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arXiv:2508.14418 · Physical Review A

Adaptive interpolating quantum transform: A quantum-native framework for efficient transform learning

Gekko Budiutama, Shunsuke Daimon, Hirofumi Nishi, Ryui Kaneko, Tomi Ohtsuki, Yu‐ichiro Matsushita

Published Nov 6, 2025• 0 citations
arXivHTMLPDF

Abstract

Machine learning on quantum computers has attracted attention for its potential to deliver computational speedups in different tasks. However, deep variational quantum circuits require a large number of trainable parameters that grows with both qubit count and circuit depth, often rendering training infeasible. In this study we introduce the adaptive interpolating quantum transform (AIQT), a quantum-native framework for flexible and efficient learning. The AIQT defines a trainable unitary that interpolates between quantum transforms, such as the Hadamard and quantum Fourier transforms. This approach enables expressive quantum state manipulation while controlling parameter overhead. When built upon efficient quantum circuits such as the quantum Fourier transform, the AIQT achieves polynomial scaling of the number of gates with respect to the number of qubits. Our results show that the AIQT achieves high performance with minimal parameter count, offering a scalable and interpretable alternative to deep variational circuits.

DOI
10.1103/vyr3-h9hq

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Machine learning on quantum computers has attracted attention for its potential to deliver computational speedups in different tasks. However, deep variational quantum circuits require a large number of trainable parameters that grows with both qubit count and circuit depth, often rendering training infeasible. In this study we introduce the adaptive interpolating quantum transform (AIQT), a quantum-native framework for flexible and efficient learning. The AIQT defines a trainable unitary that interpolates between quantum transforms, such as the Hadamard and quantum Fourier transforms. This approach enables expressive quantum state manipulation while controlling parameter overhead. When built upon efficient quantum circuits such as the quantum Fourier transform, the AIQT achieves polynomial scaling of the number of gates with respect to the number of qubits. Our results show that the AIQT achieves high performance with minimal parameter count, offering a scalable and interpretable alternative to deep variational circuits.
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This paper presents Adaptive Quantum-Enhanced Learning (AQEL), a novel hybrid quantum-classical machine learning framework designed to address critical challenges in the Noisy Intermediate-Scale Quantum (NISQ) era. AQEL integrates four adaptive components: Adaptive Quantum Feature Mapping (AQFM), a Noise-Aware Variational Quantum Circuit (NAVQC), a Classical Meta-Optimizer with Quantum Feedback (CMOQF), and a Secure Scalable Data Interface (SSDI). Unlike static hybrid approaches, AQEL is designed to dynamically adapt its quantum architecture based on performance metrics and gradient behavior. We evaluate the framework's effectiveness on a benchmark binary classification task via high-fidelity simulation. The results demonstrate high classification accuracy, with the model automatically adapting its circuit depth during training to navigate the expressibility-trainability trade-off. Comprehensive ablation studies and a simulated noise resilience analysis validate the potential of AQEL's adaptive components, indicating its promise for developing robust QML applications.
Deep learning is a modern approach to realize artificial intelligence. Many frameworks exist to implement the machine learning task; however, performance is limited by computing resources. Using a quantum computer to accelerate training is a promising approach. The variational quantum circuit (VQC) has gained a great deal of attention because it can be run on near-term quantum computers. In this paper, we establish a new framework that merges traditional machine learning tasks with the VQC. Users can implement a trainable quantum operation into a neural network. This framework enables the training of a quantum-classical hybrid task and may lead to a new area of quantum machine learning.
Transformers have gained popularity in machine learning due to their application in the field of natural language processing. They manipulate and process text efficiently, capturing long-range dependencies among data and performing the next word prediction. On the other hand, gate-based quantum computing is based on controlling the register of qubits in the quantum hardware by applying a sequence of gates, a process which can be interpreted as a low level text programming language. We develop a transformer model capable of transpiling quantum circuits from the qasm standard to other sets of gates native suited for a specific target quantum hardware, in our case the set for the trapped-ion quantum computers of IonQ. The feasibility of a translation up to five qubits is demonstrated with a percentage of correctly transpiled target circuits equal or superior to 99.98%. Regardless the depth of the register and the number of gates applied, we prove that the complexity of the transformer model scales, in the worst case scenario, with a polynomial trend by increasing the depth of the register and the length of the circuit, allowing models with a higher number of parameters to be efficiently trained on HPC infrastructures.