The quantum approximate optimization algorithm: optimization problems and implementations
Doctoral thesis, 2023

This thesis explores the Quantum Approximate Optimization Algorithm (QAOA), a hybrid classical-quantum algorithm designed to solve combinatorial optimization problems. The goal of this algorithm is to iteratively optimize a variational state to approximate the ground state of a cost Hamiltonian that encodes a combinatorial optimization problem. The focus of this thesis is the application of QAOA to the Exact Cover problem, an abstraction of the Tail Assignment problem – a problem omnipresent in aviation.

This thesis also includes a demonstration of the practical implementation of QAOA on a superconducting quantum computer, demonstrating empirical proof of QAOA's functionality. It also investigates running QAOA using noise-biased qubits, namely cat qubits, which exhibit resilience to certain types of errors.

This thesis also explores novel multi-qubit gates obtained from the simultaneous application of two controlled-Z gates on current quantum hardware, leading to the efficient creation of large entangled states.

Lastly, the thesis delves into virtual distillation, an error-mitigation protocol, and assesses its performance under various types of errors.

Overall, this thesis validates the promise of QAOA in solving real-world optimization problems while also offering insights into error mitigation.

Quantum approximate optimization algorithm

quantum computing

error mitigation

cat qubits

Kollektorn, Kemivägen 9
Opponent: Prof. Sophia Economou, Virginia Tech, United States

Author

Pontus Vikstål

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Fast Multiqubit Gates through Simultaneous Two-Qubit Gates

PRX Quantum,;Vol. 2(2021)

Journal article

Vikstål, P. Ferrini, G. Puri, S. Study of noise in virtual distillation circuits for quantum error mitigation

Vikstål, P. García-Álvarez, L. Puri, S. Ferrini, G. Quantum Approximate Optimization Algorithm with Cat Qubits

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.

Areas of Advance

Nanoscience and Nanotechnology

Subject Categories

Computational Mathematics

Physical Sciences

ISBN

978-91-7905-893-7

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5359

Publisher

Chalmers

Kollektorn, Kemivägen 9

Opponent: Prof. Sophia Economou, Virginia Tech, United States

More information

Latest update

8/7/2023 8