Comparing performance of Grover's algorithm with and without phase flip error correction

Abstract: Quantum physics tells of our reality being probabilistic at the microscopic level. Expanding on that research, quantum computing was born, which leverages these microscopic entities with probabilistic properties to perform computation. These units of computation in quantum computing are so-called qubits. The primary challenge with qubits is their sensitivity to noise and consequently occuring erroneous states. This thesis explores the specific quantum algorithm Grover’s algorithm in the context of executing with and without a quantum error correcting code. Execution of quantum circuits was primarily done in a simulator through usage of the Qiskit SDK. Normal and error corrected versions for qubit counts two through five were executed. Results show the error correcting code at low qubit counts has decreased performance compared to the normal circuit. This difference is attributed to the increased circuit complexity error correction introduces. Qubit counts four and five showed insufficient performance in both versions, which highlights a scaling issue for the quantum circuit given the simulator’s default noise model. Nevertheless the endeavour investigates and shines light on an active research area of interest for the development of fault tolerant quantum computers.