Quantum technologies are rapidly moving from laboratory research toward industrialization, commercialization, and capital formation, while introducing new sources of financial risk associated with technological uncertainty, cybersecurity and post-quantum cryptography (PQC) migration, regulatory change, supply-chain resilience, and investment timing. In 2024, the U.S. National Institute of Standards and Technology (NIST) finalized and published three foundational PQC standards, FIPS 203, FIPS 204, and FIPS 205. In 2025, the Bank for International Settlements (BIS) advanced Project Leap to test quantum-safe cryptography in financial infrastructure, while the OECD published its A Quantum Technologies Policy Primer. In 2026, the Hong Kong Monetary Authority (HKMA) introduced the first Quantum Preparedness Index (QPI), with an initial sector-level score of 2.3 out of 10, indicating that quantum preparedness in the banking sector remains at an early stage. These developments highlight a growing need to integrate technological, cybersecurity, institutional, and financial-risk perspectives within a coherent decision architecture. This paper develops a Prim-Lex Quantum Finance framework based on Prim-Lex Theory (Economic Climatology), integrating five Prim-Fires, eight-dimensional coherence, and Nine-Nexus guidance. The Five Prim-Fires comprise Technological-Capability Prim-Fire, Security-Resilience Prim-Fire, Institutional-Governance Prim-Fire, Industrial-Commercial Prim-Fire, and Earth-System Intelligence-Coherence Prim-Fire. The Prim-Lex Eight-Dimensional Quantum Finance State Space (PL-8D-QF) characterizes quantum-technology investment projects across eight dimensions: Technological Capability; Security and Quantum Readiness; Policy and Regulatory Alignment; Technology Maturity and Lifecycle; Ex-ante Financial Viability; Supply-Chain and Systemic Resilience; Temporal Synchronization and Transition Readiness; and Information Quality and Transparency. Building on this state space, the paper introduces the Quantum Investment Coherence Index (QICI), which combines a weighted geometric aggregation of eight-dimensional state strengths with a Kuramoto-based coherence measure derived from dynamic phase information extracted using the Hilbert transform. The central testable proposition is that multidimensional coherence contains incremental predictive information about financial risk beyond the information contained in dimension strengths alone. The framework further specifies a quantitative transmission mechanism from QICI to Probability of Default (PD), Expected Loss (EL), risk-adjusted returns, and financing costs or credit spreads, while distinguishing the Quantum Sovereignty Index (QSI) for national strategic assessment from QICI for project- and investment-level decision-making. The paper formulates 12 testable hypotheses and develops an empirical validation design incorporating panel data, predictive modeling, data-driven critical phase-threshold identification, block bootstrap procedures, out-of-sample validation, and falsification or placebo tests. The critical phase threshold is not imposed ex ante as a universal constant, such as , but is identified from predictive performance in the data; is retained only as a falsifiable theoretical benchmark. The framework then links QICI to risk pricing, investment timing, capital allocation, risk mitigation, and exit decisions, thereby establishing a decision chain from quantum-technology state assessment to financial-risk pricing and capital allocation. The paper seeks to extend the assessment of quantum technologies from technological evaluation to financial evaluation and from compliance-oriented assessment to risk-sensitive allocation optimization. It provides a quantifiable, testable, programmable, and auditable analytical framework for quantum-technology investment, institutional quantum preparedness, post-quantum cryptography migration, and emerging quantum-climate-finance research.
On May 28, 2026, the OECD Council adopted the Recommendation of the Council on Quantum Technologies (OECD/LEGAL/0508), the world's first intergovernmental standard for quantum technologies, marking the official transition of quantum technology governance from "academic discussion" to "institutional construction". At the same time, Academician Pan Jianwei of the Chinese Academy of Sciences warned at the 2026 Future Science Forum that excessive capital enthusiasm and conceptual hype in the quantum information industry are rampant, calling for the establishment of a national-level technology evaluation mechanism and industry access standards. The disruptive impact of quantum computing on existing encryption systems, the geopolitical implications of quantum communication, and the military applications of quantum sensing have made quantum technology a new frontier in great power competition. Based on the eight-dimensional framework of Prim-Lex Theory (Economic Climatology), this paper introduces, for the first time, quantum technology governance into the mathematical expression of a complexified unified field. From Prim-Unity·Prim-Fire (quantum computing energy consumption and qubit coherence time) to Eight Trigrams·Eight Information (entropy governance of quantum information networks), it constructs a quantitative assessment system for quantum technology governance dimension by dimension. Using three empirical anchors——the US-China-Europe quantum competition, post-quantum cryptography (PQC) standardization and migration, and the quantum-safe encryption standards debate——this paper demonstrates the application pathway of the eight-dimensional framework in identifying "phase differences" and "critical windows" in quantum governance, providing a quantifiable, programmable, and auditable mathematical language and governance tool for the transition of global quantum technology from "technological competition" to "sustainable governance."