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NTT technical review

Activities toward New-principle Computers

Shiro Saito, Hideki Gotoh

Published May 1, 2021• 2 citations
Publisher

Abstract

Non-von Neumann-type computers, such as quantum computers and Ising machines that operate on principles different from those of present-day computers, are attracting attention.They are particularly powerful when applied to specific types of problems such as combinatorial optimization problems, quantum chemical calculations, and prime factorization, and since solutions to problems such as these can have a significant impact on society, research of new-principle computers is moving forward at a vigorous pace.The following Feature Articles in this issue introduce theoretical and experimental activities regarding new-principle computers at NTT laboratories while describing recent advances in this field.

DOI
10.53829/ntr202105fa1

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近年、組合せ最適化問題の高効率解法として期待されている量子アニーリングをはじめとしたイジングマシンが注目を集めている。イジングマシンで組合せ最適化問題を解く際には、組合せ最適化問題の目的関数ならび制約条件をイジングモデルのエネルギー関数で表現し、基底状態(エネルギー最小状態)を探索する。イジングマシンによって動作原理が異なり、その動作原理に基づくイジングモデルの設計やハイパーパラメータの調整を行うことによって、イジングマシンの性能を最大限引き出す計算処理が可能となる。 本研究課題では、大きく分けて以下の3つのトピックに関して研究を行った。(1)量子アニーリングの性能を引き出す量子ゆらぎの導入方法の検討、(2)イジングマシンにおけるハイパーパラメータ調整法の検討、(3)イジングマシンの応用探索 (1)では、ランダムな大きさの相互作用を持つ1次元イジングスピンモデルに対する量子アニーリングの性能を統計力学の知見に基づき検討した。相互作用のランダムネスに対応したランダムな横磁場を印加することで、量子アニーリングの性能が高まることが示された。この成果については現在論文投稿中である(プレプリント版は、arXiv:2007.07439に掲載)。(2)では、いくつかのイジングマシンにおいて必須の「埋め込みアルゴリズム」におけるハイパーパラメータの調整方法について統計力学シミュレーション(モンテカルロシミュレーション)に基づき解析を行った。この成果についてはIEEE Accessに掲載された。また、いくつかのイジングマシンにおいて必要なビット幅削減についてもまとめIEEE Transactions on Computersに掲載された。(3)では、部分グラフ検出ならびにスロット配置問題と呼ばれる具体的な組合せ最適化問題に対してイジングマシンを用いる方法を考案し、実際のイジングマシンで計算処理を行った結果をまとめた。ともに、IEICE Transactions on Information and Systemsに掲載された。 In recent years, Ising machines such as quantum annealing, which is expected to be a highly efficient solution method for combinatorial optimization problems, have attracted much attention. When solving a combinatorial optimization problem with an Ising machine, the combinatorial optimization problem's objective function and constraints are expressed by the energy function of the Ising model, and the ground state (minimum energy state) is searched. Each Ising machine has a different operating principle, and by designing an Ising model based on the operating principle and adjusting the hyperparameters, it is possible to perform computational processing that maximizes the Ising machine's performance. In this research project, we have studied the following three major topics. In this research project, we studied the following three topics: (1) how to introduce quantum fluctuations to maximize the performance of quantum annealing, (2) how to tune hyperparameters in Ising machines, and (3) how to explore applications of Ising machines. In (1), the performance of quantum annealing for a one-dimensional Ising spin model with randomly sized interactions was investigated based on the knowledge of statistical mechanics. It is shown that quantum annealing performance is enhanced by applying a random transverse magnetic field corresponding to the randomness of the interaction. This result is now under submission for publication (preprint version is available at arXiv:2007.07439). In (2), we analyzed how to tune the hyperparameters in the "embedding algorithm," which is essential for some Ising machines, based on statistical mechanics simulation (Monte Carlo simulation). This result was published in IEEE Access. We also summarized the bit-width reduction required for some Ising machines and published it in IEEE Transactions on Computers. In (3), we devised a method using an Ising machine for a specific combinatorial optimization problem called the subgraph detection and slot placement problem and summarized the computational processing results on an actual Ising machine. Both papers were published in IEICE Transactions on Information and Systems.

