Quantum Hyperdimensional Computing: a foundational paradigm for quantum neuromorphic architectures

TL;DR

This paper introduces Quantum Hyperdimensional Computing (QHDC), a novel quantum-native paradigm that maps classical hyperdimensional operations onto quantum processes, enabling efficient quantum neuromorphic algorithms for complex cognitive tasks.

Contribution

It presents the first framework for QHDC, demonstrating direct mappings of hyperdimensional operations onto quantum primitives and validating the approach on real quantum hardware.

Findings

Successful implementation on a 156-qubit IBM quantum processor

Validated mappings through symbolic reasoning and classification tasks

QHDC is a viable, resource-efficient quantum neuromorphic computing paradigm

Abstract

A significant challenge in quantum computing (QC) is developing learning models that truly align with quantum principles, as many current approaches are complex adaptations of classical frameworks. In this work, we introduce Quantum Hyperdimensional Computing (QHDC), a fundamentally new paradigm. We demonstrate that the core operations of its classical counterpart, Hyperdimensional Computing (HDC), a brain-inspired model, map with remarkable elegance and direct correspondence onto the native operations of a QC. This suggests HDC is exceptionally well-suited for a quantum-native implementation. We establish a direct, resource-efficient mapping: (i) hypervectors are mapped to quantum states, (ii) the bundling operation is implemented as a quantum-native averaging process using a Linear Combination of Unitaries (LCU) and Oblivious Amplitude Amplification (OAA), (iii) the binding operation is realized via quantum phase oracles, (iv) the permutation operation is implemented using the Quantum Fourier Transform (QFT), and (v) vector similarity is calculated using quantum state fidelity measurements based on the Hadamard Test. We present the first-ever implementation of this framework, validated through symbolic analogical reasoning and supervised classification tasks. The viability of QHDC is rigorously assessed via a comparative analysis of results from classical computation, ideal quantum simulation, and execution of a 156-qubit IBM Heron r3 quantum processor. Our results validate the proposed mappings and demonstrate the versatility of the framework, establishing QHDC as a physically realizable technology. This work lays the foundation for a new class of quantum neuromorphic algorithms and opens a promising avenue for tackling complex cognitive and biomedical problems intractable for classical systems.