High-level description of how QPC-SRD detects financial crash phase transitions. Proprietary QPC core logic is not disclosed.
The global financial system is modeled as a network of 128 nodes (banks, asset managers, central banks, insurers). Each node has a stress state (stable or stressed). Connections between nodes represent credit exposure and derivatives counterparty risk.
Matrices used:
wi = node stress from leverage and derivatives exposure. Jij = interaction (exposure × correlation). si = 0 (stable) or 1 (stressed). High H corresponds to high systemic risk (crash-like configuration).
R is computed from the probability distribution of sampled quantum outcomes.
S = system coherence. When the coherence change ΔS exceeds threshold θ, the network is in a collapse-prone state (liquidity cascade, correlated defaults). The threshold θ is derived from the 90th percentile of H across quantum samples.
A key scientific element of the QPC crash-detection experiment is the interpretation of systemic financial instability as a phase transition in a complex network.
Because the financial system is modeled through a Hamiltonian interaction structure, the global network behaves mathematically in a way similar to many systems studied in statistical physics. As stress propagates through inter-institution exposures, the system can transition from a stable regime into an unstable regime in which correlated defaults become self-reinforcing.
In this framework, high-energy configurations of the systemic Hamiltonian correspond to financial collapse states of the network. The collapse threshold θ therefore marks the boundary between stable and unstable regimes of the system.
Quantum sampling allows the exploration of a large ensemble of possible network configurations. By analyzing the probability distribution of these states, the QPC computation identifies the onset of systemic phase transitions, where cascading failures across the financial network become increasingly probable.
This interpretation links the crash-detection model to well-known concepts in complex-systems science, such as percolation transitions, contagion cascades, and network criticality, providing a physically grounded framework for understanding systemic financial crises.
In this sense, the QPC computation acts as a quantum probe of the systemic stability landscape, allowing the identification of critical configurations where the financial network approaches a collapse phase transition.
Because the network contains 128 institutions, the financial system can theoretically exist in 2128 possible stress configurations (≈ 3.4 × 1038). Quantum sampling allows the exploration of this enormous systemic configuration space and the identification of high-risk regions associated with financial collapse scenarios.
We use the Quantum Approximate Optimization Algorithm (QAOA) to search for configurations that maximize systemic energy H. QAOA alternates between:
Measurement yields a probability distribution over 2128 possible configurations. High-probability outcomes correspond to high-risk states.
The QPC architecture introduces a polycontextural computational representation in which heterogeneous financial actors—such as banks, asset managers, insurers, and central banks—are encoded within distinct but interacting contextual layers of the computational state space.
This representation allows systemic interactions to be modeled not only as pairwise financial exposures but also as cross-context dependencies between different classes of institutions and financial functions. As a result, the systemic Hamiltonian operates on a structured state space that captures both intra-context and inter-context contagion dynamics.
Such a representation is particularly suited for modeling complex financial networks where stability emerges from the interaction of multiple institutional roles and market mechanisms.