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.
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. 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.
The thesis optimizes quantum state exploration using bandit algorithms.
problem Maximizing reward in online learning of quantum state properties.
method Multi-armed bandit approach to select observables, minimizing regret.
result Optimal strategies with matching upper and lower bounds for regret.
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 quantum state reconstruction method accelerates convergence.
problem Quantum state reconstruction for larger systems.
method Momentum-Inspired Factored Gradient Descent (MiFGD) combining compressed sensing, non-convex optimization, and acceleration.
result Converges to true density matrix at an accelerated linear rate, provably close to the true matrix.
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.
Method learns topological states from randomized measurements.
problem Detecting topologically ordered two-dimensional states on quantum processors.
method Variational tensor network tomography with randomized measurements.
result Demonstrated ability to learn ground states of surface code and quantum spin liquid states.
New method for QPT without needing to know or prepare specific input states.
problem Quantum process characterization with unknown input states.
method Blind Quantum Process Tomography (BQPT) with single-preparation methods.
result Ability to characterize quantum processes using arbitrary unknown input states.
Improved algorithm for low-rank matrix problems with convex constraints.
problem Low-rank matrix problems with specific norm-constraints.
method Projected Factored Gradient Descent (ProjFGD) using Burer-Monteiro factorization.
result Non-convex projected gradient descent favors linear convergence in the factored space.
Variational autoencoders improve state representation for hard quantum systems.
problem Simulating and storing quantum states is computationally infeasible.
method Introduced variational autoencoders for quantum state representation.
result Deep networks better represent hard quantum states, suggesting compositional structure.
The paper establishes minimax bounds for estimating low-rank quantum density matrices.
problem Estimating low-rank quantum density matrices with optimal error rates.
method Developed minimax lower bounds and upper bounds for least squares estimator with von Neumann entropy penalization.
result Sharp upper and lower bounds for various distances (Kullback-Leibler, Hellinger, Schatten p-norm) are attained.
Adversarial learning approximates unknown quantum states on near-term quantum computers.
problem Approximating unknown quantum pure states on near-term quantum computers.
method Two parametrized circuits optimized adversarially, with resilient backpropagation and bipartite entanglement entropy.
result Resilient backpropagation algorithms perform well in optimizing the two circuits.
We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum …
New quantum states capture more information, enabling advanced processing tasks.
problem Quantum information processing challenges with limited statistical information.
method Introducing Random-Coefficient Pure States (RCPS) and exploiting their higher-order statistics.
result RCPS provide richer information than density operators, enabling new quantum tasks.
Injective transform for manifolds with convex boundary, solving integral geometry problems.
problem Injectivity of the geodesic X-ray transform with matrix weights.
method Reduction to local invertibility near strict convexity, detailed layer stripping analysis.
result Connection and Higgs field uniquely determined by scattering relation.
Global stability bounds for matrix frames in phase retrieval problems.
problem Phase retrieval for matrix frames in various applications.
method Computable global stability bounds for the quasi-linear analysis map β, using Whitney stratification of positive semidefinite matrices of low rank.
result Novel conditions for a frame to be generalized phase retrievable.
Least squares estimation works well for symmetric positive semidefinite matrices without regularization.
problem Estimation of symmetric positive semidefinite matrices without regularization.
method Simple least squares estimation with extsf{spd} constraint.
result Constrained least squares estimation performs as well as regularization-based approaches.
Estimates quantum system states using Pauli measurements with improved convergence rates.
problem Estimating low rank density matrices of quantum systems.
method Developed Dantzig estimator for Pauli measurements, proving optimal convergence rates in Schatten norms.
result Improved convergence rates for estimating low rank density matrices, including sharp rates in Kullback-Leibler divergence.
New proof shows 11 measurements needed for phase retrieval in 4D complex space.
problem Determining the minimal number of intensity measurements for phase retrieval in 4D complex space.
method Leveraged characteristic classes and cohomology groups from differential topology.
result Proved that 11 is the exact minimum number of measurements required for phase retrieval in 4D complex space.
This paper compares classical shadows and direct quantum measurement for efficient information extraction.
problem Efficiently extracting classical information from quantum states with limited classical post-processing.
method Quantitative resource analysis comparing classical shadows and direct quantum measurement.
result An efficiency frontier between classical shadows and direct quantum measurement is identified.
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unle…
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 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…
Paper generalizes VB-FTRL for online learning of quantum states with logarithmic loss.
problem Online learning of quantum states with logarithmic loss.
method Generalizes VB-FTRL algorithm for LL-OLQS with polynomial-time implementation.
result Achieves a regret rate of O ( d 2 log ( d + T ) ) O (d^2 \log (d + T)) O ( d 2 log ( d + T )) for LL-OLQS. Unified approach for learning quantum operations from measurements.
problem Accurate reconstruction of unknown quantum operations from noisy measurements.
method Matrix sensing techniques, randomized measurement design, blockwise measurement design, alternating least squares (ALS).
result The proposed method provides theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise.
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.
Improved computed tomography reconstruction with deep learning and deep image prior.
problem Low data efficiency in computed tomography reconstruction.
method Combining learned primal-dual methods with deep image prior for improved quality and generalization.
result Proposed methods outperform state-of-the-art in low data regime.
