{"id": "card_joint_sign_problem", "kind": "note", "title": "The lattice sign problem is NP-hard", "body": "Troyer and Wiese (2005): the fermion sign problem of quantum Monte Carlo - the obstacle to simulating lattice gauge theory at finite density - is NP-hard. A proof that P = NP would remove it; its hardness is a statement about computation sitting inside a statement about gauge fields.", "source": {"label": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "url": "", "domain": "mathematics", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "joint", "bands": ["joint", "two trees", "millennium", "floor", "sign problem", "np-hard", "lattice"], "subject": "The lattice sign problem is NP-hard", "connections": [{"to_card_id": "card_floor_millennium", "relationship": "part_of", "evidence": "a joint that is proven or observed - a part of the floor"}, {"to_card_id": "card_question_yang_mills", "relationship": "connects_at", "evidence": "The lattice sign problem is NP-hard. troyer wiese 2005. Cited, not sealed: no arithmetic to recompute"}, {"to_card_id": "card_question_p_vs_np", "relationship": "connects_at", "evidence": "The lattice sign problem is NP-hard. troyer wiese 2005. Cited, not sealed: no arithmetic to recompute"}, {"to_card_id": "card_src_mill_troyer_wiese_2005", "relationship": "cites", "evidence": "the record the joint stands on"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.joint", "facets": {"subject": ["floor", "lattice", "millennium", "np-hard", "sign problem", "two trees"]}, "presentation": {"glyph": "•", "kind_label": "joint", "by": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "relationship": "part of", "why": "a joint that is proven or observed - a part of the floor", "href": "/card/card_floor_millennium", "resolved": true}, {"id": "card_question_yang_mills", "title": "Yang-Mills existence and the mass gap", "relationship": "connects at", "why": "The lattice sign problem is NP-hard. troyer wiese 2005. Cited, not sealed: no arithmetic to recompute", "href": "/card/card_question_yang_mills", "resolved": true}, {"id": "card_question_p_vs_np", "title": "P versus NP", "relationship": "connects at", "why": "The lattice sign problem is NP-hard. troyer wiese 2005. Cited, not sealed: no arithmetic to recompute", "href": "/card/card_question_p_vs_np", "resolved": true}, {"id": "card_src_mill_troyer_wiese_2005", "title": "M. Troyer 2005 — Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations", "relationship": "cites", "why": "the record the joint stands on", "href": "/card/card_src_mill_troyer_wiese_2005", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_joint_sign_problem", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_joint_sign_problem"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}