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変数量子 Eigensolver を使ってマルチクラスポートフォリオの最適化,ディッケ状態の代替で
J V S Scursulim1, Gabriel M Langeloh2, Victor L Beltran2
1Instituto de Ciência e Tecnologia Itaú, São Paulo, Brazil. jose.scursulim@itau-unibanco.com.br.
Scientific reports
|February 13, 2026
まとめ
この研究は,多様化に配慮したポートフォリオの最適化のための新しい量子フレームワークを導入しています. Dicke state ansatzは,実行可能な解決策を確保し,既存の方法よりも優れたパフォーマンスを提供することにより,パフォーマンスを大幅に向上させます.
科学分野:
- 量子コンピューティング
- コンピューティング・ファイナンス
- オプティマイゼーション アルゴリズム
背景:
- ポートフォリオの最適化は金融において極めて重要ですが,多様化についてはしばしば無視されます.
- ポートフォリオ最適化のための既存の量子アルゴリズムには,明示的な多様化制約がない.
- 現実的な金融モデルは,実用的な適用のために多様化を組み込むことを要求します.
研究 の 目的:
- 多種多様なポートフォリオの最適化のための新しい量子フレームワークを開発し,多様化を明示的に組み込む.
- 多様化制約を本質的に満たす変数量子エイゲンソルバー (VQE) の新しい代替案を導入する.
- このハイブリッド量子-古典的アプローチの性能に対する古典的最適化器の影響を分析する.
主な方法:
- 多数のパラメータ化されたディッケ状態をVQEの代替として使って,多様化制約をエンコードした.
- 量子システムを実行可能な状態の重置で初期化し,検索スペースを縮小し,ペナルティ項の必要性を排除しました.
- CMA-ES最適化器を中心に,さまざまな古典的な最適化器でパフォーマンスを評価しました.
主要な成果:
- ディッケ・ステート・アンサツは,多元化制約を成功裏にコードし,実行可能なポートフォリオ状態のみを調査することを保証しました.
- ハイブリッド量子-古典的アプローチ,特にCMA-ES最適化器は,優れた収束率,近似比率,および測定確率を示しました.
- この方法は,ペナルティ用語を回避することで,計算上の検索スペースを大幅に削減しました.
結論:
- 提案された量子フレームワークは,実践的で多様化に配慮したポートフォリオ最適化のための有望なソリューションを提供します.
- ディッケ・ステート・アンサッツは,量子最適化における制約を効率的に扱うための重要な革新である.
- このアプローチは,現実のポートフォリオ管理の課題に取り組むために,金融セクターでの応用に大きな可能性を持っています.
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