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Open problems in Quantum machine learning

Lack of provable guarantees for quantum machine learning models1 paper raises it · 2 address it
Without guarantees on performance, trainability, and efficient inference, quantum models risk being unreliable or impractical for real-world use.
- Supervised Learning with Quantum Hamiltonian Embeddingsraises · addresses
- Margin-Based Generalization for Quantum Machine Learning with Classical Data Encodingaddresses
Noise-oblivious quantum software testing1 paper raises it · 0 address it
NISQ hardware noise and probabilistic execution require testing methods that explicitly account for these constraints to ensure robustness.
- Noise-Awareness in Quantum Software Testing: An Empirical Landscape Analysisraises
Scalable quantum data embedding optimization1 paper raises it · 1 addresses it
Pairwise fidelity evaluations in embedding optimization create computational bottlenecks, limiting scalability for large datasets.
- Prototype-Guided Optimization of Quantum Data Embeddings with Linear Costraises · addresses
Task-aligned inductive biases in quantum circuits1 paper raises it · 1 addresses it
Without task-specific architectural biases, quantum circuits may fail to generalize well from limited data or align with problem structure.
- Task-aligned spectral inductive biases in parameterized quantum circuitsraises · addresses
Efficient discovery of high-performance quantum error-correcting codes1 paper raises it · 1 addresses it
Existing algebraic constructions for QECCs struggle to balance encoding rate and distance, limiting fault-tolerant quantum computation.
- LiftDiff: Guided Discrete Diffusion for Quantum Code Constructionraises · addresses

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quantum machine learning · quantum neural networks · learning quantum125 papers24 this week

Topics in this field

Active contributors · 90 days

Joongheon KimA Tutorial on Quantum Amplitude Embedding with Data Re-Uploading4
Daniel K. ParkMargin-Based Generalization for Quantum Machine Learning with Classical Data Encoding3
Tak HurMargin-Based Generalization for Quantum Machine Learning with Classical Data Encoding3
Muhammad UsmanWhen do quantum views help? Complementary classical-quantum representations in multi-view fusion3
Hyojun AhnA Tutorial on Quantum Amplitude Embedding with Data Re-Uploading3
Alberto MarchisioQBFF: Deep Quantum Bottleneck for Automatic Speaker Verification Anti-Spoofing3

