Incremental Structural Learning for Noisy Quantum Simulations of Tavis-Cummings and Heisenberg Spin Chain Systems

No Thumbnail Available

Files

URL

Journal Title

Journal ISSN

Volume Title

Perustieteiden korkeakoulu | Bachelor's thesis
Electronic archive copy is available locally at the Harald Herlin Learning Centre. The staff of Aalto University has access to the electronic bachelor's theses by logging into Aaltodoc with their personal Aalto user ID. Read more about the availability of the bachelor's theses.
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.

Authors

Date

2024-12-27

Department

Major/Subject

Quantum Technology

Mcode

SCI3103

Degree programme

Aalto Bachelor’s Programme in Science and Technology

Language

en

Pages

43

Series

Abstract

Digital quantum simulation (DQS) provides a powerful polynomial-time method for studying the dynamics of quantum systems, which would otherwise require exponential runtime on classical hardware. However, near-term noisy intermediatescale quantum (NISQ) hardware introduces challenges such as significant gate errors, limited qubit counts and constrained two-qubit gate connectivity. These limitations necessitate the development of noise reduction techniques, such as quantum error mitigation (QEM) techniques and variational quantum algorithms (VQAs). This thesis evaluates the performance of incremental structural learning (ISL), a VQA-based noise reduction approach for Trotterised time evolution, and compares it to zero noise extrapolation (ZNE) across two physical models: the Heisenberg Spin Chain (HSC) and the Tavis-Cummings model (TCM). Quantum circuits were simulated using a noise model inspired by real NISQ hardware, implemented in IBM Qiskit, with optimisation routines applied to enhance circuit fidelity. The findings reveal that ISL outperforms ZNE and plain Trotterisation in HSC systems, leveraging the near-uniform coupling patterns of the Hamiltonian to provide with effective ansatz construction. This advantage persists even with the increased circuit depths introduced by Trotter steps, which pose significant challenges for alternative methods. In contrast, ISL underperforms in TCM systems, where the star-like coupling topology complicates the optimisation of the ansatz, leading to lagging time evolution curves and overall reduced accuracy. Overall, this thesis highlights the potential for ISL to enhance noisy quantum simulations, particularly in systems with uniform Hamiltonian coupling topologies, while identifying areas for improvement in its optimisation process, such as refined layer selection. Future work should explore the application of ISL to systems with more complex interaction patterns, real quantum hardware with constrained connectivity, and its performance relative to alternative noise reduction protocols tailored to time evolution.

Description

Supervisor

Raasakka, Matti

Thesis advisor

Raasakka, Matti

Keywords

quantum computing, quantum simulation, variational quantum algorithm, quantum error mitigation, NISQ

Other note

Citation

Permanent link to this item

https://urn.fi/URN:NBN:fi:aalto-202502182444

Collections

[kand] Perustieteiden korkeakoulu / SCI