A quantum reinforcement learning algorithm reduces sample complexity.
problem Quantum reinforcement learning under model-free settings with quantum oracle access.
method Quantum Natural Policy Gradient (QNPG) algorithm replacing random sampling with deterministic gradient estimation.
result QNPG achieves a sample complexity of i l d e O ( ε − 1.5 ) ilde{\mathcal{O}}(ε^{-1.5}) i l d e O ( ε − 1.5 ) for queries to the quantum oracle, significantly improving classical lower bound. Quantum method generates unbiased samples from discrete graphical models.
problem Sampling from discrete graphical models is challenging and intractable in high dimensions.
method Embedding graphical models into unitary operators and using quantum circuits.
result Provably generates unbiased and independent samples from general discrete factor models.
New algorithm improves efficiency of quantum system modeling.
problem Intractable complexities in quantum Hamiltonian learning and Gibbs sampling.
method Generalized quantum natural gradient descent and Quantum-Probabilistic Mirror Descent.
result Data sample efficiency proven using information geometry and quantum metrology.
This work proposes efficient classical training protocols for IQP circuits to train quantum generative models.
problem Training quantum generative models on industrially relevant probability distributions is challenging due to high computational cost.
method Developed protocols for classical training of IQP circuits, which are hard to sample but have efficient gradient computation.
result Classically trained IQP circuits can efficiently sample from target probability distributions, demonstrating practical quantum advantage.
Quantum Boltzmann Machines trained on quantum annealers produce noisy synthetic data.
problem Training quantum Boltzmann machines on quantum annealers for financial data generation.
method Used D-Wave Advantage 4.1 quantum annealer to train QBMs and compare with classical RBMs.
result Quantum Boltzmann Machines trained on quantum annealers are noisier and less effective than classical RBMs.
Quantum dynamics algorithm learns manifold from data.
problem Learning manifolds from high-dimensional datasets.
method Simulation of quantum dynamics on a graph embedding of data.
result Algorithm reveals connections between data sampling and quantization.
Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. O…
Quantum Proof-of-Work uses boson sampling to secure blockchain consensus.
problem Ensuring secure and efficient blockchain consensus.
method Proposes using quantum boson sampling as a Proof-of-Work scheme for blockchain.
result Demonstrates a robust and energy-efficient PoW scheme.
New classical algorithm outperforms quantum in neural network subnetwork selection.
problem Selecting sparse subnetworks from large neural networks efficiently.
method Quantum-inspired classical algorithm using ridgelet transform sampling.
result Runs in polynomial time, outperforming naive classical methods.
Protocol learns pure quantum states with minimal disturbance.
problem Efficiently learn quantum states with minimal disturbance.
method Sequential measurements with minimal disturbance.
result Achieves maximal precision with polylogarithmic regret.
New metrics improve quantum ensemble learning efficiency and power.
problem Quantum ensembles' distances poorly understood due to measurement constraints.
method Introduce MMD- k k k hierarchy of integral probability metrics for quantum ensembles. result MMD- k k k requires fewer samples for full discriminative power at higher k k k . Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
problem Sampling from solutions of stochastic differential equations.
method Differentiable quantum circuits (DQCs) encoding latent variables, quantile mechanics.
result Quantum algorithm generates time-series from SDEs.
Quantum algorithm improves portfolio construction accuracy.
problem Efficiently constructing portfolios with real-world constraints.
method Sampling-based CVaR Variational Quantum Algorithm (VQA) combined with local-search post-processing.
result Achieved a relative solution error of 0.49% on IBM Heron processors.
Unified framework for learning quantum models from limited measurements.
problem Sample complexity and measurement shots in classical learning of quantum models.
method Unified learning framework considering probabilistic quantum measurements.
result Asymmetrical effects and interplay of sample size and measurement shots on learning performance.
Extends quantum learning theory to multiclass and online settings.
problem Quantum learning theory for batch and online learning.
method Adapts classical models to quantum settings, introduces new online learning model.
result Quantum and classical sample complexities have the same form for various learning scenarios.