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arXiv quant-phSep 29
Optimal Quantum-Classical Separations for Exact Learning
Srinivasan Arunachalam, Amin Shiraz Gilani, Nikhil S. Mande
We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonical quantum speedups in this model are witnessed by Grover search and Bernstein-Vazirani, leading to the longstanding conjecture $$ \mathsf{R}(\mathcal C)=O(\mathsf{Q}(\mathcal C)^2+\mathsf{Q}(\mathcal C)\log N). $$ We first refute this conjecture by constructing concept classes $\mathcal C$ and $\mathcal C'$ satisfying \[ \mathsf{R}(\mathcal C)=Ω\!\left(\frac{\mathsf{Q}(\mathcal C)^3\log N}{\log \mathsf{Q}(\mathcal C)}\right) \qquad\text{and}\qquad \mathsf{D}(\mathcal C')=Ω(\mathsf{Q}(\mathcal C')^3\log N). \] The first bound matches the upper bound of Arunachalam et al.~[Quantum'21] up to constant factors, while the second matches the upper bound of Servedio and Gortler~[SICOMP'04]. In particular, this shows that the saving in the randomized upper bound of Arunachalam et al. fundamentally relies on randomness. Apart from characterizing the optimal relationship…
PDF arXiv
arXiv cs.LGSep 29
Beyond Diagonal State Space Models: Exact Non-Abelian Group Tracking, Solvability Barriers, and Geometric Physical Manifolds
Zeyu Jia
Selective state space models (SSMs), such as Mamba, S4D, and LRU, are bounded by transition matrix commutativity (A_t A_t' = A_t' A_t) and solvable affine transformation groups (Aff_D of derived length <= 2). Consequently, stacked multi-layer diagonal networks face severe optimization degradation on non-solvable simple groups such as A_5 due to the exponential circuit emulation depth required to simulate non-abelian commutators. We propose Non-Commutative State Space Models (NC-SSM), their real-orthogonal counterpart SO(3)-SSM, and arbitrary-dimension Cayley-SSM, lifting state transitions to compact Lie groups SU(2), SO(3), and SO(N). Via closed-form Euler-Rodrigues maps and rational Cayley transforms, NC-SSM achieves exact norm-preserving isometry (||U_t|| = 1). We introduce pure Hopf-fibration Bloch projective readouts (S^3/{+-1} =~ S^2 =~ SO(3)) to eliminate sign ambiguity, true quaternion parallel prefix scans (9.06x speedup at T=2048), and Identity-Gated Lie SSMs to eliminate sparse syntax phase drift. Extensive benchmarks across 14 experimental regimes show: (1) NC-SSM achieves 100% tracking on S_3, D_4, Q_8 and simple group A_5, where a 3-layer deep diagonal baseline…
PDF arXiv
arXiv quant-phSep 29
SQUARE: Structured Quantum Representation Adapters as Compact Quadratic Feature Maps for Frozen Language Models
Emily Jimin Roh, Hyojun Ahn, Hoyeong Lee, Soohyun Park, Sung Whan Yoon +2
Frozen language models (LMs) are increasingly used as fixed feature extractors for downstream reranking, scoring, and preference modeling, raising a practical question: how should a compact module represent interactions among features in a fixed low-dimensional bottleneck? Common linear and low-rank adapters remain linear at the adaptation module itself, whereas explicit second-order alternatives introduce pairwise interactions through direct parameterization or predefined factorizations. We propose SQUARE, a Structured QUAntum REpresentation adapter that amplitude-encodes the bottleneck vector, applies a parameterized quantum circuit, and measures the resulting state. We show that each basis-probability feature is exactly a normalized quadratic form in the bottleneck coordinates, while the additional Pauli-$Z$ readouts are signed linear combinations of these probabilities. The measured map can therefore parameterize interactions over $O(d^2)$ coordinate pairs through a small set of shared circuit parameters, where $d$ is the bottleneck dimension. It provides a structured parameterization within, rather than beyond, the classical normalized-quadratic feature class. In a disjoint…
PDF arXiv
arXiv quant-phSep 29
Digital Twin Modeling of Quantum Dynamical Systems: Dissipative Quantum Reservoir Computing
Abhijit Sen, Bikram Keshari Parida, Shital Chauhan, Mahima Arya, Denys I. Bondar
Modeling the response of driven many-body quantum systems from input--output data is difficult: the dynamics are nonlinear, history dependent, and expensive to simulate as system size grows. A paradigmatic case is High-Harmonic Generation~(HHG), where a strong field drives a medium to emit radiation that is highly sensitive to the drive and encodes long-range temporal correlations. We introduce a dissipative quantum reservoir computing~(DQRC) framework that builds a digital twin of such a system, learning its input--output map directly from data while the reservoir---itself a small open quantum system---stays fixed and only a classical readout is trained. We show that a minimal single-qubit reservoir reproduces the HHG response of a substantially larger Ising spin chain, and on a representative benchmark matches and on several metrics surpasses previously reported temporal convolutional and Kolmogorov--Arnold-network models, while using a simpler, physically realizable system. A single fixed reservoir further generalizes across a broad range of drives, indicating that it learns a shared physical response structure rather than memorizing trajectories. These results establish…
PDF arXiv
arXiv quant-phSep 29
Quantum Fidelity Landscape-Guided Prior Calibration for Single-Circuit QGAN Image Generation
Xue Yang, Rigui Zhou, Dax Enshan Koh, Siong Thye Goh, Yitao Tang +3
Quantum Generative Adversarial Networks (QGANs) have emerged as representative generative models in the Noisy Intermediate-Scale Quantum (NISQ) era and have attracted increasing attention in quantum machine learning. However, most existing QGAN methods rely on patch-based decomposition strategies, which weaken the global consistency of generated images and increase quantum resource overhead. In this work, we investigate a simpler approach: pixel-level, end-to-end image generation using a single-quantum-circuit QGAN. By analyzing the structural matching relationship between the quantum prior and the target data distribution in Hilbert space, we provide a new theoretical perspective for understanding the training behavior of naive end-to-end QGANs. Specifically, we introduce the Quantum Fidelity Landscape (QFL), defined as the pairwise-fidelity structure induced by an ensemble of quantum states and preserved under shared unitary transformations of the quantum generation process. We show that, under a fixed Lipschitz readout, this invariant imposes a one-sided bound on decoded sample separation, motivating calibration of the prior-induced QFL before adversarial training. To validate…
PDF arXiv
arXiv quant-phSep 29
Quantum Computing for Network Security Classification: Near-Term Classification and Long-Term Memory Efficiency
Yuqing Li, Poonam Bala Nehru, Yunpeng Zhang, Danindu Gammanpilage, Xin Jin +2
Quantum computing has already been explored in several network-security applications. However, how quantum computing may contribute to network-security classification in both the near term and the longer term has not been systematically discussed. This paper studies this question through two complementary experiments. First, we evaluate near-term quantum-kernel support vector machines (SVMs) on practical network-security classification tasks and compare them with classical SVM baselines on KDD Cup 1999, CICIDS2017, and BoT-IoT. Across these runs, quantum kernels are competitive. They can match or improve classical baselines in some settings, while classical RBF kernels remain stronger in others. This suggests that near-term quantum-kernel methods should be evaluated as practical, dataset-dependent alternatives to classical kernels rather than as uniformly superior replacements. Second, we use quantum oracle sketching (QOS) to study a longer-term memory advantage for classification with streaming classical samples. In QOS, samples are processed online and used to incrementally construct an approximate quantum oracle, which provides coherent query access for downstream quantum…
PDF arXiv

