スペクトルギャップの未決定性
Toby S Cubitt1,2, David Perez-Garcia3,4, Michael M Wolf5
1Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK.
Nature
|December 15, 2015
まとめ
量子多体物理学におけるスペクトルギャップ問題は 決定不能である. つまり 量子システムがギャップかギャップレスかを 判断できる一般的なアルゴリズムはなく 物理学の基礎研究に影響を与えます
科学分野:
- 量子多体物理学
- 計算上の複雑性理論
背景:
- 量子システムの理解には 極めて重要です 量子力学では 量子力学では 量子力学では
- ハルダーン推論とトポロジカル・フェーズを含む物理学の多くの重要な問題は,スペクトルギャップの周りに回っています.
研究 の 目的:
- 量子多体系におけるスペクトルギャップ問題の決定性を決定する.
- 他の低エネルギー特性に対する未決定性の影響を調査する.
主な方法:
- 特定の相互作用型の2D格子上の量子スピンシステムの構築.
- ハミルトン的な複雑性と無周期的なタイルを使用します.
- 量子相推定アルゴリズムと システムの基本状態内の ユニバーサル・チューリング・マシンをコードする.
主要な成果:
- 変換的に不変の近隣相互作用を持つ量子スピンシステムのスペクトルギャップ問題は決定不能であることが証明されている.
- この未決定性は,基底相関崩壊のような他の低エネルギー特性にも広がります.
- スペクトルギャップの決定は,停止問題の結果と関連しています.
結論:
- 任意の量子モデルがギャップかギャップレスかを判断する普遍的なアルゴリズムはありません.
- 特定の量子モデルは,数学的公理から独立したスペクトルギャップ特性を示す.
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