Variational quantum algorithms
Variational quantum algorithms (VQAs) are proposed to solve relevant computational problems on near-term quantum devices. Popular versions are variational quantum eigensolvers (VQEs) and quantum approximate optimization algorithms (QAOAs) that solve ground state problems from quantum chemistry and binary optimization problems, respectively. They are based on the idea of using a classical computer to train a parameterized quantum circuit.
Limitations
We identify challenges in training VAQs. In general, their training is NP-hard, even for logarithmically few qubits and free fermions, see https://arxiv.org/abs/2101.07267.
Moreover, minimizing the depth of VQAs is QCMA-hard even if only needs to be done approximately with an approximation error that is allowed to grow with the number of qubits, see https://arxiv.org/abs/2211.12519.
VQA read-out
We develop efficient measurement strategies that allow for a more efficient read-out of the quantum device, see
https://arxiv.org/abs/2210.06484 (Bayesian extensions of the generalized parameter shift rule).