Papers

Topics in this field

quantum machine learning · quantum neural networks · learning quantum125 papers24 this week

Recent papers

All in Research →

arXiv quant-phSep 29
Optimal Quantum-Classical Separations for Exact Learning
Srinivasan Arunachalam, Amin Shiraz Gilani, Nikhil S. Mande
We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonical quantum speedups in this model are witnessed by Grover search and Bernstein-Vazirani, leading to the longstanding conjecture $$ \mathsf{R}(\mathcal C)=O(\mathsf{Q}(\mathcal C)^2+\mathsf{Q}(\mathcal C)\log N). $$ We first refute this conjecture by constructing concept classes $\mathcal C$ and $\mathcal C'$ satisfying \[ \mathsf{R}(\mathcal C)=Ω\!\left(\frac{\mathsf{Q}(\mathcal C)^3\log N}{\log \mathsf{Q}(\mathcal C)}\right) \qquad\text{and}\qquad \mathsf{D}(\mathcal C')=Ω(\mathsf{Q}(\mathcal C')^3\log N). \] The first bound matches the upper bound of Arunachalam et al.~[Quantum'21] up to constant factors, while the second matches the upper bound of Servedio and Gortler~[SICOMP'04]. In particular, this shows that the saving in the randomized upper bound of Arunachalam et al. fundamentally relies on randomness. Apart from characterizing the optimal relationship…
PDF arXiv
arXiv cs.LGSep 29
Beyond Diagonal State Space Models: Exact Non-Abelian Group Tracking, Solvability Barriers, and Geometric Physical Manifolds
Zeyu Jia
Selective state space models (SSMs), such as Mamba, S4D, and LRU, are bounded by transition matrix commutativity (A_t A_t' = A_t' A_t) and solvable affine transformation groups (Aff_D of derived length <= 2). Consequently, stacked multi-layer diagonal networks face severe optimization degradation on non-solvable simple groups such as A_5 due to the exponential circuit emulation depth required to simulate non-abelian commutators. We propose Non-Commutative State Space Models (NC-SSM), their real-orthogonal counterpart SO(3)-SSM, and arbitrary-dimension Cayley-SSM, lifting state transitions to compact Lie groups SU(2), SO(3), and SO(N). Via closed-form Euler-Rodrigues maps and rational Cayley transforms, NC-SSM achieves exact norm-preserving isometry (||U_t|| = 1). We introduce pure Hopf-fibration Bloch projective readouts (S^3/{+-1} =~ S^2 =~ SO(3)) to eliminate sign ambiguity, true quaternion parallel prefix scans (9.06x speedup at T=2048), and Identity-Gated Lie SSMs to eliminate sparse syntax phase drift. Extensive benchmarks across 14 experimental regimes show: (1) NC-SSM achieves 100% tracking on S_3, D_4, Q_8 and simple group A_5, where a 3-layer deep diagonal baseline…
PDF arXiv
arXiv quant-phSep 29
SQUARE: Structured Quantum Representation Adapters as Compact Quadratic Feature Maps for Frozen Language Models
Emily Jimin Roh, Hyojun Ahn, Hoyeong Lee, Soohyun Park, Sung Whan Yoon +2
Frozen language models (LMs) are increasingly used as fixed feature extractors for downstream reranking, scoring, and preference modeling, raising a practical question: how should a compact module represent interactions among features in a fixed low-dimensional bottleneck? Common linear and low-rank adapters remain linear at the adaptation module itself, whereas explicit second-order alternatives introduce pairwise interactions through direct parameterization or predefined factorizations. We propose SQUARE, a Structured QUAntum REpresentation adapter that amplitude-encodes the bottleneck vector, applies a parameterized quantum circuit, and measures the resulting state. We show that each basis-probability feature is exactly a normalized quadratic form in the bottleneck coordinates, while the additional Pauli-$Z$ readouts are signed linear combinations of these probabilities. The measured map can therefore parameterize interactions over $O(d^2)$ coordinate pairs through a small set of shared circuit parameters, where $d$ is the bottleneck dimension. It provides a structured parameterization within, rather than beyond, the classical normalized-quadratic feature class. In a disjoint…
PDF arXiv
arXiv quant-phSep 29
Digital Twin Modeling of Quantum Dynamical Systems: Dissipative Quantum Reservoir Computing