Quantum algorithms speed up reinforcement learning policies in large state-action spaces.
problem Limitations of quantum access in training reinforcement learning policies.
method Designing quantum algorithms to train reinforcement learning policies.
result Quantum algorithms offer full quadratic speed-ups in sample complexity for well-behaved policies.
Quantum algorithm speeds up learning from big data exponentially.
problem Scalable learning from big data with optimized random features.
method Quantum algorithm for sampling optimized random features.
result Exponential speedup in runtime compared to classical algorithms.
Study shows limitations and possibilities of learning quantum circuit output distributions.
problem Learnability of output distributions of local quantum circuits.
method Investigated within two oracle models: statistical query model and direct sample access model.
result Output distributions of super-logarithmic depth Clifford circuits are not efficiently learnable in the statistical query model.
Bayesian approach optimizes quantum circuits for noisy hardware.
problem Optimizing parameterized quantum circuits on noisy quantum hardware.
method Reformulate classical optimisation as Bayesian posterior, combining cost function and prior distribution. Apply dimension reduction and posterior sampling strategies.
result Bayesian approach generates faster, less noisy circuits than classical methods.
Quantum tech speeds up financial risk assessment.
problem Improving credit valuation adjustments using quantum mechanics.
method Developed a quantum algorithm using Bayesian quantum amplitude estimation and engineered likelihood functions.
result Significant speedup in quantum computations for CVA over classical methods.
Quantum channels' contraction under privacy constraints studied.
problem Understanding the privacy constraints on quantum channel contractions.
method Established upper bounds on contraction coefficients for specific divergences under QLDP constraints.
result Upper bounds and full characterization of contraction coefficients for specific quantum distances.
We present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted …
Study online learning of quantum processes, showing feasibility for certain types.
problem Learning quantum processes adaptively, especially for bounded gate complexity and Pauli channels.
method Online learning, mistake-bounded model, multiplicative weights update algorithm, Bell sampling.
result Online learning feasible for quantum channels of bounded gate complexity and Pauli channels.
New algorithms improve MCMC efficiency for complex distributions.
problem High variance and low effective sample size in MCMC samplers.
method Antithetic Riemannian Manifold and Quantum-Inspired Hamiltonian Monte Carlo.
result Improved effective sample size and variance reduction.
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on investigating the information-theoretic upper bounds of sample complexity - how ma…
Quantum reservoirs risk bounds are analyzed using Rademacher complexity.
problem Bounding generalization errors of quantum reservoirs.
method Using Rademacher complexity, specific bounds are derived for quantum reservoir classes.
result Risk bounds converge with increasing training samples and qubits.
Quantum GBS boosts asset clustering for robust statistical arbitrage portfolios.
problem Identifying co-moving assets from correlation matrices for statistical arbitrage.
method Mapping S&P 500 correlation data to GBS-compatible adjacency matrices, benchmarking classical and quantum clustering algorithms.
result Quantum GBS generates superior alpha during high volatility periods, persisting under low-loss conditions.
Quantum computers can simulate flow models efficiently.
problem Efficiently simulating continuous flow models on quantum computers.
method Relating flow models to the Schrödinger equation and proving efficient Hamiltonian simulation.
result Quantum computers can prepare qsamples for flow models efficiently.
A new optimizer saves significant shots in quantum machine learning.
problem Training variational QML algorithms is challenging due to large datasets and shot-count overhead.
method Proposed Refoqus optimizer that samples over both dataset and measurement operators.
result Refoqus can save several orders of magnitude in shot cost compared to existing methods.
Study on learning quantum dynamics without direct interaction.
problem Learning quantum dynamics incoherently without direct interaction.
method Analyze sample complexity and prove bounds for incoherent learning.
result Prove that arbitrary measurements allow efficient learning of unitary processes incoherently.
