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Quantum annealing machines based on superconducting qubits, which have the potential to solve optimization problems faster than digital computers, are of great interest not only to researchers but also to the general public. Here, we propose a quantum annealing machine based on a semiconductor floating gate (FG) array. We use the same device structure as that of the commercial FG NAND flash memory except for small differences such as thinner tunneling barrier. We theoretically derive an Ising Hamiltonian from the FG system in its single-electron region. Recent high-density NAND flash memories are subject to several problems that originate from their small FG cells. In order to store information reliably, the number of electrons in each FG cell should be sufficiently large. However, the number of electrons stored in each FG cell becomes smaller and can be countable. So we utilize the countable electron region to operate single-electron effects of FG cells. Second, in the conventional NAND flash memory, the high density of FG cells induces the problem of cell-to-cell interference through their mutual capacitive couplings. This interference problem is usually solved by various methods using a software of error-correcting codes. We derive the Ising interaction from this natural capacitive coupling. Considering the size of the cell, 10 nm, the operation temperature is expected to be approximately that of a liquid nitrogen. If a commercial 64 Gbit NAND flash memory is used, ideally we expect it to be possible to construct 2 megabytes (MB) entangled qubits by using the conventional fabrication processes in the same factory as is used for manufacture of NAND flash memory. A qubit system of highest density will be obtained as a natural extension of the miniaturization of commonly used memories in this society.
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