Quantum Data Encoding

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16 papers3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Oct 15, 2026

Same Spectrum, Harder First-Order Training: Phase-Locking in Single- versus Multi-Qubit Re-Uploading Circuits

Angle-encoded variational quantum circuits implement truncated Fourier series. For one-dimensional inputs, a single-qubit re-uploading (serial) circuit represents every function that a multi-qubit circuit with the same encoding budget

E

can; we find that this exchange of width for depth is not free in first-order training. Because its state lives on the Bloch sphere, all parameters of the serial circuit move the state, at each input, along one complex direction, which we call phase-locking. We prove that this costs no Fourier direction but leaves no direction to spare: however many parameters it has, the serial circuit has at most

2E+2

tangent directions, one more than its

2E+1

Fourier coefficients need, while a two-qubit control with the same encoding budget and model class generically has at least

6E+6

. The cost in training is measured against this control, as the number of runs out of 100 that reach the optimum within a fixed step budget. On an exact loss with flat-spectrum targets the gap grows with

E

; at

E=32

the serial circuit converges in 3, 53 and 83 runs under gradient descent, Adam and Levenberg--Marquardt, the control in 99, 100 and 100. On three real-world series, at matched parameter counts, the serial circuit reaches the least-squares optimum in at most 9 runs under Adam and in 32 to 93 under Levenberg--Marquardt, the control in at least 98 and in all 100; its held-out error is up to about

1.5

times that of the control under Adam, but no larger in the typical run under Levenberg--Marquardt.

Michael Poppel, David Bucher, Maximilian Zorn +5

Department of Computer Science, LMU Munich, Germany · Aqarios GmbH, Munich, Germany

Quantum Circuit Trainability Quantum Machine Learning Variational Quantum Circuits Quantum Circuit Optimization Quantum Data Encoding

Oct 13, 2026

A Tutorial on Quantum Amplitude Embedding with Data Re-Uploading

Amplitude embedding lets a variational quantum model read many classical features with few qubits, but the model output is then only a quadratic form in the normalized input. Data re-uploading, which encodes the input repeatedly between trainable blocks, can be used to enrich such a model. Because every additional upload of an amplitude embedding repeats a costly state preparation, the gain that an upload buys has to be known before the gates are spent. This tutorial thus addresses the problem of explaining what data re-uploading adds to an amplitude-embedded model and how large the gain is. We express sequential re-uploading and parallel re-uploading with two copies in one notation and show that each upload raises the reachable polynomial order by two. Under one trainable circuit family and one budget of trainable parameters, simulation results show that re-uploading raises the test coefficient of determination from 0.689 to between 0.883 and 0.975 on targets of order four and from 0.337 to between 0.642 and 0.783 on targets of order six, on all ten seeds. On a quadratic target and on handwritten digits, one upload remains the best choice, and every additional upload lowers the gate error that the classifier tolerates. These results help designers match the number of uploads to the polynomial order of the task at hand.

Hyojun Ahn, Joongheon Kim

Department of Electrical & Computer Engineering, Korea University, Seoul, Republic of Korea

Quantum Circuit Expressibility Quantum Machine Learning Quantum Data Encoding Variational Quantum Circuits Quantum Feature Maps

Oct 5, 2026

Quantum data loading from the learned shared structure of real signals

Preparing quantum states from classical data can cost more than the computation they serve; most loaders tailor a circuit to each input. Here we show that the signals of a real dataset share structure that can be learned once and reused. Our quantum-native loader learns a low-dimensional description of a dataset and prepares every signal with one fixed circuit set by a few numbers. Across seven views of five public datasets it meets the targets of the strongest structured loader at equal gate cost with several times fewer numbers per signal. These numbers can be inferred from a random subset: in a preregistered blind replication the subset needed to come within ten per cent of full-signal accuracy stayed constant within a prespecified margin as signals grew sixteenfold, whereas the structured loader needed ever more. It declines what it cannot represent, covering fewer cases than that baseline and no electrocardiogram.

Pablo Herrero Gómez, Antonio Jimeno Morenilla, David Muñoz-Hernández +1

Department of Computer Science Technology and Computation, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain

Quantum Machine Learning Quantum State Preparation Quantum Data Encoding

Sep 22, 2026

When Quantum Meets AI: Quantum Methods for Machine Learning and Machine Learning Methods for Quantum Systems

This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.

