This study proposes a Quantum Fourier Transform (QFT)-enhanced quantum kernel for short-term time-series forecasting. Exogenous predictors are incorporated by convexly fusing feature-specific kernels. For both quantum and classical models, the only tuned quantities are the feature-mixing weights and the KRR ridge α; classical hyperparameters (γ, r, d) are fixed, with the same validation set size for all models. Experiments are conducted on a noiseless simulator (5 qubits; window length L=32). Limitations and ablations are discussed, and paths toward NISQ execution are outlined. Introduction Quantum Machine Learning (QML) is an emerging discipline that combines the principles of quantum physics with traditional machine learning (ML) to exploit the distinctive characteristics of quantum systems, including superposition and entanglement phenomena [1]. This distinction facilitates the expeditious execution of certain tasks [2], such as classification and dimensionality reduction, where QML has demonstrated significant acceleration [3]. QML applications have extended to time-series data, leveraging quantum phenomena to model complex temporal dependencies. The goal is to enhance the results of traditional tasks by performing computations on qubits, which can process data more efficiently than classical bits [4, 5]. For example, Thakkar et al. [6] demonstrated that quantum machine-learning methods could enhance financial forecasting by improving both churn prediction and credit-risk assessment. Likewise, Kea et al. [7] developed a hybrid quantum-classical Long Short-Term Memory (QLSTM) to improve stock-price forecasting by leveraging quantum data encoding and high-dimensional quantum representations.

Weaknesses: I think the main weakness of this paper is that the writing is too dense to parse, while on the other hand the current content in the main body is not enough to examine the correctness of Theorem 1 and 2. To be more specific, Theorem 1 and 2 are all both technical results, especially Theorem 1. From my understanding of Section 3.2 and the relevant part in the appendices, the authors used the quantum RAM as well as the quantum singular value transformation (QSVT) algorithm to achieve the speedup for sampling from the features using the quantum Fourier transform. I understand that NeurIPS submissions have page limitation, but I think all the steps should at least be highlighted. In particular, I feel that discussions are needed for: - What quantum RAM do we need for the task? - What can we use the QSVT without the sparse or low-rank assumption? On the other hand, I'm not totally sure how Section 2.3 (discretized representation of real number) and Section 2.4 (assumption on data in discretized representation) help with the overall story--I can foresee their usage, but the paper can probably shrink this space and highlight more on the proofs of Theorem 1 and 2. These are the two main technical results, but are only given in the last page (Page 8) without a comprehensive discussion. A practical solution is to fulfill more details between Line 251-272.

Central to these advancements are transformerbased architectures, including BERT and GPT, which employ self-attention mechanisms to model long-range dependencies in text, achieving superior performance compared to traditional recurrent models [1, 2]. However, the success of these architectures comes at the cost of high computational complexity, requiring substantial memory and processing power to handle increasing dataset sizes and model intricacies. While transformers have set state-of-the-art benchmarks, their resource demands make them unsuitable for real-time applications or deployment in resource-constrained environments. Concurrently, quantum computing has emerged as a disruptive paradigm, introducing principles like superposition and entanglement, which enable quantum systems to process complex computations in ways unattainable by classical systems [3, 5]. Despite its potential, quantum computing faces challenges such as limited qubit counts, high error rates, and difficulties in scaling to larger datasets [4, 6]. These limitations necessitate hybrid approaches that integrate quantum and classical systems to harness the best of both worlds. This paper addresses the computational bottlenecks of transformers by proposing a hybrid quantum-classical model.

How can we take inspiration from a typical quantum algorithm to design heuristics for machine learning? A common blueprint, used from Deutsch-Josza to Shor's algorithm, is to place labeled information in superposition via an oracle, interfere in Fourier space, and measure. In this paper, we want to understand how this interference strategy can be used for inference, i.e. to generalize from finite data samples to a ground truth. Our investigative framework is built around the Hidden Subgroup Problem (HSP), which we transform into a learning task by replacing the oracle with classical training data. The standard quantum algorithm for solving the HSP uses the Quantum Fourier Transform to expose an invariant subspace, i.e., a subset of Hilbert space in which the hidden symmetry is manifest. Based on this insight, we propose an inference principle that "compares" the data to this invariant subspace, and suggest a concrete implementation via overlaps of quantum states. We hope that this leads to well-motivated quantum heuristics that can leverage symmetries for machine learning applications.

This paper introduces an innovative and practical approach to universal quantum matrix multiplication. We designed optimized quantum adders and multipliers based on Quantum Fourier Transform (QFT), which significantly reduced the number of gates used compared to classical adders and multipliers. Subsequently, we construct a basic universal quantum matrix multiplication and extend it to the Strassen algorithm. We conduct comparative experiments to analyze the performance of the quantum matrix multiplication and evaluate the acceleration provided by the optimized quantum adder and multiplier. Furthermore, we investigate the advantages and disadvantages of the quantum Strassen algorithm compared to basic quantum matrix multiplication.

The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are restricted by the scope of the hardware development. Nevertheless, many neural network algorithms had been proposed before GPUs become powerful enough for running very deep models. Similarly, quantum algorithms can also be proposed as knowledge reserves before real quantum computers are easily accessible. Specifically, taking advantage of both the neural networks and quantum computation and designing quantum deep neural networks (QDNNs) for acceleration on Noisy Intermediate-Scale Quantum (NISQ) processors is also an important research problem. As one of the most widely used neural network architectures, convolutional neural network (CNN) remains to be accelerated by quantum mechanisms, with only a few attempts have been demonstrated. In this paper, we propose a new hybrid quantum-classical circuit, namely Quantum Fourier Convolutional Network (QFCN). Our model achieves exponential speed-up compared with classical CNN theoretically and improves over the existing best result of quantum CNN. We demonstrate the potential of this architecture by applying it to different deep learning tasks, including traffic prediction and image classification.

Nanophotonic neural networks are an exciting emerging technology which promises low-energy, ultra high-throughput machine learning systems implemented purely optically. Our lab has previously done work on these devices, and our new paper which extends programmable photonics to the quantum domain is now on arXiv! In this paper, we describe a photonic architecture for a quantum programmable gate array (QPGA) which can be dynamically reprogrammed to perform any quantum computation. We show how to exactly prepare arbitrary quantum states and operators on the device, and we apply machine learning techniques to automatically implement highly compact approximations to important quantum circuits. Below is an animation of a simulated QPGA being trained to implement a quantum Fourier transform on five qubits.