Efficient Methods for Tackling Error in Discrete Quantum Circuits

Abstract

Quantum computing has emerged as a groundbreaking field with the potential to solve certain complex problems that are currently intractable for classical computers. Leveraging the principles of quantum mechanics, quantum computers offer exponential speedup for specific tasks, making them a revolutionary tool for various domains, including cryptography, material science, and optimization. The unique capabilities of quantum computers, such as superposition and entanglement, enable entirely new computational paradigms with far-reaching implications. However, despite their immense potential, the practical realization of quantum computing faces significant challenges, such as high error rates and limited qubit coherence.

One of the primary obstacles in quantum computing is managing errors that arise from decoherence and imperfect quantum gate operations. These errors severely limit the performance and scalability of quantum circuits. This thesis is dedicated to developing efficient methods for addressing issues related to errors in discrete quantum circuits. By optimizing quantum circuit design and implementing robust error correction strategies, this research aims to significantly enhance the performance of quantum computations. This work is relevant for both the Noisy Intermediate-Scale Quantum (NISQ) era, characterized by quantum devices with a moderate number of qubits prone to noise and errors, and the future era of fault-tolerant quantum computers where error correction can be integral.

The contributions in this thesis comprising of two parts, are novel techniques for circuit optimization and error correction that are tailored to the unique challenges of both NISQ devices and more advanced error-corrected quantum computers of the future. The research encompasses both theoretical advancements and practical implementations, providing a comprehensive framework for improving the fidelity and efficiency of quantum computations. Specifically, the thesis explores innovative methods for circuit design optimizations, strategies to enhance qubit coherence and gate fidelity and error correction.

In the NISQ era, the focus is on developing strategies to reduce noise and errors to make practical use of the currently available quantum devices. This involves exploring methods as noise-aware circuit design that can operate effectively despite the presence of noise. For the fault-tolerant era, error syndrome detection which is indispensable for error correction, is a computationally hard problem. In this thesis, machine learning based approaches to address this problem have been proposed, implemented and validated.

Overall, this thesis provides a comprehensive exploration of efficient methods for tackling errors in discrete quantum circuits, offering valuable contributions to enhance the performance and reliability of quantum computations. Through a combination of theoretical insights and practical implementations, this research advances the state of the art in quantum error correction and circuit optimization, setting the stage for the future of quantum computing.