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 algorithms accelerate financial risk computation.
problem Accelerating the computation of financial market risk.
method Quantum gradient estimation algorithms for market sensitivities.
result Significant reduction in resource requirements for financial quantum advantage.
Quantum method speeds up VB estimation in machine learning.
problem Prohibitively expensive natural gradient in high dimensions.
method Regression-based natural gradient estimation with quantum matrix inversion.
result Quantum method enables efficient VB estimation.
SGLBO optimizes quantum circuits with fewer measurements, improving accuracy and noise resilience.
problem Efficiently optimizing parameterized quantum circuits with reduced measurement shots and noise.
method Developed SGLBO combining SGD and BO, with adaptive measurement-shot strategy and suffix averaging.
result Significantly reduces measurement-shot cost while improving accuracy and noise resilience.
Researchers propose a non-monotone quantum natural gradient for quantum systems.
problem Applying natural gradient methods to quantum systems without monotonicity.
method Introducing a non-monotone quantum natural gradient (QNG) and demonstrating its superiority over conventional QNG.
result Non-monotone QNG outperforms conventional QNG in terms of convergence speed.
Improves VQAs by balancing classical and quantum training resources.
problem Challenges in trainability and resource costs of VQAs on quantum hardware.
method Adopting HELIA Ansatz and combining classical and quantum methods for gradient estimation and training.
result Achieves higher accuracy and success rates in VQE and improved test accuracy in quantum phase classification.
A new hybrid framework reduces quantum runtime and noise effects.
problem Challenges in deploying deep QFMs on real quantum hardware.
method Iterative Quantum Feature Maps (IQFMs) combining shallow QFMs and classical augmentation weights.
result Numerical experiments show IQFMs outperforming quantum convolutional neural networks.
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.
New methods optimize training VQAs without barren plateaus, improving efficiency and applicability.
problem Barren plateaus in training variational quantum algorithms.
method Derive adaptive learning rates and use Gaussian kernels to optimize movement in parameter space.
result Optimized training methods outperform other routines and can train VQAs free of barren plateaus.
Quantum method improves neural density estimation in high dimensions.
problem High-dimensional density estimation with poor performance and high computational complexity.
method Adaptive Fourier features based on quantum density matrices, integrated with neural networks.
result Competitive performance compared to state-of-the-art methods in various datasets.
Study evaluates capacity and trainability of parametrized quantum circuits.
problem Finding the best type of circuits for hybrid quantum-classical algorithms.
method Geometric structure of parameter space, effective quantum dimension, and circuit expressiveness.
result Identifies a transition in quantum geometry leading to decay of quantum natural gradient for deep circuits.
Quantum neural networks improve causal inference in biomedical studies, especially for small samples.
problem Addressing selection bias in comparing surgical techniques using observational data.
method Developed QNN-based propensity score models focusing on four key covariates (Age, Sex, Stage, BMI). Employed a linear ZFeatureMap for data encoding, SummedPaulis for predictions, and CMA-ES for optimization. Integrated noise modeling to enhance predictive stability.
result QNNs, particularly with noise-aware strategies, outperformed classical models in small samples, achieving AUC up to 0.750 for n=100.
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. Quantum annealer speeds up RBM training for image classification.
problem Training RBM with contrastive divergence (CD) is slow and computationally expensive.
method Used D-Wave 2000Q quantum annealer to calculate model expectation of gradient learning for RBM.
result Quantum training yields similar classification performance to CD but faster.
Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical …
A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of…
Develops an analytic theory for quantum imaginary time evolution.
problem Lack of a first-principle understanding of quantum imaginary time evolution.
method Interprets QITE as a form of VQA trained with QNGD and connects it to the geometric geodesic distance in the quantum Fisher information metric.
result QITE converges faster than vanilla gradient descent-based VQAs, though the advantage is suppressed by Hilbert space dimensionality.
Quantum systems learn like machine learning models, influenced by dissipation.
problem Understanding how quantum systems learn and evolve.
method Hydrodynamical formulation of quantum mechanics, gradient descent model, empirical demonstration.
result Quantum systems follow a disrupted gradient descent model, influenced by dissipation.
Quantum kernel improves probabilistic time series forecasting.
problem Quantifying uncertainty in probabilistic time series predictions.
method Integrates quantum kernel with Gaussian process regression.
result Quantum kernel enhances forecasting performance.
Derives exact gradients for linear optics with single photons.
problem Gradient estimation for linear optics with single photons.
method Generalized parameter shift rule for linear optics.
result Derives analytical formula for gradients in linear optics.
Quantum machine learning faces challenges similar to variational quantum algorithms in training.
problem Challenges in training quantum machine learning models.
method Bridge between variational quantum algorithms and quantum machine learning, applying gradient scaling results.
result Gradient scaling results for variational quantum algorithms can also be applied to quantum machine learning models, revealing new trainability issues.
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.
Warm starts improve variational quantum algorithms by avoiding barren plateaus.
problem Barren plateaus in variational quantum algorithms limit scaling.
method Exploring warm starts in iterative variational methods for quantum circuits.
result Warm starts can lead to substantial gradients in small regions, suggesting trainability.
Gradient-free optimizers are ineffective on barren plateaus in quantum computing.
problem Effect of barren plateaus on gradient-free optimization in quantum computing.
method Numerical simulations and theoretical analysis of gradient-free optimization algorithms.
result Gradient-free optimizers are not effective in barren plateau landscapes due to exponentially suppressed cost function differences.
