Executive Overview
The Nasdaq Solvers project investigates the application of quantum non-locality and entanglement to multi-agent decision-making and coordination tasks. Inspired by high-frequency trading (HFT) scenarios where geographical separation (such as data centers in New Jersey) and the finite speed of light prevent real-time communication, the project explores whether quantum entanglement can serve as a superior resource over classical strategies to prevent trading algorithms from acting at cross-purposes.
Theoretical Framework: Non-Local Games & Bell's Theorem
The coordination challenge involves two cooperating agents (Alice and Bob) making simultaneous decisions based on localized information without communication. While classical agents rely on pre-arranged strategies and shared random numbers, John Bell’s 1964 theorem proves that sharing entangled quantum particles allows agents to generate joint behavioral patterns that no classical plan can reproduce. Payoff tensors ($V[x, y, a, b]$) quantify the score when referee inputs are $x, y$ and player responses are $a, b$. Positive Operator-Valued Measures (POVMs) represent quantum measurements as sets of positive semidefinite Hermitian matrices summing to the identity. The Born Rule dictates the probability of joint outcomes based on the shared density matrix $\rho$ and respective POVM elements.
Problem Breakdown & Implementations
Warmup (The CHSH Game): A foundational 2-player, 2-input, 2-output non-local game where classical strategies achieve a maximum win probability of $75\%$ ($\frac{3}{4}$), while quantum strategies breach this limit to reach Tsirelson's bound of $\cos^2(\pi/8) \approx 85.35\%$.
Problem 1 (CHSH with a Sign-Flipped State): Adapts POVM strategies for a shared state with flipped off-diagonal entries ($\frac{1}{\sqrt{2}}(\vert{}00\rangle - \vert{}11\rangle)$) by negating Alice’s $X$-basis measurement ($A_1 = -X$) to preserve the maximal quantum win rate.
Problem 2 (A High-Frequency Trading Simulation): Models an asynchronous market signal and order-management game between data centers separated by latency constraints, maximizing expected payoff beyond the classical baseline.
Problem 3 & 4 (Small-Scale Quantum Advantage): Exhaustively analyzes all $65,536$ unique binary games with 2 questions and 2 answers per player to calculate maximum quantum advantages and frequency of help.
Problem 5 (Random Large-Scale Non-Local Games): Evaluates complex games with 10 questions and 2 answers per player using statistical lower-bound confidence scoring via binomial trials. Key Findings &
Conclusions
The study identified a peak observed quantum advantage of 11.11% over classical baseline expectations in specific game configurations. Quantum advantages are mathematically constrained and relatively rare, occurring in less than 1% of games within the tested uniform distribution styles. While entanglement does not enable faster-than-light communication, it provides a superior correlation resource that fundamentally optimizes decentralized decision-making under strict latency constraints
Built With
- python
- qbraid
