Khovanov homology helps create quantum error-correcting codes.
problem Creating robust quantum error-correcting codes.
method Using Khovanov homology and its extensions to define and analyze quantum codes.
result New families of quantum codes with desirable properties.
Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.
problem Improving quantum error correction performance with hyperbolic lattices.
method Unified framework using Hyperbolic Cycle Basis algorithm for CSS codes construction and benchmarking.
result Achieved higher encoding rates and lower qubit overhead in hyperbolic quantum error correction codes.
Generative AI decodes quantum codes without labeled data.
problem Efficient decoding of quantum error-correcting codes.
method Generative Transformers learn logical operators from unsupervised syndromes.
result Significantly better decoding accuracy than traditional methods.
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance nε. Their rate is evaluated via Euler characteristic arguments and their distance using Z2-systolic geometry. This construction answers …
We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in other kinds of quantum error-correcting codes. In particular, we use fibre bundles …
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liqu…
Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep neural decoders and apply them to analyze several fault-tolerant error correctio…
Quantum machine learning generalizes well from limited data.
problem Generalization in quantum machine learning from few training data.
method Optimizing parameterized quantum circuits on training data sets and analyzing generalization error.
result Generalization error scales at worst as √(T/N) and improves to √(K/N) when only K gates change.
Quantum codes linked to abelian varieties, providing mathematical rigor.
problem Quantum error correction through complex abelian varieties.
method Mathematical formulation of Gottesman-Kitaev-Preskill codes using abelian varieties.
result Asymptotic isometry of encoding, precise gate realizations, and failure probability optimization.
Lossy compression of statistical data using quantum annealing.
problem Efficiently compressing statistical floating-point data.
method Representation learning with binary variables, classical optimization of basis vectors, quantum annealing for coefficients, bias correction.
result Quantum annealing shows promising results with 3.5x better compression than neural-network autoencoders.
We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.
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.
Noise-resilient optimization on noisy quantum computers.
problem Noise's impact on hybrid quantum-classical optimization.
method Iterative quantum circuit with noise consideration, using Quantum Fisher Information bound.
result Algorithm robustness against different noise strengths.
Quantum reservoir computing tackles noisy quantum computers for temporal tasks.
problem Efficiently process input sequences on noisy quantum computers.
method Quantum reservoir computing using dissipative quantum dynamics.
result Small and noisy quantum reservoirs can handle high-order nonlinear temporal tasks.
Study on topological order on fractal geometries, proving no-go theorem and fault-tolerant gates.
problem Investigating topological order on fractal geometries embedded in n dimensions.
method Using quantum error-correcting codes and systolic geometry to diagnose topological order.
result Proves no-go theorem for topological order on 2D fractals, survival on higher dimensions, and construction of fault-tolerant gates.
The paper develops methods to assess and correct model uncertainties in graphical models.
problem Model uncertainty in probabilistic graphical models.
method Information-theoretic and non-parametric stress tests.
result Ranking and correcting impactful sources of uncertainty in graphical models.
We define the quantum correction of the Teichmüller space T of Calabi-Yau manifolds. Under the assumption of no weak quantum correction, we prove that the Teichmüller space T is a locally symmetric space with the Weil-Petersson metric. For Calabi-Yau threefolds, we show that no strong quantum co…
Post-Quantum Secure Federated DeFi for Inclusive Banking
problem Financial systems and DeFi ecosystems are vulnerable to quantum computing threats.
method Post-Quantum Secure Federated DeFi framework using lattice-based FHE.
result End-to-end homomorphic computation enables inter-bank collaboration.
QTAML models quantum tunneling errors for AI robustness.
problem Quantum tunneling errors in AI inference.
method Derives weight-error distribution using WKB approximation, introduces TAC algorithm.
result TAC achieves 95% clean accuracy with 3.4-33.6x less ECC overhead.
Given the Lagrangian fibration T4→T2 and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study, in the context of mirror symmetry, the ``quantum'' corrections necessary to solve the monodromy of the holomorphic structure of the mirror bundle on the dual fibration.
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion in various fields such as the financial market and the low-ra…
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n>p) and stabilizer constraints with faces of dimension (p±1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into $N = 2^…
Quantum field theory connects deep neural networks to criticality.
problem Understanding the criticality and training dynamics of deep neural networks.
method Constructing quantum field theory for deep neural networks, computing corrections to correlation functions.
result Found precise analogy with O(N) vector model, providing corrections to correlation length. A model corrects Lithuanian grammatical errors.
problem Lack of language skills and typing errors in Lithuanian.
method Transformer architectures for subword and byte-level approaches.
result F0.5=0.92 for Lithuanian grammatical error correction. The study examines methods to correct measurement error in nutritional epidemiology studies.
problem Measurement error in nutritional studies leads to biased and underconfident estimates.
method The article reviews various bias-correction models for exposure variables in nutritional epidemiology.
result Bias-correction methods are essential for accurate inference in nutritional studies.
