サイ トあた りⅣ 状態を取 り得る 1 次元確率過程模型 ( 以後､｢ 1 次元 Ⅳ 状態確率過程模型｣と呼 ぶ) 回 には､厳密な ｢ ( サイ トによらない) 行列積型定常状態ベク トル｣( ma t r i x -p r o d u c t s t a t i o n a r y s t a t e ; 以下では MPS Sと略す)【 2 】 を持つ ものがある｡ このタイプの定常状態 を使 うと､カ レン ト や相関関数を比較的簡単に､しかも厳密に求めることが可能 となる｡この時､q直交多項式の理論 が役立つ事 も明 らかにされている [ 3 , 4 , 5 ] ｡最近では､MPS Sが非平衡統計力学での ｢ 自由エネル ギー｣ の計算 [ 6 ] にも用 いられた｡ 行列積型ベク トルそのものは､あちこちに現れる｡確率過程模型での最初の発見 [ 7 】 よ りも先 に､( 行列積型基底状態ベク トルとして) 量子スピン模型で発見されてお り､ 基底状態での厳密な物 理量の計算を可能 としていた 【 8 】 ｡ その後に登場 した密度行列 くりこみ群 の方法 ( De n s i t yMa t r i x Re n o r ma l i z a t i o nGr o u p ; DMRG と略される事が多い) [ 9 ] においては､ 近似的な行列横型ベク ト ルが重要な役割 を果た している事が明 らかにされている ( DMRG の高次元模型への拡張 [ 1 0 】 にお いては､行列積をテンソル積へ と拡張 したものが用いられる事 もある) ｡ 話を厳密な MPS Sに戻すと､ 1 次元 Ⅳ 状態確率過程模型の厳密な MPS Sをシステマティック に求める方法は明 らかでなか った｡ これ故 に､厳密な MPS Sは ごく少数知 られているに過 ぎな い｡システマティックに求める上での､数値的なヒン トを得る方法は P e s c h e lとⅠ く a u l k eらによっ て与え られていた t l l い 彼等は DMRG における密度行列のスペク トラムを観察することが厳密な MPS Sを数値的に発見するのに重要だとだけ主張 していた｡我々は彼等の主張について考え､ま ず数値的な厳密解 を構成する方法を作 った｡そ して数式処理の助けも借 りると厳密解を求めるこ ともできることに気付き､さらに方法を少 し見通 しよ くできることが分か った｡本稿で述べるの は､その厳密解 を求める方法である｡ 本研究の目的は MPS Sをシステマティックに求める方法を明らかにすることである｡現在 まで
Although the network architecture of the Quantum Internet has not yet been established, a hierarchical structure similar to that of the classical Internet has been proposed in recent years. However, discussions on the application layer, the highest layer in the hierarchy, are still in their early stages, and a major challenge lies in the non-trivial task of converting applications into a form that can be accepted by the lower layers. In this study, we propose a framework that defines the necessary information and procedures for executing applications on the Quantum Internet, aiming for seamless integration of the quantum network stack, including the application layer. Our framework builds upon the RuleSet-based protocol, which enables connectivity below the application layer. Before application execution, it clarifies inter-node communication procedures, organizes essential application information, and introduces new Rules for application execution, thereby embedding application-specific information into RuleSets. Through this process, applications are transformed into a format executable on the Quantum Internet. The feasibility of our proposed protocol is validated by converting into an intermediate representation (IR) format that can be executed on nodes within QuISP, a large-scale quantum network simulator. This approach facilitates seamless connectivity from the application layer to the physical layer in the quantum network architecture, reducing barriers to deploying future Quantum Internet applications.
Quantum computing introduces a new computing paradigm that promises to solve problems that cannot be solved by classical computers efficiently. Thus, quantum applications will be more and more integrated in classical applications. To bring these composite applications into production, technologies for an automated deployment and orchestration are required to avoid manual error-prone and time-consuming processes. For non-quantum applications, a variety of deployment technologies have been developed in recent years. However, the deployment of quantum applications currently differs significantly from non-quantum applications and thus, leads to a different modeling procedure for the deployment of quantum applications. To overcome these problems, we propose TOSCA4QC that introduces two deployment modeling styles based on the Topology and Orchestration Specification for Cloud Applications (TOSCA) standard for automating the deployment and orchestration of quantum applications: (i) SDK-specific modeling style to cover all technical deployment details and (ii) SDK-agnostic modeling style supporting common modeling principles. We further show how existing model-driven development (MDD) approach can be applied to refine a SDK-agnostic model to an executable SDK-specific model. We demonstrate the practical feasibility by a prototypical implementation as an extension of the TOSCA ecosystem OpenTOSCA and three case studies with IBMQ and a quantum simulator.
Layered architectures for the Quantum Internet have been proposed, inspired by that of the classical Internet, which has demonstrated high maintainability even in large-scale systems. While lower layers in the Quantum Internet, such as entanglement generation and distribution, have been extensively studied, the application layer - responsible for translating user requests into executable quantum-network operations - remains largely unexplored. A significant challenge is translating application-level requests into the concrete instructions executable at lower layers. In this work, we introduce a RuleSet-based framework that explicitly incorporates the application layer into the layered architecture of the Quantum Internet. Our framework builds on a RuleSet-based protocol, clarifying communication procedures, organizing application request information, and introducing new Rules for application execution by embedding application specifications into RuleSets. To evaluate feasibility, we constructed state machines from the generated RuleSets. This approach enables a transparent integration from the application layer down to the physical layer, thereby lowering barriers to deploying new applications on the Quantum Internet.