2021
DOI: 10.1103/physreva.104.032401
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Progress toward favorable landscapes in quantum combinatorial optimization

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Cited by 37 publications
(32 citation statements)
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“…(displayed version) In this thesis we expand upon the results that led to the paper [1] of Lee et al, arXiv:2105.01114 (2021. In particular, we give more details on the oracular formulation of variational quantum algorithms, and the relationship between properties of Ansätze and the strength of their corresponding oracles.…”
mentioning
confidence: 87%
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“…(displayed version) In this thesis we expand upon the results that led to the paper [1] of Lee et al, arXiv:2105.01114 (2021. In particular, we give more details on the oracular formulation of variational quantum algorithms, and the relationship between properties of Ansätze and the strength of their corresponding oracles.…”
mentioning
confidence: 87%
“…Nevertheless, it has also been shown that the choice of the two-qubit gate CNOT was not unique in the above Lemma (1), and in fact:…”
Section: Quantum Computing Basicsmentioning
confidence: 99%
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“…However, as quantum typicality makes the energy landscape of VQA Hamiltonians flattened [11,23], the circuit parameter optimization via local gradient search becomes more difficult with highly entangled circuits [4][5][6][7][8]. A known remedy for the flattened energy landscape is overparametrization of variational ansatz [9,10,12,24], developing multiple steep directions that lead to the robust success of the gradient descent method [11]. This comes with a classical computational cost for storing and manipulating variables.…”
Section: B Optimization and Expressibilitymentioning
confidence: 99%
“…Entanglement is a valuable resource for achieving quantum advantage, but it also becomes a hurdle for successful optimization of circuit control parameters at the same time, specifically when random circuit states are much more highly entangled than the ground state of the Hamiltonian encoding the task [4][5][6][7][8]. Quantum information in such highly entangled states is scrambled, and a successful adjustment of circuit parameters via local gradient search typically requires over-parametrization [9][10][11][12].…”
Section: Introductionmentioning
confidence: 99%