Paper presents a new VMBQC model with fewer parameters for better generative modeling.
problem Limited generative power of VMBQC due to more parameters than unitary models.
method Introduces a restricted VMBQC model with a single additional trainable parameter.
result Minimal extension of VMBQC model generates distributions not learnable by unitary models.
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.
Study loop corrections in random feature models affecting training and test errors.
problem Analyzing loop corrections in random feature models to understand training and test errors.
method Statistical physics and effective field theory approach to study loop corrections.
result Derived loop corrections to training error, test error, and generalization gap.
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.
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.
In this paper, we study the quantum sl(n) representation category using the web space. Specially, we extend sl(n) web space for n≥4 as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial Pn(q) specialized to a one variable polynomial …
We show that using the family of adapted Kähler polarizations of the phase space of a compact, simply connected, Riemannian symmetric space of rank-1, the obtained field Hcorr of quantum Hilbert spaces produced by geometric quantization including the half-form correction is flat if M is the 3-dimensional sphere …
Correction for Error estimates for binomial approximations of game options [math.PR/0607123]
Fault-tolerant neural networks inspired by biological error correction codes.
problem Achieving reliable computation with unreliable neurons.
method Using biological error correction codes from grid cells in the mammalian cortex to develop a fault-tolerant neural network.
result Noisy biological neurons operate below a fault-tolerance threshold, suggesting a mechanism for reliable computation in the brain.
Quantum Kerr learning shows enhancements in convergence and generalization for kernel-based methods.
problem Improving convergence and generalization in kernel-based methods for quantum computing.
method Combining quantum mechanics with neural tangent kernel theory and first-order perturbation theory.
result Quantum enhancements in terms of convergence time and generalization error.
SCaSML improves PDE solvers by correcting errors efficiently.
problem Reliable and error-free high-dimensional PDE solutions.
method Defect correction method to derive a Structural-preserving Law of Defect.
result SCaSML achieves faster convergence and reduced errors in high-dimensional PDEs.
Given, in the Lagrangian torus fibration R4→R2, a Lagrangian submanifold L, endowed with a trivial flat connection, the corresponding mirror object is constructed on the dual fibration by means of a family of Morse homologies associated to the generating function of L, and it is provided with a holomorphic s…
Proposes a model combining difference-attention and error-correction LSTMs for improved time series prediction.
problem Improving accuracy in time series prediction.
method Combines difference-attention LSTM and error-correction LSTM in a cascade approach.
result Improves prediction accuracy in time series.
Quantum neural tangent kernels help understand variational quantum circuits in machine learning.
problem Designing and predicting performance of variational quantum circuits.
method Using quantum neural tangent kernels and dynamical equations for loss functions.
result Analytical solutions for training dynamics in variational quantum circuits.
The study examines how quantum resources enhance the complexity of quantum circuits.
problem Quantum resource enhancement on circuit complexity.
method Utilizing quantum resource theories, the study analyzes statistical complexities of quantum circuits with limited quantum resources.
result Bounds for statistical complexities of quantum circuits are derived and applied to specific cases.
Quantum algorithms improve perceptron learning efficiency.
problem Improving quantum algorithms for perceptron learning.
method Revisiting and correcting a flawed quantum version space perceptron algorithm, proposing quantum-enhanced cutting-plane algorithms.
result Improved complexity bounds for quantum perceptron learning.
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problem…
Renormalization in neural networks linked to quantum field theory.
problem Implementing renormalization in neural networks.
method Mapping neural networks to quantum field theory, applying renormalization techniques.
result Changing weight standard deviation corresponds to a renormalization flow.
New method combines machine learning with data assimilation for model error correction.
problem Correcting model errors using sparse and noisy observations.
method Hybrid machine learning and data assimilation methods.
result Tendency correction outperforms resolvent correction in data assimilation experiments.
String geometry theory uniquely determines classical action with T-symmetry.
problem Non-renormalizability and loop corrections in string theory.
method Distinguishes effects of β and ħ parameters, proving no loop corrections.
result No loop corrections in string geometry theory, avoiding non-renormalizability.
Autonomy and adaptation of machines requires that they be able to measure their own errors. We consider the advantages and limitations of such an approach when a machine has to measure the error in a regression task. How can a machine measure the error of regression sub-components when it does not have the ground truth…
Quantum-enhanced method improves stock return prediction accuracy.
problem Improving precision of stock return forecasting.
method Quantum Gramian Angular Field (QGAF) combining quantum computing and CNNs.
result Significantly improved prediction accuracy (25% MAE, 48% MSE reduction).
We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.