@article{15122,
  abstract     = {Quantum computers are increasing in size and quality but are still very noisy. Error mitigation extends the size of the quantum circuits that noisy devices can meaningfully execute. However, state-of-the-art error mitigation methods are hard to implement and the limited qubit connectivity in superconducting qubit devices restricts most applications to the hardware's native topology. Here we show a quantum approximate optimization algorithm (QAOA) on nonplanar random regular graphs with up to 40 nodes enabled by a machine learning-based error mitigation. We use a swap network with careful decision-variable-to-qubit mapping and a feed-forward neural network to optimize a depth-two QAOA on up to 40 qubits. We observe a meaningful parameter optimization for the largest graph which requires running quantum circuits with 958 two-qubit gates. Our paper emphasizes the need to mitigate samples, and not only expectation values, in quantum approximate optimization. These results are a step towards executing quantum approximate optimization at a scale that is not classically simulable. Reaching such system sizes is key to properly understanding the true potential of heuristic algorithms like QAOA.},
  author       = {Sack, Stefan and Egger, Daniel J.},
  issn         = {2643-1564},
  journal      = {Physical Review Research},
  number       = {1},
  publisher    = {American Physical Society},
  title        = {{Large-scale quantum approximate optimization on nonplanar graphs with machine learning noise mitigation}},
  doi          = {10.1103/PhysRevResearch.6.013223},
  volume       = {6},
  year         = {2024},
}

@phdthesis{14622,
  abstract     = {This Ph.D. thesis presents a detailed investigation into Variational Quantum Algorithms
(VQAs), a promising class of quantum algorithms that are well suited for near-term quantum
computation due to their moderate hardware requirements and resilience to noise. Our
primary focus lies on two particular types of VQAs: the Quantum Approximate Optimization
Algorithm (QAOA), used for solving binary optimization problems, and the Variational Quantum
Eigensolver (VQE), utilized for finding ground states of quantum many-body systems.
In the first part of the thesis, we examine the issue of effective parameter initialization for
the QAOA. The work demonstrates that random initialization of the QAOA often leads to
convergence in local minima with sub-optimal performance. To mitigate this issue, we propose
an initialization of QAOA parameters based on the Trotterized Quantum Annealing (TQA).
We show that TQA initialization leads to the same performance as the best of an exponentially
scaling number of random initializations.
The second study introduces Transition States (TS), stationary points with a single direction
of descent, as a tool for systematically exploring the QAOA optimization landscape. This
leads us to propose a novel greedy parameter initialization strategy that guarantees for the
energy to decrease with increasing number of circuit layers.
In the third section, we extend the QAOA to qudit systems, which are higher-dimensional
generalizations of qubits. This chapter provides theoretical insights and practical strategies for
leveraging the increased computational power of qudits in the context of quantum optimization
algorithms and suggests a quantum circuit for implementing the algorithm on an ion trap
quantum computer.
Finally, we propose an algorithm to avoid “barren plateaus”, regions in parameter space with
vanishing gradients that obstruct efficient parameter optimization. This novel approach relies
on defining a notion of weak barren plateaus based on the entropies of local reduced density
matrices and showcases how these can be efficiently quantified using shadow tomography.
To illustrate the approach we employ the strategy in the VQE and show that it allows to
successfully avoid barren plateaus in the initialization and throughout the optimization.
Taken together, this thesis greatly enhances our understanding of parameter initialization and
optimization in VQAs, expands the scope of QAOA to higher-dimensional quantum systems,
and presents a method to address the challenge of barren plateaus using the VQE. These
insights are instrumental in advancing the field of near-term quantum computation.},
  author       = {Sack, Stefan},
  issn         = {2663-337X},
  pages        = {142},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Improving variational quantum algorithms : Innovative initialization techniques and extensions to qudit systems}},
  doi          = {10.15479/at:ista:14622},
  year         = {2023},
}