Abhijit Sen, Bikram Keshari Parida, Shital Chauhan, Mahima Arya, Denys I. Bondar
Modeling the response of driven many-body quantum systems from input--output data is difficult: the dynamics are nonlinear, history dependent, and expensive to simulate as system size grows. A paradigmatic case is High-Harmonic Generation~(HHG), where a strong field drives a medium to emit radiation that is highly sensitive to the drive and encodes long-range temporal correlations. We introduce a dissipative quantum reservoir computing~(DQRC) framework that builds a digital twin of such a system, learning its input--output map directly from data while the reservoir---itself a small open quantum system---stays fixed and only a classical readout is trained. We show that a minimal single-qubit reservoir reproduces the HHG response of a substantially larger Ising spin chain, and on a representative benchmark matches and on several metrics surpasses previously reported temporal convolutional and Kolmogorov--Arnold-network models, while using a simpler, physically realizable system. A single fixed reservoir further generalizes across a broad range of drives, indicating that it learns a shared physical response structure rather than memorizing trajectories. These results establish…
PDF arXiv
arXiv quant-phSep 29
Quantum Fidelity Landscape-Guided Prior Calibration for Single-Circuit QGAN Image Generation
Xue Yang, Rigui Zhou, Dax Enshan Koh, Siong Thye Goh, Yitao Tang +3
Quantum Generative Adversarial Networks (QGANs) have emerged as representative generative models in the Noisy Intermediate-Scale Quantum (NISQ) era and have attracted increasing attention in quantum machine learning. However, most existing QGAN methods rely on patch-based decomposition strategies, which weaken the global consistency of generated images and increase quantum resource overhead. In this work, we investigate a simpler approach: pixel-level, end-to-end image generation using a single-quantum-circuit QGAN. By analyzing the structural matching relationship between the quantum prior and the target data distribution in Hilbert space, we provide a new theoretical perspective for understanding the training behavior of naive end-to-end QGANs. Specifically, we introduce the Quantum Fidelity Landscape (QFL), defined as the pairwise-fidelity structure induced by an ensemble of quantum states and preserved under shared unitary transformations of the quantum generation process. We show that, under a fixed Lipschitz readout, this invariant imposes a one-sided bound on decoded sample separation, motivating calibration of the prior-induced QFL before adversarial training. To validate…
PDF arXiv
arXiv quant-phSep 29
Quantum Computing for Network Security Classification: Near-Term Classification and Long-Term Memory Efficiency
Yuqing Li, Poonam Bala Nehru, Yunpeng Zhang, Danindu Gammanpilage, Xin Jin +2
Quantum computing has already been explored in several network-security applications. However, how quantum computing may contribute to network-security classification in both the near term and the longer term has not been systematically discussed. This paper studies this question through two complementary experiments. First, we evaluate near-term quantum-kernel support vector machines (SVMs) on practical network-security classification tasks and compare them with classical SVM baselines on KDD Cup 1999, CICIDS2017, and BoT-IoT. Across these runs, quantum kernels are competitive. They can match or improve classical baselines in some settings, while classical RBF kernels remain stronger in others. This suggests that near-term quantum-kernel methods should be evaluated as practical, dataset-dependent alternatives to classical kernels rather than as uniformly superior replacements. Second, we use quantum oracle sketching (QOS) to study a longer-term memory advantage for classification with streaming classical samples. In QOS, samples are processed online and used to incrementally construct an approximate quantum oracle, which provides coherent query access for downstream quantum…
PDF arXiv