Tak Hur

Department of Statistics and Data Science Graduate School Yonsei University

Neural Quantum States Quantum Error Correction Quantum Machine Learning Quantum Data Encoding Quantum Neural Networks

Sep 14, 2026

Structure-Preserving Quantum Circuit Architectures for Robot Kinematics

Structured spatial data require quantum encodings that preserve geometric relations, expose measurable observables, and remain implementable on finite-depth hardware. This work introduces a quantum representation and circuit architecture for rigid-body transformations and specializes it to Denavit--Hartenberg kinematics of serial open-chain manipulators. Each translational contribution is factorized into a classical metric magnitude and a signed unit direction encoded by a single-qubit Bloch vector, while parameterized rotations reproduce the ordered propagation of frame directions. A selector register prepares probabilities proportional to the contribution magnitudes, and the reduced state of a designated readout qubit encodes their normalized weighted sum. The retained classical scale then reconstructs the metric end-effector position. Two additional readout qubits encode terminal-frame axes, providing a compact and geometrically interpretable pose interface. At the ideal expectation-value level, measured Pauli observables reproduce the corresponding classical kinematic quantities. Alternative circuit architectures realize the same representation with different tradeoffs in qubit count, circuit depth, controlled operations, and measurement requirements. Validation on a serial manipulator yields numerically negligible position and orientation reconstruction errors under ideal simulation. Finite-shot simulations, noisy executions, transpilation analysis, and a hardware demonstration further characterize statistical error, noise sensitivity, and implementation overhead without asserting computational advantage.

Andrea Morghen, Pierluigi Arpenti, Roberto Schiattarella +2

Department of Electrical Engineering and Information Technology (DIETI), University of Naples Federico II, 80125 Naples, Italy · Department of Physics “Ettore Pancini”, University of Naples Federico II, 80126 Naples, Italy

Robot Kinematics Robotics Quantum Data Encoding

Aug 31, 2026

Fractal dimension predicts quantum kernel collapse in angle-encoded data

Angle-encoded quantum kernels on tabular data collapse when the feature map is wider than the intrinsic dimension of the data. We propose the correlation fractal dimension D2 as an a priori qubit budget: encode D2 coordinates chosen by FD-ASE instead of the PCA-95% width or all E attributes. On nine data sets and a statevector simulator (n= 32), a one-layer ZZ fidelity kernel at q=D2 stays geometrically alive while the same kernel at the PCA-95% width has already collapsed. The budget is map-dependent: product-state and IQP maps overshoot it; a second ZZ layer undershoots it. Packed dense-angle and re-uploading encodings still live at the fractal q, but not when PCA-95% features are stacked onto those qubits. Shrinking the angle bandwidth moves the ZZ knee later; stretching it kills the kernel earlier. On IBM Quantum (ibm_fez, 256 shots, n=8) the one-layer ZZ kernel at the fractal width matches the exact kernel (MAE 0.021); past that width both hardware and simulator have collapsed. The ceiling is a property of the map-data pair at a stated bandwidth, not of the classical table alone.

Ana Paula Appel

Quantum Feature Maps Intrinsic Dimensionality Quantum Machine Learning Quantum Kernel Methods Quantum Data Encoding

Jul 15, 2026

Quantum Topological Data Encoding

Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce quantum topological data encoding (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.

Adam Wesołowski, Dimitrios Thanos, Daniel Leykam +1

Royal Holloway University of London, Department of Computer Science, UK · Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Leiden, The Netherlands · Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, Singapore +1

Quantum Machine Learning Quantum Data Encoding Topological Data Analysis

Jul 13, 2026

Overcoming Fourier Locking in Quantum Data Re-uploading Classifiers via Spectral Homotopy

Data re-uploading parameterized quantum circuits (DRU-PQCs) are universal function approximators, yet their expressivity produces oscillatory, non-convex loss landscapes that resist gradient-based optimization. We show that the primary optimization bottleneck in DRU-PQCs is not insufficient capacity but a structural failure mode we term Fourier locking (FL): because encoding weights and entangling layers are nonlinearly coupled, random initialization on high-frequency targets collapses the encoding parameters into spurious local minima. Two Fisher diagnostics characterize FL. The input-space quantum Fisher information

F_x

measures the effective frequency content of the encoded state; the Fisher discriminant ratio of the measured features measures their alignment with the class labels. In two independent 50-seed experiments, the locking is literal: trapped circuits hold

F_x

frozen for the entire run, while escaping circuits migrate their frequency content (direct training:

r_{pb} = -0.48

; curriculum:

d = 1.34

; both

p < 0.001

). The replicated signature is this spectral mobility, not any endpoint value of

F_x

, and trapped circuits retain a fully non-degenerate parameter-space QFIM (

r_{pb} \approx 0

): the failure is spectral misalignment of a responsive state, not a loss of geometric sensitivity. A frequency-staged homotopy protocol that paces the target frequency (

f: 1.0 \to 3.0

) convexifies the early loss landscape; escaping circuits raise

F_x

in step with the curriculum, and the escape rate triples (18% vs. 6%). Fourier locking is a frequency-alignment problem, and its remedy is frequency pacing.

