Recommendation has become especially crucial during the COVID-19 pandemic as a significant number of people rely on online shopping from home. Existing recommendation algorithms, designed to address issues like cold start and data sparsity, often overlook the time constraints of users. Specifically, users expect to receive recommendations for products of interest in the shortest possible time. To address this challenge, we propose a novel collaborative filtering recommendation algorithm that leverages the advantages of quantum computing circuits based on data reconstruction. This approach allows for the rapid identification of users similar to the target user, thereby improving recommendation speed. In our method, we utilize the information of known users to linearly reconstruct that of the target users, forming a relational matrix. Subsequently, we employ \(l_{2,1}-\) norm and \(l_{1}-\) norm to sparsely constrain the relationship matrix, deducing the weight of each known user. The final step involves providing similar recommendations to target users based on these weights. Furthermore, we implement the proposed algorithm using a quantum circuit, enabling exponential acceleration. The final weight matrix is derived from the quantum state outputted by the circuit. The speed of this process is theoretically demonstrated in detail. Experimental results indicate that our algorithm outperforms state-of-the-art methods in terms of root mean squared error (RMSE), mean absolute error (MAE) and normalized discounted cumulative gain (NDCG). Compared to state-of-the-art comparison algorithms, the proposed algorithm achieves the fastest recommendation speed across eight public datasets.
Recommendation has become especially crucial during the COVID-19 pandemic as a significant number of people rely on online shopping from home. Existing recommendation algorithms, designed to address issues like cold start and data sparsity, often overlook the time constraints of users. Specifically, users expect to receive recommendations for products of interest in the shortest possible time. To address this challenge, we propose a novel collaborative filtering recommendation algorithm that leverages the advantages of quantum computing circuits based on data reconstruction. This approach allows for the rapid identification of users similar to the target user, thereby improving recommendation speed. In our method, we utilize the information of known users to linearly reconstruct that of the target users, forming a relational matrix. Subsequently, we employ (l_{2,1}-) norm and (l_{1}-) norm to sparsely constrain the relationship matrix, deducing the weight of each known user. The final step involves providing similar recommendations to target users based on these weights. Furthermore, we implement the proposed algorithm using a quantum circuit, enabling exponential acceleration. The final weight matrix is derived from the quantum state outputted by the circuit. The speed of this process is theoretically demonstrated in detail. Experimental results indicate that our algorithm outperforms state-of-the-art methods in terms of root mean squared error (RMSE), mean absolute error (MAE) and normalized discounted cumulative gain (NDCG). Compared to state-of-the-art comparison algorithms, the proposed algorithm achieves the fastest recommendation speed across eight public datasets.
As digital content expands, the need to deliver recommendations quickly becomes increasingly important. In traditional recommendation methods the online recommendation time scales linearly with the number of items, making such approaches less effective as datasets grow. Quantum computing offers novel techniques for parallel computation and sampling, yet current hardware remains constrained by noise and limited scalability. Variational quantum algorithms (VQAs), which rely on shallow circuits, are better suited for noisy quantum machines. In this work, we explore a scheme for variational quantum recommendation system (VQRS), which combines classical matrix factorization (MF) and data re-uploading in the offline phase with quantum sampling in the online phase, aiming to accelerate inference. Using noiseless simulations on small-size standard datasets, we assess the method's performance and analyze its computational resource requirements. Our findings indicate that the scheme is capable of learning accurate recommendations on small datasets, but faces scalability challenges and may requires long offline training. Nonetheless, the results show that the proposed quantum circuit design supports the inference of user preferences, and that a relatively small number of online circuit executions suffices to yield moderately accurate predictions. This highlights a trade-off between inference time and accuracy, which may be of interest in applications where online speed is prioritized over precision.
Recommender systems are crucial for customizing user experiences across diverse sectors such as e-commerce and entertainment. Traditional correlation methods have been employed to forecast user preferences; however, they frequently prove inadequate when addressing intricate, high-dimensional datasets. Quantum computing presents a new approach for enhancing correlation computations, potentially resulting in more precise recommendations. This study seeks to address and compare the efficiency of classical and quantum correlation techniques in recommender systems utilizing four distinct datasets: Supermarket Sales, IMDB Top 250 movies, MovieLens 10k, and BigBasket products. The Item Recommendation and Quantum Correlation (IRQC) method, makes use of parameterized quantum circuits with rotation gates and entanglement. The experimental methodology comprised the utilization of both classical and quantum correlation approaches, evaluating their efficacy through critical metrics including mean absolute error (MAE) and root mean squared error (RMSE). The results demonstrated that quantum correlations consistently surpassed classical correlations across all datasets. The proposed Quantum Correlation approach obtains lower mean absolute errors of 0.99, 0.30, 0.90, and 0.92 in BigBasket, Supermarket Sales, IMDB Top 250 Movies, and MovieLens 10K datasets, respectively, than 1.20, 1.48, 1.10, and 1.00 with the classical methods. This study underlines the potential of quantum computing in machine learning applications, notably for boosting recommendation systems.
