This work shows how to efficiently simulate parts of quantum landscapes using classical computers.
problem Identifying where quantum computers are advantageous and offloading computations.
method Developed a quantum-enhanced classical algorithm to simulate sub-regions of quantum landscapes.
result It is possible to generate a classical surrogate of a sub-region of a quantum landscape.
This work reveals symmetries in quantum circuits and develops a noise-aware optimization method.
problem Understanding and optimizing the cost landscape of parametrized quantum circuits.
method Analytical proof of symmetries and their resilience to noise, followed by the development of SYMH optimization method.
result Symmetries in PQCs lead to degeneracy in the cost landscape and can be exploited to improve optimization under noise.
Overparametrization improves QNN trainability by reducing spurious local minima.
problem Understanding how overparametrization affects the loss landscape of QNNs.
method Rigorous analysis of overparametrization in QNNs with periodic structure.
result Overparametrization corresponds to a computational phase transition improving QNN trainability.
Variational quantum computing faces a flat optimization landscape problem.
problem Barren Plateaus (BP) in optimization landscapes.
method Theoretical and heuristic methods to understand and mitigate BPs.
result All algorithm components can lead to BPs if not well-suited.
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.
Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learn…
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.
A new approach to quantum machine learning circuits reduces training difficulties.
problem Challenges in training deep quantum circuits due to flat training landscapes.
method Variable structure approach (VAns) to build ansatzes, applying rules for gate growth and removal.
result VAns successfully mitigates trainability and noise-related issues, improving performance in various applications.
Quantum circuits reveal pathways to dequantization in machine learning models.
problem Navigating the complex landscape of quantum machine learning models and algorithms.
method Introducing a framework connecting quantum circuit structure to function representability.
result Fundamental properties of quantum circuits determine classical simulability of models.
New approach connects quantum phases to VQA trainability, enabling better scaling.
problem Scalability issues in VQAs, especially barren plateaus.
method Analog VQA ansätze composed of quenches of a disordered Ising chain, tuning disorder strength.
result Thermalized and MBL phases reach maximal expressivity at large M, but barren plateaus emerge at smaller M in the thermalized phase. New method uses adiabatic principles to improve ground-state preparation in quantum computing.
problem Challenges in variational training of complex energy landscapes.
method Iterative Hamiltonian deformation complemented with adiabatic principles.
result Consistent convergence to target ground state through sequence of intermediate problems.
Quantum circuit models learn better with specific initialization strategies.
problem Understanding and improving the optimization landscape of IQP-based generative models.
method Proved barren plateaus for random initialization, established lower bounds, and developed data-dependent initialization.
result Data-dependent initialization leads to faster convergence and better minimums.
Unified geometric framework for quantum states using dual number algebras.
problem Representing quantum states in a geometrically unified way.
method Smooth embeddings into higher-order dual number algebras and algebraic flows.
result Established nilpotent dual algebras as a geometric landscape for quantum kinematics.
Quantum models avoiding barren plateaus can also be efficiently simulated classically.
problem Understanding the limitations of barren plateaus in quantum computing.
method Analyzing commonly used models and their ability to be simulated classically.
result Many quantum models with barren plateau-free landscapes can also be efficiently simulated classically.
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.
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 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.
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 …
Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable qua…
Quantum machine learning aims to solve learning problems more efficiently.
problem Solving learning problems more efficiently using quantum processors.
method Leveraging quantum processors for optimization, supervised, unsupervised, reinforcement learning, and generative modeling.
result Quantum approaches may offer real benefits under certain conditions.
Study combines quantum and classical deep learning for better credit risk assessment.
problem Enhancing accuracy and efficiency in credit risk evaluation.
method Hybrid Quantum-Classical Deep Neural Network for Row-Type Dependent Predictive Analysis.
result Proposed framework enhances predictive models for different loan categories.
Quantum computing offers new solutions for financial optimization, pricing, risk, and security.
problem Core financial bottlenecks in combinatorial search, expectation estimation, and rare-event analysis.
method Identify bottlenecks, specify quantum primitives, compare with classical benchmarks, assess under constraints.
result Strongest near-term case for quantum finance in hybrid workflows, constrained search, and amplitude-estimation.
Quantum kernel methods can lead to trivial models due to exponential concentration of kernel values.
problem Exponential concentration of quantum kernel values can lead to trivial models in QML.
method Analyzing the resources needed to accurately estimate quantum kernel values and identifying four sources of concentration.
result Quantum kernel values can be exponentially concentrated, leading to trivial models.
We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests…
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.
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.
