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arXiv:1706.07565 · Bulletin of the American Physical Society

Quantum Annealing Machine based on Floating Gate Array

Tetsufumi Tanamoto, Y. Higashi, Takao Marukame, Jun Deguchi

Published Jun 23, 2017• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1706.07565

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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. In this paper, we propose a quantum annealing machine based on a semiconductor floating gate (FG) array. The purpose of using the architecture of nand flash memories is to reuse a mature technology to create large arrays of silicon qubits. Current high-density nand flash memories use sufficiently small FG cells to make the number of electrons stored in each cell small and countable. The high packing density of these cells creates mutual capacitive couplings that can be used to generate cell-to-cell interactions. We explore these characteristics to derive an Ising Hamiltonian for the FG system in the single-electron regime. Considering the size of a cell (10 nm), the ideal operation temperature of a quantum annealer based on FG cells is estimated to be approximately that of liquid nitrogen. Assuming the parameters of a commercial 64 Gbit nand, we estimate that it is possible to create 2-megabyte (MB) qubit systems solely using conventional fabrication processes. Our proposal demonstrates that a large qubit system can be obtained as a natural extension of the miniaturization of commercial-grade electronics, although more effort will likely be required to achieve high-quality qubits.
The development of quantum annealing machines (QAMs) based on superconducting qubits has progressed greatly in recent years and these machines are now widely used in both academia and commerce. On the other hand, QAMs based on semiconductor nanostructures such as quantum dots (QDs) appear to be still at the initial elementary research stage because of difficulty in controlling the interaction between qubits. In this paper, we review a QAM based on a semiconductor nanostructures such as floating gates (FGs) or QDs from the viewpoint of the integration of qubits. We theoretically propose the use of conventional high-density memories such as NAND flash memories for the QAM rather than the construction of a semiconductor qubit system from scratch. A large qubit system will be obtainable as a natural extension of the miniaturization of commercial-grade electronics, although further effort will likely be required to achieve high-quality qubits.
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures for quantum computation: gate-based quantum computers and quantum annealing. In gate-based quantum computation, we implement a sequence of quantum gates that manipulate qubits. This approach allows us to perform universal quantum computation, yet they pose significant experimental challenges for large-scale integration. On the other hand, with quantum annealing, the solution of the optimization problem can be obtained by preparing the ground state. Conventional quantum annealing devices with transverse-field Ising Hamiltonian, such as those manufactured by D-Wave Inc., achieving around 5000 qubits, are relatively more amenable to large-scale integration but are limited to specific computations. In this paper, we present a practical method for implementing universal quantum computation within the conventional quantum annealing architecture using the transverse-field Ising Hamiltonian. Our innovative approach relies on an adiabatic transformation of the Hamiltonian, changing from transverse fields to a ferromagnetic interaction regime, where the ground states become degenerate. Notably, our proposal is compatible with D-Wave devices, opening up possibilities for realizing large-scale gate-based quantum computers. This research bridges the gap between conventional quantum annealing and gate-based quantum computation, offering a promising path toward the development of scalable quantum computing platforms.
Abstract One of the major problems of quantum computing applications is that the required number of qubits to solve a practical problem is much larger than that of today's quantum hardware. In this work, we introduce the large-system sampling approximation (LSSA) algorithm to solve Ising problems with sizes up to Ngb2Ngb by an Ngb-qubit gate-based quantum computer, and problems with sizes up to Nan2Ngb by a hybrid computational architecture of an Nan-qubit quantum annealer and an Ngb-qubit gate-based quantum computer. By dividing the full-system problem into smaller subsystem problems, the LSSA algorithm then solves the subsystem problems by either gate-based quantum computers or quantum annealers, and optimizes the amplitude contributions of the solutions of the different subsystems with the full-problem Hamiltonian by the variational quantum eigensolver (VQE) on a gate-based quantum computer to determine the approximated ground-state configuration. LSSA has polynomial time complexity and can be further extended to a deeper level of approximation with computational overhead that grows linearly with the problem size. The effects of different subsystem sizes, numbers of subsystems, and full problem sizes on the performance of LSSA are investigated on both simulators and real hardware. The completely new computational concept of the hybrid gate-based and annealing quantum computing architecture opens a promising possibility to investigate large-size Ising problems and combinatorial optimization problems, making practical applications by quantum computing possible in the near future.
To date, conventional computers have never been able to efficiently handle certain tasks, where the number of computation steps is likely to blow up as the problem size increases. As an emerging technology and new computing paradigm, quantum computing has a great potential to tackle those hard tasks efficiently. Among all the existing quantum computation models, quantum annealing has drawn significant attention in recent years due to the realization of the commercialized quantum annealer, sparking research interests in developing applications to solve problems that are intractable for classical computers.However, designing and implementing algorithms that manage to harness the enormous computation power from quantum annealer remains a challenging task. Generally, it requires mapping of the given optimization problem into quadratic unconstrained binary optimization(QUBO) problem and embedding the subsequent QUBO onto the physical architecture of quantum annealer. Additionally, practical quantum annealers are susceptible to errors leading to low probability of the correct solution.In this study, we focus on solving Boolean satisfiability (SAT) problem using quantum annealer while addressing practical limitations. We have proposed a mapping technique that maps SAT problem to QUBO, and we have further devised a tool flow that embeds the QUBO onto the architecture of a quantum annealing device. Additionally, We have optimized the proposed embedding flow to reduce run-time in addition to shortening the qubit chain length, leading to robust quantum annealing. To further improve the reliability of quantum annealing, we have also developed a post processing embedding technique that enlarges the energy gap between ground state and the first excited state. To demonstrate the effectiveness of proposed methods, we have conducted experiments on real quantum annealing devices manufactured by D-Wave Systems, showing compelling result of using quantum annealer to solve SAT problem.