Abstract Recommendation system is a kind of information filtering system, which plays an increasingly important role in the era of big data. In this work, we present a novel quantum recommender system, which can also be regarded as a quantum version of the matrix reconstruction algorithm. In order to obtain two factors in the quantum state form, a quantum version of the alternating least squares algorithm is designed. And based on the factor matrices, the reconstruction matrix of the original rating matrix is calculated. The complexity analysis shows that our quantum algorithm may achieve an exponential speedup relative to the classical counterpart under certain conditions.
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions, which is hardware demanding. In particular, recent advances on dequantization have revealed that the quantum advantage is more of a mere artifact of strong input assumptions. In this work, we propose a variant of these algorithms, leveraging both classical and quantum resources. Provided the classical knowledge (the entries) of the matrix/vector of interest, a classical procedure is used to pre-process this information. Then they are fed into a quantum circuit which is shown to be a block encoding of the matrix of interest. From this block-encoding, we show how to use it to tackle a wide range of problems, including principal component analysis, linear equation solving, Hamiltonian simulation, preparing ground state, and data fitting. We also analyze our protocol, showing that both the classical and quantum procedure can achieve logarithmic complexity in the input dimension, thus implying its potential for near term realization. We then discuss several implications and corollaries of our result. First,, our results suggest there are certain matrices/Hamiltonians where our method can provide exponential improvement compared to the existing ones with respect to the sparsity. Regarding dense linear systems, our method achieves exponential speed-up with respect to the inverse of error tolerance, compared to the best previously known quantum algorithm for dense systems. Last, and most importantly, regarding quantum data fitting, we show how the output of our quantum algorithms can be leveraged to predict unseen data. Thus, it provides an end-to-end application, which has been an open aspect of the previous quantum data fitting algorithm.
This paper presents a comprehensive review and systematic coverage of foundational quantum optimization algorithms-QAOA, Quantum Annealing, VQE, VQLS, and HHL-tracing their development all the way from Schrödinger's equation through gate-based quantum computing (Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, QFT, Shor's, and Grover's algorithms) to hybrid quantum-classical approaches for NISQ-era hardware. We also present the transverse field Ising model's role in quantum annealing as well as practical hardware implementations with the Chimera, Pegasus, and Zephyr topologies of the D-Wave quantum annealer, addressing key challenges including barren plateaus, circuit trainability, and noise resilience. In the simulations section, quantum computing applications to collaborative filtering and social network optimization have been presented. We introduce two original contributions: (1) a quantum collaborative filtering model based on VQE principles that leverages quantum entanglement to represent user-item relationships, requiring logarithmically fewer parameters than classical embedding methods while accessing exponentially larger state spaces, and demonstrating test RMSE of 0.85 on synthetic data; and (2) a Quantum Social Network (QSN) framework modeling belief dynamics through superposition and entanglement, revealing emergent consensus and polarization phenomena validated via Qiskit simulations. By demonstrating that variational quantum algorithms can tackle real-world recommendation and network optimization problems on current hardware, we bridge theoretical quantum computing with practical machine learning applications and identify concrete pathways toward quantum advantage beyond traditional combinatorial optimization.
A recommendation system uses the past purchases or ratings of n products by a group of m users, in order to provide personalized recommendations to individual users. The information is modeled as an m×n preference matrix which is assumed to have a good rank-k approximation, for a small constant k. In this work, we present a quantum algorithm for recommendation systems that has running time O(poly(k)polylog(mn)). All known classical algorithms for recommendation systems that work through reconstructing an approximation of the preference matrix run in time polynomial in the matrix dimension. Our algorithm provides good recommendations by sampling efficiently from an approximation of the preference matrix, without reconstructing the entire matrix. For this, we design an efficient quantum procedure to project a given vector onto the row space of a given matrix. This is the first algorithm for recommendation systems that runs in time polylogarithmic in the dimensions of the matrix and provides an example of a quantum machine learning algorithm for a real world application.