•Jan 1, 2020•0 citations
Non-von Neumann-type computers, such as quantum computers and Ising machines that operate on principles different from those of present-day computers, are attracting attention.They are particularly powerful when applied to specific types of problems such as combinatorial optimization problems, quantum chemical calculations, and prime factorization, and since solutions to problems such as these can have a significant impact on society, research of new-principle computers is moving forward at a vigorous pace.The following Feature Articles in this issue introduce theoretical and experimental activities regarding new-principle computers at NTT laboratories while describing recent advances in this field.
The demand for efficient solvers of complicated combinatorial optimization problems, especially those classified as NP-complete or NP-hard, has recently led to increased exploration of novel computing architectures. One prominent collective state computing paradigm embodied in the so-called Ising machines has recently attracted considerable research attention due to its ability to optimize complex problems with large numbers of interacting variables. Ising model-inspired solvers, thus named due to mathematical similarities to the well-known model from solid-state physics, represent a promising alternative to traditional von Neumann computer architectures due to their high degree of inherent parallelism. While there are many possible physical realizations of Ising solvers, just as there are many possible implementations of any binary computer, photonic Ising machines (PIMs) use primarily optical components for computation, taking advantage of features like lower power consumption, fast calculation speeds, the leveraging of physical optics to perform the calculations themselves, possessing decent scalability and noise tolerance. Photonic computing in the form of PIMs may offer certain computational advantages that are not easily achieved with non-photonic approaches and is nonetheless an altogether fascinating application of photonics to computing. In this review, we provide an overview of Ising machines generally, introducing why they are useful, what types of problems they can tackle, and how different Ising solvers can be compared and benchmarked. We delineate their various operational mechanisms, advantages, and limitations vis-à-vis non-photonic Ising machines. We describe their scalability, interconnectivity, performance, and physical dimensions. As research in PIMs continues to progress, there is a potential that photonic computing could well emerge as a way to handle large and challenging optimization problems across diverse domains. This review serves as a comprehensive resource for researchers and practitioners interested in understanding capabilities and potential of PIMs in addressing such complex optimization problems.
We are now ready to assemble quantum subroutines into quantum algorithms. A reasonable first question is: Are there problems which can be solved efficiently on a quantum computer? In his analysis of a universal quantum computer [25], Deutsch illustrated quantum parallelism by constructing a procedure to compute the parity f (0) ⊕ f (1) of a function on one bit. In a generalization of this context, Deutsch and Jozsa [27] defined a quantum algorithm that could solve a problem more efficiently than is possible on a classical computer. This problem helped motivate the search for algorithms that could solve “real” problems, and Simon [67] provided an example that inspired Shor’s subsequent work on the factoring problem and on the discrete logarithm problem. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
近年、組合せ最適化問題の高効率解法として期待されている量子アニーリングをはじめとしたイジングマシンが注目を集めている。イジングマシンで組合せ最適化問題を解く際には、組合せ最適化問題の目的関数ならび制約条件をイジングモデルのエネルギー関数で表現し、基底状態(エネルギー最小状態)を探索する。イジングマシンによって動作原理が異なり、その動作原理に基づくイジングモデルの設計やハイパーパラメータの調整を行うことによって、イジングマシンの性能を最大限引き出す計算処理が可能となる。 本研究課題では、大きく分けて以下の3つのトピックに関して研究を行った。(1)量子アニーリングの性能を引き出す量子ゆらぎの導入方法の検討、(2)イジングマシンにおけるハイパーパラメータ調整法の検討、(3)イジングマシンの応用探索 (1)では、ランダムな大きさの相互作用を持つ1次元イジングスピンモデルに対する量子アニーリングの性能を統計力学の知見に基づき検討した。相互作用のランダムネスに対応したランダムな横磁場を印加することで、量子アニーリングの性能が高まることが示された。この成果については現在論文投稿中である(プレプリント版は、arXiv:2007.07439に掲載)。(2)では、いくつかのイジングマシンにおいて必須の「埋め込みアルゴリズム」におけるハイパーパラメータの調整方法について統計力学シミュレーション(モンテカルロシミュレーション)に基づき解析を行った。この成果についてはIEEE Accessに掲載された。また、いくつかのイジングマシンにおいて必要なビット幅削減についてもまとめIEEE Transactions on Computersに掲載された。(3)では、部分グラフ検出ならびにスロット配置問題と呼ばれる具体的な組合せ最適化問題に対してイジングマシンを用いる方法を考案し、実際のイジングマシンで計算処理を行った結果をまとめた。ともに、IEICE Transactions on Information and Systemsに掲載された。 In recent years, Ising machines such as quantum annealing, which is expected to be a highly efficient solution method for combinatorial optimization problems, have attracted much attention. When solving a combinatorial optimization problem with an Ising machine, the combinatorial optimization problem's objective function and constraints are expressed by the energy function of the Ising model, and the ground state (minimum energy state) is searched. Each Ising machine has a different operating principle, and by designing an Ising model based on the operating principle and adjusting the hyperparameters, it is possible to perform computational processing that maximizes the Ising machine's performance. In this research project, we have studied the following three major topics. In this research project, we studied the following three topics: (1) how to introduce quantum fluctuations to maximize the performance of quantum annealing, (2) how to tune hyperparameters in Ising machines, and (3) how to explore applications of Ising machines. In (1), the performance of quantum annealing for a one-dimensional Ising spin model with randomly sized interactions was investigated based on the knowledge of statistical mechanics. It is shown that quantum annealing performance is enhanced by applying a random transverse magnetic field corresponding to the randomness of the interaction. This result is now under submission for publication (preprint version is available at arXiv:2007.07439). In (2), we analyzed how to tune the hyperparameters in the "embedding algorithm," which is essential for some Ising machines, based on statistical mechanics simulation (Monte Carlo simulation). This result was published in IEEE Access. We also summarized the bit-width reduction required for some Ising machines and published it in IEEE Transactions on Computers. In (3), we devised a method using an Ising machine for a specific combinatorial optimization problem called the subgraph detection and slot placement problem and summarized the computational processing results on an actual Ising machine. Both papers were published in IEICE Transactions on Information and Systems.