{{{\boldsymbol{\beta }}})\left\vert {0}^{n}\right\rangle =\mathop{\prod }\limits_{k=1}^{p}\left({e}^{-i{\beta }_{k}\mathop{\sum }\limits_{i}^{n}{X}_{i}}{e}^{-i{\gamma }_{k
The elements in sets of size 2 are either adjacent or of the form j−1,j+1. The elements of sets of size three are of the form j−1,j,j+1. We, therefore, get Lemma 4. Lemma 4 For each symbol a, let Loca be the set of indices in which it appears in the substrings P1...
Finally, on output, the algorithm produces an approximate factorization [C.sup.T] C - [mu]I [approximately equal to] [LDL.sup.T] with D having only 0, [+ or -] 1 as diagonal elements. Computing singular values of large matrices with an inverse-free preconditioned Krylov subspace method...
After the final layer, the RBM is parametrized by θopt, approximating the final QAOA target state \(\left|{\boldsymbol{\gamma }},{\boldsymbol{\beta }}\right\rangle\). Full size image Simulation results for 20 qubits In this section we present our simulation results for Max-Cut QAOA ...
(i) All the eigenvalues have finite multiplicity equal to the dimension of the corresponding eigenspace . (ii) Let be a basis of the for every then the eigenvectors form a complete orthonormal system in the space Hence for all we have If we put then we get . (iii) Also, the eigenfuncti...
(insertions, deletions, or replacements) in the sequence that lead to small structural changes, such as the breaking of a base pair, are not supported. This often hampers the creation of patterns that are specific but generalized enough to match all family members. An algorithm presented in [...
Communication systems are prone to error weather wired or wireless. The error in wireless communication system has well defined structure. The receiver decode this erroneous symbol in such a way that the erroneous symbol is good approximation of the transmitted symbol as compare to a randomly chosen...
⪈ greater-than and single-line not equal to U+2A88 ⪊ greater-than and not approximate U+2A8A Glyphs · · · DejaVu Sans, Book Chart · · · U+2A00 - U+2AFF 0 1 2 3 4 5 6 7 8 9 A B C D E F 2A0 ⨀ ⨁ ⨂ ⨃ ⨄ ⨅ ⨆ ⨇ ⨈ ⨉ ⨊ ...
(R removal and I infection times), nI is the number of infected individuals, Lepi is the length of epidemic, µ( · ) and σ( · ) are the mean and standard deviation of the infection or removal times, IT0I0T is the number of infection events over equal time intervals;...
By introducing the smooth rank function (SRF), this paper proposes a new tensor rank nonconvex substitution function that performs adaptive weighting on different singular values to avoid the performance deficiency caused by the equal treatment of all singular values. On this basis, a novel tensor ...