TRex framework improves sparse view X-ray tomography reconstruction.
problem Sparse view X-ray tomography reconstruction challenges.
method Flexible Tomographic Reconstruction framework using proximal algorithms.
result Superior reconstruction quality compared to state-of-the-art methods.
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coeffic…
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the ℓ 1 \ell_1 ℓ 1 -norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank a…
Study travel time tomography for transversely isotropic media using modified pseudodifferential calculus.
problem Travel time tomography problem for transversely isotropic media.
method Modified scattering pseudodifferential calculus to solve the tomography problem.
result Construction and use of modified pseudodifferential calculus to solve the tomography problem.
Lecture notes on analysis tools for X-ray tomography.
problem Understanding X-ray tomography using mathematical analysis.
method Overview of analysis tools and ideas, minimal assumptions.
result Broad overview of analysis tools for X-ray tomography.
Summary of tensor tomography proofs on manifolds with boundaries.
problem Proving injectivity of tensor tomography on compact Riemannian manifolds with boundaries.
method Summarized proofs from previous studies.
result Summary of proofs for s-injectivity.
Improved Bandit PCA with optimal regret bound.
problem Minimizing regret in online PCA with bandit feedback.
method Combines online mirror descent and multiscale exploration.
result Minimax optimal regret bound of r d T r\sqrt{dT} r d T . Paper addresses travel time tomography stability and statistical inversion.
problem Determining conformal factors of metrics from geodesic lengths.
method Established forward and inverse stability estimates; applied to Bayesian statistical inversion.
result Consistency of statistical inversion technique for travel time tomography.
Non-convex gradient descent accelerates convergence in matrix factorization models.
problem Non-convex optimization in matrix factorization models.
method Factored gradient descent with acceleration.
result Acceleration leads to linear convergence rate in non-convex settings.
QGAA learns latent quantum states, reducing errors in quantum data generation.
problem Learning latent representations for quantum data generation.
method Quantum Generative Adversarial Autoencoder (QGAA) combining QAE and QGAN.
result Average errors in energies for H2 and LiH are 0.02 Ha and 0.06 Ha respectively, demonstrating QGAA's potential.
Neural-Network Quantum States connect to Tensor-Network states, enhancing quantum state representation.
problem Describing complex quantum wave functions efficiently.
method Introducing Neural-Network Quantum States and showing their connections to Tensor-Network states.
result Neural-Network Quantum States and String-Bond States can approximate chiral topological states with better accuracy.
This paper solves the normalizability crisis in sequential inference by introducing bounded information geometry.
problem Structural failure in standard sequential inference architectures when dealing with extreme outliers.
method Non-parametric field actions and bounded information geometry to truncate infinite tails of spatial distributions.
result Empirical benchmarks across three domains show robust estimation without infinite-tailed distributional assumptions.
Study uses machine learning to solve photoacoustic tomography's inverse problem.
problem Solving the full inverse problem in photoacoustic tomography.
method Developed an approach using variational autoencoders for Bayesian estimation of the posterior distribution.
result Evaluated the approach with numerical simulations and compared it to a Bayesian solution.
Score-based models improve diffuse optical tomography accuracy.
problem Improving accuracy in diffuse optical tomography with uncertainty quantification.
method Score-based diffusion models with a mixed score function to prevent overfitting.
result Data-driven prior distribution results in posterior samples with low variance and centred around the ground truth.
Meta-learning algorithms prepare quantum Gibbs states efficiently for NISQ devices.
problem Efficiently preparing quantum Gibbs states for NISQ devices.
method Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT) algorithms.
result Meta-learned parameters significantly outperform random initializations in optimization tasks.
Machine learning, specifically LSTM, models quantum experiments efficiently.
problem Modeling complex quantum states with high-dimensional entanglement.
method Used a long short-term memory (LSTM) neural network to predict quantum experiment outcomes.
result LSTM neural networks can accurately predict quantum experiment outcomes without computing the states themselves.
Quantum circuits learn to classify non-orthogonal quantum states.
problem Classifying non-orthogonal quantum states is crucial in quantum information.
method Trained quantum circuits using Adam optimization to discover parameters of unknown POVMs.
result Shallow quantum circuits can learn to discriminate among various quantum states with comparable performance to optimal POVMs.
Gradient descent recovers low-rank matrices from random rank-one measurements.
problem Recovering low-rank matrices from random rank-one measurements.
method Directly estimate the low-rank factor by minimizing a nonconvex quadratic loss function via vanilla gradient descent with tailored spectral initialization.
result The algorithm converges to the ground truth with near-optimal sample and computational complexity when the true rank is small.
Quantum datasets improve QML performance.
problem Benchmarking QML on classical datasets is uncertain.
method Introduced NTangled dataset of quantum states with varying entanglement.
result QML models trained on NTangled dataset outperform classical models.
Quantum machine learning classification depends on mutual informations between state and parameter spaces.
problem Generalization in quantum machine learning models.
method Link between quantum machine learning and quantum hypothesis testing, using mutual informations.
result Quantum classifier accuracy and generalization depend on mutual informations between state and parameter spaces.