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the L 1 L_1 L 1 norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fr…
Quantum models improve data generation from noisy quantum processors.
problem Creating complex probability distributions from limited data.
method Quantum-noise-driven generative diffusion models.
result Quantum noise can be harnessed to generate more complex distributions efficiently.
Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However, training of quantum circuits can be more challenging compared to classical neural net…
D-Wave quantum annealing fails to improve sampling quality from RBMs compared to Gibbs sampling.
problem Improving sampling quality from RBMs using D-Wave quantum annealing.
method Comparison of D-Wave quantum annealing and Gibbs sampling for RBM sampling.
result D-Wave sampling does not significantly improve the number of local valleys compared to Gibbs sampling.
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM a…
Quantum circuits represent binary classification trees with binary features.
problem Classifying data using binary classification trees with binary features.
method Quantum circuits and probabilistic approach for traversing decision trees.
result First realization of a decision tree classifier on a quantum device.
In the past decade, the field of quantum machine learning has drawn significant attention due to the prospect of bringing genuine computational advantages to now widespread algorithmic methods. However, not all domains of machine learning have benefited equally from quantum enhancements. Notably, deep learning and rein…
In Deep Learning, a well-known approach for training a Deep Neural Network starts by training a generative Deep Belief Network model, typically using Contrastive Divergence (CD), then fine-tuning the weights using backpropagation or other discriminative techniques. However, the generative training can be time-consuming…
Quantum correlations enhance generative models, providing a new resource for machine learning.
problem Capturing complex probability distributions in unsupervised learning.
method Theoretical and numerical analysis of quantum correlations in generative models.
result Quantum nonlocality and contextuality provide an expressivity advantage over classical models.
Quantum states can be learned efficiently using gentle measurements.
problem Efficiently learning quantum states with minimal measurements.
method Introducing α-LGM measurements and proving strong quantum DPI.
result The number of states needed for accurate learning is of order 1/(ε^2 α^2).
New method uses quantum computing to process classical data efficiently.
problem Inefficient quantum machine learning due to data loading and trainability issues.
method Linear Hamiltonian-based machine learning with ground state problems for k-local Hamiltonians.
result Demonstrated the effectiveness and scalability of the method on up to 50 qubits.
Quantum Gaussian processes enable scalable quantum learning.
problem Lack of simple, interpretable, scalable learning frameworks for quantum data.
method Bayesian framework using Gaussian processes with quantum kernels.
result Provable and scalable quantum Gaussian processes for quantum learning.
A new method speeds up quantum state estimation.
problem Exponential growth in sample size and dimension for quantum state tomography.
method Stochastic mirror descent with Burg entropy.
result Optimization error vanishes at a O ( ( 1 / t ) d log t ) O (\sqrt{ ( 1 / t ) d \log t }) O ( ( 1/ t ) d log t ) rate. New method bounds hardware noise without assumptions.
problem Estimating hardware noise without assumptions.
method Machine Learning and Conformal Prediction.
result Theoretical upper bounds of fidelity.
Develops a framework for designing quantum neural networks that respect symmetries.
problem Trainability and generalization issues in quantum neural networks.
method Equivariant quantum neural networks (EQNN) for any symmetry group.
result Efficient construction of equivariant layers for EQNNs, including QCNNs.
Quantum ML predicts data with improved speed and accuracy.
problem Predicting data using maximum likelihood in a quantum setting.
method Quantum states embedding and minimization of quantum relative entropy.
result Unified framework for classical and quantum LLMs with performance guarantees.
New method uses quantum annealing and VAN for better statistical mechanics calculations.
problem Difficulty in computing partition function in statistical mechanics.
method Combines quantum annealing samples with variational autoregressive networks.
result Enhanced accuracy in finite-size Sherrington-Kirkpatrick model.
Quantum algorithm estimates multivariate mean with near-optimal efficiency.
problem Estimating the mean of multivariate random variables efficiently in quantum computing.
method Combines amplitude amplification, quantum singular value transformation, and Bernstein-Vazirani algorithm.
result Quantum estimator outperforms classical estimators outside low-precision regime.