Spencer Topel

Moth, Brooklyn, New York

Quantum Machine Learning Variational Quantum Circuits Quantum Circuit Trainability Quantum Data Encoding

Jul 11, 2026

Qubit-Efficient Quantum Search for Hyperdimensional Decomposition via Logarithmic Encoding

Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension

D

. In hypervector decomposition, the objective is to recover

F

constituent hypervectors, each drawn from a codebook of size

N

, from a bound target hypervector. This requires searching over

N^F

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)

-qubit hypervector representations. We propose a qubit-efficient quantum framework for HDC decomposition that reduces the representation cost to

O(\log D)

. 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(\sqrt{N^F})

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

D

-qubit hypervector encodings, achieving up to

2{,}000\times

fewer qubits.

Sanggeon Yun, Hyunwoo Oh, Ryozo Masukawa +2

University of California, Irvine

Hyperdimensional Computing Quantum Data Encoding

Jun 24, 2026

Tailor Made Embeddings for Quantum Machine Learning

Autoencoders transformed classical machine learning by solving the curse of dimensionality, enabling principled weight initialization and learning compact, structured representations. In this work, we extend this paradigm to quantum machine learning by introducing a variational autoencoder framework that learns task-specific quantum embeddings of classical data. We demonstrate that high-dimensional datasets, including ImageNet, can be compressed into a 13-qubit quantum representation while remaining reconstructable through a learned decoder. On MNIST (3 vs 5), our approach achieves 98.5% validation accuracy using a circuit-centric quantum classifier, within 1.2 percentage points of a classical neural network baseline (99.7%) and more than 30 percentage points above a naive amplitude-embedding approach. Unlike amplitude embeddings, which require full quantum state tomography for recovery, or angle embeddings, which generally rely on circuit inversion under restrictive assumptions, the proposed framework reconstructs the original data from only a polynomial number of measurements. The framework was further validated on IBM quantum hardware, confirming that the learned embeddings remain stable and reconstructable under real device noise.

Aldo Lamarre, Dominik Šafránek

Department of Electrical Engineering, KAIST, Daejeon, South Korea · Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon - 34126, Korea · Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Praha 2, Czech Republic

Variational Autoencoders Quantum Machine Learning Quantum Data Encoding Quantum Neural Networks

May 29, 2026

Generative Quantum Data Embeddings for Supervised Learning

Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an a priori diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.

Jaewoong Heo, Daniel K. Park

Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea · Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea · Department of Quantum Information, Yonsei University, Seoul 03722, Republic of Korea

Quantum Machine Learning Classification Quantum Data Encoding

May 23, 2026

A Matched Spectral Benchmark of Quantum Inspired Feature Maps

Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed data-encoding map. Amplitude, angle, and basis encoding are evaluated as deterministic feature maps for classical supervised learning under matched output dimensionality and strong classical controls. The benchmark compares these encodings against raw linear models, random Fourier features, polynomial features, PCA, RBF SVMs, and shallow neural networks across diverse classical datasets. Rather than treating performance as a single endpoint, we analyze the geometry of each representation through effective rank, condition number, centered kernel alignment, predictive performance, and practical overhead. The resulting picture is mechanistic: amplitude encoding can remove magnitude information through unit-sphere normalization, angle encoding can become geometrically redundant with raw linear features, and basis encoding can impose a binary Hamming geometry that is poorly aligned with smooth decision structure. These findings do not argue against quantum computation, however, they show that fixed quantum-inspired encoding geometry alone is not a reliable source of machine-learning advantage on classical data.

Toheeb Ogunade, Taofeek Kassim, Etinosa Osaro

Department of Computer Science, University of Lagos, Lagos, Nigeria · Department of Physics, University of Lagos, Lagos, Nigeria · Department of Chemical Engineering, University of Notre Dame, Indiana, USA

Quantum Feature Maps Quantum Machine Learning Quantum-Inspired ML Quantum Data Encoding

Apr 14, 2026

Magnitude Is All You Need? Rethinking Phase in Quantum Encoding of Complex SAR Data

