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Knowledge-Based Systems

Quantum-enhanced hyperdimensional computing for graph representation

Ali Zakeri, Prathyush Poduval, Mohsen Imani

Published Jun 30, 2026• 0 citations
Publisher

Abstract

Representing complex structured data often involves a tradeoff between computational cost and representational quality, largely determined by the underlying encoding framework. Hyperdimensional Computing (HDC), also known as Vector Symbolic Architecture (VSA), has been recognized for its ability to represent complex structures through high-dimensional encoding. Conventional representation techniques in HDC, which in many cases rely on the cognitive operation of bundling for data memorization, suffer from quality and capacity limitations. Association through the binding operation offers a potential alternative, but its use is complicated by the difficult decomposition process, where classical factorization methods, such as resonator networks, can become challenging as the number of candidate factors and bound components increases. In this work, we explore a novel approach based on a quantum factorization algorithm inspired by Grover’s quantum search algorithm within HDC. This approach not only addresses the complexity challenges inherent in the decomposition of bound HDC representations, but also significantly mitigates noise and improves representational fidelity. Focusing on graph data structures, our framework Quark is analyzed through theoretical derivations and classical simulations of the quantum decoding process, demonstrating improved graph reconstruction quality across different graph sizes and dimensionalities. This integration of quantum computing and HDC provides a promising direction for scalable and high-fidelity graph representation.

DOI
10.1016/j.knosys.2026.116550

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This paper addresses the decomposition of holographic feature vectors in Hyperdimensional Computing (HDC) aka Vector Symbolic Architectures (VSA). HDC uses high-dimensional vectors with brain-like properties to represent symbolic information, and leverages efficient operators to construct and manipulate complexly structured data in a cognitive fashion. Existing models face challenges in de-composing these structures, a process crucial for under-standing and interpreting a composite hypervector. We ad-dress this challenge by proposing the HDC Memorized-Factorization Problem that captures the common patterns of construction in HDC models. To solve this problem efficiently, we introduce HDQMF, a HyperDimensional Quantum Memorized-Factorization algorithm. HDQMF is unique in its approach, utilizing quantum computing to of-fer efficient solutions. It modifies crucial steps in Grover's algorithm to achieve hypervector decomposition, achieving quadratic speed-up.
This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and information retrieval. HDC employs high-dimensional vectors and efficient operators to encode and manipulate information, representing complex objects from atomic concepts. When one attempts to decode a hypervector that is the product (binding) of multiple hypervectors, the factorization becomes prohibitively costly with classical optimization-based methods and specialized recurrent networks, an inherent consequence of the binding operation. We propose HDQF, an innovative quantum computing approach, to address this challenge. By exploiting parallels between HDC and quantum computing and capitalizing on quantum algorithms' speedup capabilities, HDQF encodes potential factors as a quantum superposition using qubit states and bipolar vector representation. This yields a quadratic speedup over classical search methods and effectively mitigates Hypervector Factorization capacity issues.
Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension DDD. In hypervector decomposition, the objective is to recover FFF constituent hypervectors, each drawn from a codebook of size NNN, from a bound target hypervector. This requires searching over NFN^FNF candidate tuples, making the task computationally prohibitive at scale. Recent quantum approach provides a quadratic search advantage, but typically rely on qubit-inefficient O(D)O(D)O(D)-qubit hypervector representations. We propose a qubit-efficient quantum framework for HDC decomposition that reduces the representation cost to O(log⁡D)O(\log D)O(logD). The framework introduces logarithmic hypervector and binding encodings, together with a reversible hypervector lookup operator for circuit-level manipulation of dense hypervectors. Combined with a modified Dürr-Høyer search procedure, the method preserves O(NF)O(\sqrt{N^F})O(NF​) search complexity while substantially reducing qubit usage. Experimental results validate correct similarity computation, accurate decomposition in executable regimes, and significantly improved qubit scaling over baselines based on explicit DDD-qubit hypervector encodings, achieving up to 2,000×2{,}000\times2,000× fewer qubits.
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.
Quantum state tomography (QST) is a fundamental technique for characterizing quantum systems, but it often suffers from significant experimental challenges, including high measurement complexity and resource demands. This paper explores the potential of hyperdimensional computing (HDC) as a viable alternative to traditional QST. HDC leverages high-dimensional vectors to represent and manipulate quantum states, allowing for the development of algorithms that exploit inherent correlations to reconstruct quantum state information with reduced measurement requirements. The core claim is that HDC offers a potentially efficient and scalable approach to QST. This work details the theoretical framework, outlining key algorithms and highlighting the advantages of utilizing HDC for quantum state characterization. The focus is on demonstrating the feasibility of this approach through conceptual design, emphasizing the reduced complexity compared to conventional QST methods. We propose a framework for representing quantum states within HDC vectors and present a simplified reconstruction algorithm.
Hyperdimensional Computing (HDC) is a robust computational framework inspired by human cognition characterized by simple and efficient operations within high-dimensional vector spaces. Quantum-enhanced Hyperdimensional Computing (QeHDC) extends classical HDC by leveraging quantum mechanical properties to enhance computational efficiency. In this paper, we propose a novel Quantum HDC framework featuring a one-pass training method, leveraging sinusoidal and quantum encoding to project classical data into quantum amplitude states efficiently. Our framework introduces an innovative reference-state-based quantum binding operation realized via quantum circuits. Furthermore, we propose a density-matrix-based superclass generation strategy employing eigenvalue decomposition to extract critical quantum state features effectively, enabling a more accurate and robust class representation. Experimental evaluations conducted on standard benchmark datasets demonstrate our approach's superior performance, robustness to noise, and computational feasibility compared to traditional classical and existing quantum-enhanced approaches. The results highlight the practical benefits and potential of Quantum HDC for quantum-enhanced classification tasks and pave the way for future advancements in quantum-inspired computational paradigms.