then, we introduce the basic elements of Pauli channel model, and two basic quantum error correction codes to stabilize the quantum channel.Hence, the proposed system to simulate the quantum three-repetition codes and quantum Shor codes are discussed.
This document contains the Python simulation code for the M²FA model as described in NCT VII.XI (Vibrating Strings — The Oscillation Between Inverted States). The code validates the five predictions P43-P47 of the theoretical note. The simulation runs 10,000 Monte Carlo iterations and confirms:• P43 — String detection: 99.6% detection rate (CONFIRMED)• P44 — Harmonic modes: 83.1% harmonic detection (CONFIRMED)• P45 — Memory modulation: 100.0% modulation rate (CONFIRMED)• P46 — Human action: 100.0% action effect (CONFIRMED)• P47 — Vibratory residues: 70.6% residue detection (CONFIRMED)The simulation reveals that vibrating strings are the dynamic interval between inverted states. They are detectable, produce harmonic modes, are modulated by memory, respond to human action, and leave vibratory residues that constitute materiality. Keywords: M²FA, NCT VII.XI, vibrating strings, oscillation, dynamic interval,tension, potential, memory, interferences, residues, vibratory modes. Related publications:• NCT VII.XI: 10.5281/zenodo.22133220• NCT VII.X: 10.5281/zenodo.22116378• NCT VII.IX: 10.5281/zenodo.22096362• NCT VII.VIII: 10.5281/zenodo.22085607