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It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization.
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In reference to QLC, ⟨ H p ⟩ \langle H_{\textrm{p}}\rangle essentially serves as a control Lyapunov function, though in practice it may not be strictly positive or meet all of the requirements to be true Lyapunov function
Cited in the paper.
Estimating each A k A_{k} can be accomplished by first expanding it in the Pauli operator basis as A k = ⟨ ψ k | i [ H d , H p ] | ψ k ⟩ = Σ j = 1 N α j ⟨ ψ k | P j | ψ k ⟩ A_{k}=\langle\psi_{k}|i[H_{\textrm{d}},H_{\textrm{p}}]|\psi_{k}\rangle=\Sigma_{j=1}^{N}\alpha_{j}\langle\psi_{k}|P_{j}|\psi_{k}\rangle , where α j \alpha_{j} are scalar coefficients and P j P_{j} are Pauli strings, and then measuring the expectations of each P j P_{j} in order to evaluate the weighted sum. The value of N N depends on H p H_{\textrm{p}} and H d H_{\textrm{d}} . For the MaxCut examples we consider, N ≤ n ( n − 1 ) N\leq n(n-1)
Cited in the paper.
2021
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A. B. Magann, K. M. Rudinger, M. D. Grace, and M. Sarovar, Lyapunov-control-inspired strategies for quantum combinatorial optimization, Phys. Rev. A 106
2022
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