Synthetic Aperture Radar (SAR) data is inherently complex-valued, while quantum machine learning (QML) models operate in complex Hilbert spaces. This similarity suggests that using both the magnitude and phase of SAR data in quantum encoding should help automatic target recognition in SAR images. In this study, we test this assumption by comparing five encoding strategies for quantum models: magnitude-only encoding, joint magnitude-phase encoding, in-phase and quadrature encoding, preprocessed phase encoding, and a purely quantum architecture. All approaches are evaluated under a unified experimental setup on the MSTAR benchmark dataset. Surprisingly, we find that magnitude-only encoding performs better than phase-inclusive encodings in hybrid quantum-classical models. It achieves 99.57 percent accuracy on the 3-class task and 71.19 percent accuracy on the 8-class task, outperforming complex-valued alternatives under the same framework. Adding phase information provides little or no improvement and can sometimes degrade performance. However, in purely quantum models with only 184 to 224 trainable parameters and no classical neural-network layers, phase information becomes much more important, improving accuracy by up to 21.65 percentage points. These findings show that the usefulness of phase information depends not only on the data, but also on the architecture used to process it. Hybrid models can compensate for missing phase information through their classical components, while pure quantum models rely more strongly on phase information for class discrimination. The results provide practical guidance for encoding complex-valued data in quantum machine learning and highlight the importance of jointly designing encoding strategies and model architectures for current quantum systems.

Sakthi Prabhu Gunasekar, Prasanna Kumar Rangarajan

Dept. of Computer Science & Engineering, Amrita School of Computing, Amrita Vishwa Vidyapeetham, India

SAR ATR Quantum Data Encoding Quantum Machine Learning Quantum Neural Networks Hybrid Quantum-Classical ML

Apr 7, 2026

Shot-based quantum encoding: a data-loading paradigm for quantum neural networks

Efficient data loading remains a bottleneck for near-term quantum machine learning. Existing schemes (angle, amplitude, and basis encoding) either underuse the exponential Hilbert-space capacity or require circuit depths that exceed the coherence budgets of noisy intermediate-scale quantum hardware. We introduce shot-based quantum encoding (SBQE), a data embedding strategy that distributes the hardware's native resource, shots, according to a data-dependent classical distribution over multiple initial quantum states. By treating the shot counts as a learnable degree of freedom, SBQE produces a mixed-state representation whose expectation values are linear in the classical probabilities and can therefore be composed with nonlinear activation functions. We show that SBQE is structurally equivalent to a multilayer perceptron whose weights are realized by quantum circuits, and we describe a hardware-compatible implementation protocol. Benchmarks on three image datasets, with 10 independent initializations per model, show that SBQE achieves 89.1% +- 0.9% test accuracy on Semeion (reducing error by 5.3% relative to amplitude encoding and matching a width-matched classical network), 80.95% +- 0.10% on Fashion MNIST (exceeding amplitude encoding by +2.0% and a linear multilayer perceptron by +1.3%), and 90.25% +- 0.18% on MNIST (exceeding amplitude encoding by 2.1 percentage points and the width-matched classical network by 0.3), all without any data-encoding gates.

Basil Kyriacou, Viktoria Patapovich, Maniraman Periyasamy +1

Terra Quantum AG, 9000 St. Gallen, Switzerland

Quantum Data Encoding Quantum Machine Learning Quantum Neural Networks Hybrid Quantum-Classical ML Quantum Feature Maps

Feb 18, 2026

Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on quantum hardware. In this work, we propose TNQE, a circuit-efficient quantum data encoding framework built on structured unitary tensor network (TN) representations. TNQE first represents each classical input via a TN decomposition and then compiles the resulting tensor cores into an encoding circuit through two complementary core-to-circuit strategies. To make this compilation trainable while respecting the unitary nature of quantum operations, we introduce a unitary-aware constraint that parameterizes TN cores as learnable block unitaries, enabling them to be directly optimized and directly encoded as quantum operators. The proposed TNQE framework enables explicit control over circuit depth and qubit resources, allowing the construction of shallow, resource-efficient circuits. Across a range of benchmarks, TNQE achieves encoding circuits as shallow as

0.04\times

the depth of amplitude encoding, while naturally scaling to high-resolution images (

256 \times 256

) and demonstrating practical feasibility on real quantum hardware.

Guang Lin, Toshihisa Tanaka, Qibin Zhao

RIKEN Center for Advanced Intelligence Project · Tokyo University of Agriculture and Technology

Quantum Data Encoding Quantum Machine Learning Tensor Networks Quantum Circuit Compilation

Sep 23, 2025

Re-uploading quantum data: a universal function approximator for quantum inputs

Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements, provided that sufficiently many copies of the input state and, in general, sufficiently many layers are available. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a space-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.

Hyunho Cha, Daniel K. Park, Jungwoo Lee

NextQuantum and Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Republic of Korea · Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea · Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea +1

Quantum Machine Learning Universal Approximation Quantum Data Encoding Quantum Neural Networks