Fault-tolerant Preparation of Distant Logical Bell Pair - with application in the Magic Square Game

Abstract

Quantum entanglement facilitates nonlocal correlations that defy classical physics, forming the basis for quantum technologies, including quantum computation and communication. Nonlocal games exemplify this power, where entangled players achieve outcomes unattainable by classical means. This thesis focuses on optimizing the preparation of high-fidelity logical Bell pairs in the context of the fault-tolerant magic square game, seeking to minimize Bell pair(ebit) consumption while maintaining a low logical error rate. In this thesis, we introduce a novel approach leveraging an interface circuit and entanglement purification protocol (EPP) to translate states between physical and logical qubits and purify noisy logical ebits. This method significantly reduces the number of initial ebits needed compared to conventional strategies. Our analytical and numerical analyses, particularly for the [[7k,1,3k]] concatenated Steane code, demonstrate substantial (actually, exponential) ebit savings and higher noise threshold. Analytical lower bounds for local noise threshold of 4.70 × 10−4 and initial ebit infidelity threshold of 18.3% are obtained. Additionally, we construct an analogous interface for the surface code through lattice surgery, offering further improvements in fault tolerance and compatibility with current quantum hardware. Our framework is adaptable to various quantum error-correcting codes (QECCs) and experimental platforms. We hope our protocol will not only enhance understanding of fault-tolerant nonlocal games, but also spark further exploration of interfacing between different QECCs, promoting the development of modular quantum architectures and advancing quantum internet.