Quantum Hyperdimensional Computing Qhdc

---
name: quantum-hyperdimensional-computing-qhdc
category: ai_collection
tags: [quantum, neuromorphic, hyperdimensional-computing, quantum-neuromorphic, HDC, quantum-machine-learning]
version: "1.0"
---

# Quantum Hyperdimensional Computing (QHDC)

## Overview

Quantum Hyperdimensional Computing (QHDC) is a foundational paradigm for quantum neuromorphic architectures introduced in arXiv:2511.12664. It demonstrates that the core operations of classical Hyperdimensional Computing (HDC) — a brain-inspired model — map with remarkable elegance to the native operations of a quantum computer.

## Key Mappings

The framework establishes a direct, resource-efficient mapping between HDC operations and quantum-native operations:

| HDC Operation | Quantum Native Implementation |
|---|---|
| Hypervector representation | Quantum states |
| Bundling (superposition) | Linear Combination of Unitaries (LCU) + Oblivious Amplitude Amplification (OAA) |
| Binding (association) | Quantum phase oracles |
| Permutation (position) | Quantum Fourier Transform (QFT) |
| Similarity (comparison) | Hadamard Test for quantum state fidelity |

## Implementation Steps

1. **State Preparation**: Map D-dimensional hypervectors to n-qubit quantum states (n = log₂D)
2. **Bundling via LCU+OAA**: Use Linear Combination of Unitaries to create superpositions of hypervectors, amplified via OAA for success probability
3. **Binding via Phase Oracles**: Implement binding as controlled-phase operations on qubit registers
4. **Permutation via QFT**: Apply Quantum Fourier Transform for circular shifts in hypervector space
5. **Similarity via Hadamard Test**: Compute inner products between quantum states using controlled operations

## Validation

- Validated through symbolic analogical reasoning and supervised classification tasks
- Comparative analysis across: classical computation, ideal quantum simulation, and 156-qubit IBM Heron r3 processor execution
- Results confirm the viability of quantum-native HDC operations

## Advantages Over Classical HDC

1. **Exponential Compression**: N-qubit system represents 2^N-dimensional hypervectors
2. **Native Parallelism**: Quantum superposition naturally implements vector bundling
3. **Efficient Similarity**: Hadamard test computes inner products in O(1) measurements vs O(D) classical operations
4. **Quantum-First Design**: Unlike many QML approaches that adapt classical frameworks, QHDC is fundamentally quantum-native

## Application Domains

- Associative memory systems
- Pattern recognition and classification
- Analogical reasoning tasks
- Cognitive computing on quantum hardware
- Biomedical signal analysis

## Activation Keywords

quantum hyperdimensional computing, QHDC, quantum neuromorphic, LCU amplitude amplification, quantum phase oracle, Hadamard test similarity, brain-inspired quantum computing, hypervector quantum states

## References

- Cumbo, F., Li, R.-H., Raubenolt, B., et al. "Quantum Hyperdimensional Computing: a foundational paradigm for quantum neuromorphic architectures." arXiv:2511.12664 (2025).