The quantum approximate optimization algorithm: optimization problems and implementations

Doctoral thesis, 2023

Today we are at the beginning of the third quantum revolution, which incorporates the development of quantum computers. The power of quantum computing lies in its exponential growth: with every additional qubit, the computational power doubles. This means that a quantum computer with 50 qubits is already challenging to simulate on a classical supercomputer. However, achieving quantum computing's full potential is a bit like balancing a pen on its tip – any small breeze or vibration could topple it. Qubits are no different; they are sensitive to the slightest environmental disturbances, which can make them lose their ``quantumness''. While quantum error correction exists that can protect qubits from losing their quantumness, it demands a significant overhead of qubits. Therefore, a large-scale error-corrected quantum computer will most likely need millions of qubits before it can solve practical problems.

However, on our journey to build large-scale error-corrected quantum computers, we encounter quantum devices with a few hundred noisy qubits. This poses the question: can we do something useful with these devices? In this thesis, we aim to delve into the current state of quantum algorithms for near-term quantum devices and try to shed light on the potential of quantum computing to tackle complex optimization problems.