arXiv research

Quantum machine learning models can approximate any continuous function.

Quantum neural networks can approximate noisy functions accurately.

Quantum dilogarithm function proven from a linear difference equation.

These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…

Quantum approach models economic decisions with probabilistic and dynamic probabilities.

Quantum invariants from $U_h\mathfrak{sl}(2|1)$ are q-holonomic.

Quantum circuits reveal pathways to dequantization in machine learning models.

We study quantum invariant Z(M) for cusped hyperbolic 3-manifold M. We construct this invariant based on oriented ideal triangulation of M by assigning to each tetrahedron the quantum dilogarithm function, which is introduced by Faddeev in studies of the modular double of the quantum group. Following Thurston and Neuma…

Quantum models can approximate any function if data encoding allows for a rich enough frequency spectrum.

Quantum computing offers a quadratic speedup for estimating non-linear functionals.

Quantum kernels offer potential speed-ups but require encoding problem-specific knowledge.

We discuss an approach to quantum gerbes over quantum groups in terms of q-deformation of transition functions for a loop group bundle. The case of the quantum group SUq(2) is treated in some detail.

New techniques prove quantum modularity for various functions.

Quantum algorithm speeds up Gibbs partition function estimation.

Quantum computer method for pricing rainbow options efficiently.

Quantum neural networks approximate periodic functions more efficiently.

Quantum algorithm finds extremal values without direct function access.

Quantum statistical models with singularities are studied for state estimation and model selection.

We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed quantum state. We also introduce quantum flows, the quantum analog of normalizing flow…

Quantum algorithm samples from SDEs using DQCs and quantile mechanics.

Quantum machine learning faces 'laziness' and 'barren plateaus', but noise can mitigate the latter.

In this paper, we study the Yang-Mills functional on quantum Heisenberg manifolds using the appratuses developed by A. Connes and M. Rieffel. It is discovered that a connection on a projective module over a quantum Heisenberg manifold is a minimum of Yang-Mills functional whicih is a critical point that is different wi…

Survey on quantum computing and neural networks.

Analyzes dynamics of quantum neural networks, predicting exponential decay of training error.

We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.

Quantum computers outperform classical methods in density modeling.

Quantum circuit optimization speeds up financial derivatives pricing.

We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier integral operators of a particular kind. They act on oscillatory wave functions, …

A new optimizer saves significant shots in quantum machine learning.

Quantum reservoirs risk bounds are analyzed using Rademacher complexity.

Paper proposes quantum methods for optimizing machine learning functions.

Extends quantum learning theory to multiclass and online settings.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for cla…

Quantum algorithm finds extrema in discrete optimisation problems.

In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model introduces quantum interference effects that can act as either a drag or a boost …

Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schrödinger equation for the stock price. Based on this theoretical framework, an example of a driven infinite quantum wel…

Quantum machine learning tackles large datasets with randomized measurements.

Perelman's Ricci flow emerges in quantum gravity, linking math and physics.

Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dime…

The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.

In this paper we construct the quantum group, at roots of unity, of abelian Chern-Simons theory. We then use it to model classical theta functions and the actions of the Heisenberg and modular groups on them.

This paper outlines an approach to the non-abelian theta functions of the $SU(2)$-Chern-Simons theory with the methods used by A. Weil for studying classical theta functions. First we translate in knot theoretic language classical theta functions, the action of the finite Heisenberg group, and the discrete Fourier tran…

Unified approach for quantum and classical learning from evaluation oracles.

Quantum neural tangent kernels help understand variational quantum circuits in machine learning.

Deep QMC methods use neural networks to solve quantum chemistry problems.

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 …

The study examines how quantum resources enhance the complexity of quantum circuits.

MPE framework proves universal approximation for quantum data distribution.