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 RNG improves financial risk metrics estimation.
problem Estimating financial risk metrics with high precision.
method Quantum-Enhanced Monte Carlo using QRNG.
result Improved accuracy in VaR and CVaR estimation.
Quantum machine learning faces 'laziness' and 'barren plateaus', but noise can mitigate the latter.
problem Quantum machine learning's loss function landscape issues.
method Theoretical analysis of quantum variational circuits, neural tangent kernels, and noise effects.
result Noise can mitigate barren plateaus in quantum machine learning.
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of th…
Analyzes dynamics of quantum neural networks, predicting exponential decay of training error.
problem Understanding convergence rate of quantum neural networks training.
method Analytic theory for gradient descent dynamics of wide quantum neural networks.
result Simple analytic formula predicts exponential decay of training error.
New algorithm Momentum-QNG improves optimization of quantum circuits.
problem Optimizing variational quantum circuits to avoid local minima.
method Applied Langevin dynamics to QNG, introducing momentum term.
result Momentum-QNG outperforms basic QNG and other optimizers.
QCNNs avoid barren plateaus, making them trainable.
problem Exponentially vanishing gradients in QNNs.
method Graph-based method to analyze Haar-distributed unitaries.
result QCNNs do not exhibit barren plateaus, implying trainability.
Quantum annealing (QA) is a hardware-based heuristic optimization and sampling method applicable to discrete undirected graphical models. While similar to simulated annealing, QA relies on quantum, rather than thermal, effects to explore complex search spaces. For many classes of problems, QA is known to offer computat…
Expressive quantum circuits are harder to train due to flatter cost landscapes.
problem Designing quantum circuits that are both expressive and trainable.
method Deriving a relationship between expressibility and gradient magnitude, extending barren plateau phenomenon.
result Highly expressive ansätze exhibit flatter cost landscapes, making them harder to train.
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.
ECD algorithm speeds up non-convex optimization, offering quantum and stochastic enhancements.
problem Non-convex optimization challenges in machine learning.
method Energy Conserving Descent (ECD) algorithm, stochastic ECD dynamics (sECD), quantum ECD Hamiltonian (qECD).
result ECD and its quantum version achieve exponential speedup over gradient descent.
New bound shows variational algorithms may struggle with barren plateaus.
problem Barren plateaus in quantum loss landscapes.
method General bound on loss variance and gradient decay.
result Exponential decay of gradients in subregions of barren plateaus.
Quantum statistical models with singularities are studied for state estimation and model selection.
problem Understanding statistical properties of quantum singular models.
method Classical singular learning theory extended to quantum state estimation and model selection using algebraic geometrical methods.
result Asymptotically unbiased estimator (QWAIC) for quantum generalization loss constructed.
TensorHyper-VQC improves VQC scalability and robustness.
problem Scalability and noise sensitivity in VQC.
method Tensor-train-guided hypernetwork framework.
result TensorHyper-VQC achieves superior performance and robust noise tolerance.
Quantum computer method for pricing rainbow options efficiently.
problem Pricing rainbow options with quantum computers.
method Iterative Quantum Amplitude Estimation and amplitude loading techniques.
result Validation of quantum pricing model on IBM QASM simulator.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
Quantum networks offer exponential communication savings for large machine learning models.
problem Training and inference of large models require efficient communication.
method Quantum encoding and gradient descent for distributed computation.
result Exponential reduction in communication for gradient descent on quantum networks.
Quantum computing speeds up neural network training and retraining.
problem Inefficient classical training and retraining of neural networks.
method Adiabatic quantum computing to optimize Kolmogorov-Arnold Networks using Bezier curves.
result Quantum optimization achieves 100x faster retraining compared to classical methods.
Sketch Tomography improves quantum state estimation accuracy.
problem Efficiently estimating quantum states, especially MPS states.
method Hybridizes classical shadow protocol with tensor train ansatz.
result Proven convergence with quadratic sample complexity.
Quantum SVT reduces credit risk analysis costs.
problem Efficiently estimating credit risk metrics using quantum computing.
method Quantum Singular Value Transformation (QSVT) to reduce state preparation costs.
result Significant reduction in implementation costs for quantum credit risk analysis.
Quantum Earth Mover's distance improves stability and efficiency in quantum learning.
problem Quantum learning's loss landscapes often lead to poor local minima and gradients.
method Introduced the quantum Earth Mover's (EM) distance and proposed a quantum Wasserstein generative adversarial network (qWGAN).
result The quantum EM distance makes quantum learning more stable and efficient.
Boosted Frank-Wolfe accelerates optimization for nonconvex problems.
problem Optimizing nonconvex and quasar-convex objectives efficiently.
method Developed a novel step size strategy for stochastic Frank-Wolfe, extending it to various gradient estimators.
result Boosted Frank-Wolfe achieves faster convergence rates than non-boosted Frank-Wolfe.
New method uses single quantum state for machine learning tasks, improving accuracy.
problem Challenges in unsupervised learning with quantum data.
method SIngle-Preparation Quantum Information Processing (SIPQIP) concept.
result Significantly more accurate estimation compared to traditional methods.
Quantum algorithm speeds up Gibbs partition function estimation.
problem Estimating partition functions in sublinear time.
method Sublinear-time quantum algorithm using quantum phase and amplitude estimation.
result First sublinear-time speed-up for partition function estimation.