Active contributors · 90 days

Joongheon KimA Tutorial on Quantum Amplitude Embedding with Data Re-Uploading4
Daniel K. ParkMargin-Based Generalization for Quantum Machine Learning with Classical Data Encoding3
Tak HurMargin-Based Generalization for Quantum Machine Learning with Classical Data Encoding3
Muhammad UsmanWhen do quantum views help? Complementary classical-quantum representations in multi-view fusion3
Hyojun AhnA Tutorial on Quantum Amplitude Embedding with Data Re-Uploading3
Alberto MarchisioQBFF: Deep Quantum Bottleneck for Automatic Speaker Verification Anti-Spoofing3

Activity · 12 weeks

Coming with more sources: repos

Fields · AI · updated 58m ago

Quantum machine learning

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117 papers this month

Open problems in Quantum machine learning

Lack of provable guarantees for quantum machine learning models1 paper raises it · 2 address it
Without guarantees on performance, trainability, and efficient inference, quantum models risk being unreliable or impractical for real-world use.
- Supervised Learning with Quantum Hamiltonian Embeddingsraises · addresses
- Margin-Based Generalization for Quantum Machine Learning with Classical Data Encodingaddresses
Noise-oblivious quantum software testing1 paper raises it · 0 address it
NISQ hardware noise and probabilistic execution require testing methods that explicitly account for these constraints to ensure robustness.
- Noise-Awareness in Quantum Software Testing: An Empirical Landscape Analysisraises
Scalable quantum data embedding optimization1 paper raises it · 1 addresses it
Pairwise fidelity evaluations in embedding optimization create computational bottlenecks, limiting scalability for large datasets.
- Prototype-Guided Optimization of Quantum Data Embeddings with Linear Costraises · addresses
Task-aligned inductive biases in quantum circuits1 paper raises it · 1 addresses it
Without task-specific architectural biases, quantum circuits may fail to generalize well from limited data or align with problem structure.
- Task-aligned spectral inductive biases in parameterized quantum circuitsraises · addresses
Efficient discovery of high-performance quantum error-correcting codes1 paper raises it · 1 addresses it
Existing algebraic constructions for QECCs struggle to balance encoding rate and distance, limiting fault-tolerant quantum computation.
- LiftDiff: Guided Discrete Diffusion for Quantum Code Constructionraises · addresses

Named by an AI from these papers' abstracts.