Theoretical guarantees for permutation-equivariant QNNs avoid barren plateaus.
problem Excessive local minima and barren plateaus in QNNs training landscapes.
method Designing Sn-equivariant QNNs to encode permutation symmetry. result Equivariant QNNs do not suffer from barren plateaus, quickly reach overparametrization, and generalize well.
We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on a D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as a combined vector, and encode the high-order correlations between them into a dictionary optimized for…
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. …
Hybrid QAOA approach optimizes portfolios with strict constraints, outperforming classical methods.
problem Combinatorial optimization under strict cardinality constraints in portfolio management.
method Constraint-preserving QAOA with XY-mixers and Trotterized initialization.
result QAOA achieves a Sharpe Ratio of 1.81, significantly outperforming classical methods.
Quantum method detects financial stress regimes from market data.
problem Detecting financial stress regimes from market data.
method Adapted Pauli Correlation Encoding to quantum topological data analysis.
result Quantum method can recover Betti numbers exactly at every scale.
The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathemat…
Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
Reviews recent findings on neural network landscapes.
problem Non-convexity of loss functions causing bad landscapes.
method Rigorous geometric analysis and empirical exploration.
result Wide neural nets may have sub-optimal local minima.
The study examines when MAML's objective has a benign landscape.
problem Understanding when MAML's objective landscape is benign.
method Analyzing the landscape of MAML objective on LQR tasks.
result The benign landscape of the MAML objective depends on task similarities.
Black holes offer insights into machine learning's loss landscapes.
problem Understanding the loss landscape in machine learning.
method Comparing machine learning loss landscapes to black hole entropy.
result Black holes provide an infinite family of potential landscapes with known minima.
Adversarial training makes logistic regression weight loss landscapes sharper.
problem Understanding why adversarial training sharpens the weight loss landscape in logistic regression.
method Theoretical analysis of linear logistic regression model with L2 norm constraints, and experiments on ResNet18.
result Adversarial training sharpens the weight loss landscape in linear logistic regression models.
AWP improves robustness by flattening weight loss landscape.
problem Improving robustness of deep neural networks against adversarial examples.
method Explicitly regularizes the flatness of weight loss landscape through adversarial weight perturbation.
result AWP forms a double-perturbation mechanism in adversarial training, leading to flatter weight loss landscape.
Efficiently infers graph edges from genetic similarity data in landscape genetics.
problem Inferring unknown graph edges from genetic similarity data in a heterogeneous landscape.
method Developed an efficient first-order optimization method to solve the inverse landscape genetics problem.
result Our method provides fast and reliable convergence, significantly outperforming existing heuristics.
Smoothed fitness landscape improves protein optimization.
problem Infeasibility of combinatorially large protein sequence space.
method Formulate protein fitness as a graph signal, smooth using Tikunov regularization, and optimize with Gibbs sampling.
result 2.5 fold fitness improvement over training set.
Researchers improve visualization of neural network loss landscapes.
problem Understanding neural network generalization performance.
method Novel 'jump and retrain' procedure, non-linear dimensionality reduction (PHATE), computational homology.
result Improved visualization and quantification of neural network generalization performance.
Deeper models have a more favorable optimization landscape, making them more robust to noise.
problem Characterizing the effect of depth on the optimization landscape of linear regression models.
method Robust and over-parameterized setting, simple sub-gradient method.
result A simple sub-gradient method converges to a balanced solution that is close to the ground truth and enjoys a flat local landscape.
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular pot…
New sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
We analyze the optimization landscape of α-loss in logistic models.
problem Optimization landscape of α-loss in logistic models.
method Tools from strictly-locally-quasi-convex functions and geometric techniques.
result Evolution of optimization landscape with respect to α.
Study reveals sharp characterisation of local minima in neural network loss landscapes.
problem Characterizing local minima in high-dimensional two-layer ReLU neural networks.
method Exact low-dimensional representation of local minima using summary statistics and link with one-pass SGD dynamics.
result Local minima in overparameterized neural networks form discrete families with varying stability and reachability.
Experimental fractal landscape dynamics observed in emulsions.
problem Understanding anomalous motions in soft glassy materials.
method Quantitative analysis of oil droplet trajectories in dense emulsions.
result Experimental fractal geometry matches computational model of soft glassy dynamics.
SGD vs quasi-Newton optimization in neural networks: different landscapes, different generalizability.
problem Understanding neural network optimization and generalizability.
method Comparison of stochastic gradient descent (SGD) and quasi-Newton optimization methods using computational tools.
result SGD solutions are separated by lower barriers than quasi-Newton solutions, but quasi-Newton solutions are deeper and more isolated.