Implementation of Quantum Error Correction Codes

Abstract

With the quantum volume of current NISQ computers growing exponentially each year, the long term goal of fault tolerant quantum computing is closer every day. This has led to a focus on quantum error correction. In this thesis, the key topic of implementation of quantum error correction codes is explored. After a brief overview of the basics of quantum information, errors in quantum computation are discussed. Demonstrating a method for detecting these errors leads to the introduction of quantum circuits capable of correcting specific errors. By building from these fundamental codes, the Shor code is constructed. With two key theorems, the notion of arbitrary error correction is realized. Through the usage of the stabilizer formalism, a general method for the implementation of the Steane code, the perfect 5-qubit code and an arbitrary distance surface code is presented. NISQ computer noise simulations of the presented error correcting codes are discussed. Additionally, error suppression under noise is demonstrated. Finally, example implementation of these quantum error correction codes is given.