Quantum Topics & Algorithms

Title: Understanding MQPA: Multi-Pathway Quantum Particle Algorithm in the Context of Grover, Shor, and MTQC Architectures

Author: Jessica McPhaul Date: March 26, 2025

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What is MQPA? MQPA (McPhaul Quantum Particle Algorithm) is a multi-pathway quantum algorithm designed to simulate, analyze, and predict the behavior of molecular or environmental particles across spatial-temporal contexts. It fuses classical geospatial data (from sources like NASA, NOAA, and OpenAQ) with quantum-encoded particle representations.

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Basic Quantum Concepts (Simplified): - Qubit: Quantum version of a bit. Can be in 0, 1, or both at once (superposition). - Superposition: Lets qubits represent multiple values simultaneously. - Entanglement: Changes to one qubit affect its pair instantly. - Measurement: Converts a quantum state to classical data (collapses it). - Unitary Gate: Quantum operator that changes a state without loss.

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MQPA Architecture (Visual Mapping): 1. Input: Molecular structure, coordinates, quantum chemical data. 2. Encoding: Qiskit, PennyLane, or Cirq used to encode data into parameterized circuits. 3. U(θ): Quantum transformation layer, varies based on input size and model goal. 4. Measurement: Either to predict energy, detect anomalies, or classify molecules. 5. Output: Used in GIS overlays, time-series forecasts, or anomaly detection heatmaps.

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Math Representation (Simple Form): MQPA core:

MQPA(x) = f(x) = argmin_θ ⟨ψ(θ)| H |ψ(θ)⟩
where |ψ(θ)⟩ = U(θ) Q(x) |0⟩

• Q(x) encodes classical data
• U(θ) transforms the state
• H is the Hamiltonian (energy or cost landscape)
• Measurement returns probability or energy

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Grover’s Algorithm (Integration): - MQPA can use Grover’s amplitude amplification to accelerate search-based molecular queries (e.g. finding a target particle configuration in a GIS time-series map). - Adaptation: Oracle is defined based on molecule or site-specific properties; Diffusion operator modifies amplitude of relevant paths.

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Shor’s Algorithm (Relevance): - While Shor’s is focused on factoring, the modular exponentiation technique inspires MQPA’s periodic simulation functions. - Key idea adapted: simulating periodic behavior of quantum states within molecules and applying it to trajectory prediction (e.g., resonance patterns).

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MTQC (Multi-Tensor Quantum Computing): - MQPA uses MTQC-style architecture to scale circuit representations across many molecular states. - Each pathway (i.e., encoding + circuit + measurement) represents a tensor stream. - Results are collated through quantum parallelism and reduced via measurement.

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Real World Use Case Example: - During a storm surge in the Gulf Coast, MQPA receives: - LiDAR elevation, wind direction, pressure - Molecular data (QM9) overlaid into spatial tiles - Quantum encoding predicts where harmful compounds migrate - GIS map shows prediction in near real time

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Conclusion (Layman Terms): Imagine a molecule as a shape shifting through space and reacting to the environment. MQPA converts that molecule into quantum code, runs it through a quantum brain that sees all paths at once, and maps the likeliest future states — like showing where oil or toxins will move during a storm.

It’s like using quantum-enhanced radar, except it’s not scanning weather — it’s scanning molecules.

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Sources Referenced: - McPhaul J. (2024). MQPA: A Multi-Pathway Approach to Quantum Computing. ResearchGate. - GHZ-state Quantum Architecture. https://www.researchgate.net/publication/355023037 - OpenAI + Qiskit + ArcGIS integrations from Capstone source code base.

More technical appendices, visual flowcharts, and code integrations available on request.