MPE framework proves universal approximation for quantum data distribution.
problem Challenges in generating quantum data from underlying distributions.
method Many-body Projected Ensemble (MPE) framework for quantum state design.
result MPE can approximate any quantum distribution within 1-Wasserstein distance error.
Quantum neural networks can approximate noisy functions accurately.
problem Approximating noisy functions with quantum neural networks.
method Universal approximation theorem with error bounds for noisy quantum neural networks.
result Quantum neural networks can approximate noisy functions with precise error bounds.
Simple construction for universal quantum gates.
problem Designing efficient quantum gates for topological computers.
method Demonstrated a simple construction for unitary solutions of the braided Yang-Baxter equation in any dimension.
result Proved the existence of universal quantum gates in any dimension.
Quantum kernels can be efficiently embedded into classical feature spaces.
problem Can all quantum kernels be efficiently embedded into classical feature spaces?
method Invoking computational universality and using techniques like random Fourier features, the authors show that certain classes of quantum kernels can be efficiently embedded.
result For shift-invariant and composition kernels, embedding quantum kernels are universal and efficient.
Quantum machine learning models can approximate any continuous function.
problem Theoretical understanding of quantum feature maps in machine learning.
method Proving universal approximation property of quantum machine learning models in quantum-enhanced feature spaces.
result Quantum machine learning models are universal approximators of continuous functions.
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.
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal R-matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that c…
New quantum knot invariants derived from Verma modules.
problem Constructing universal quantum knot invariants from Verma modules.
method Defining level N universal invariants from finite quotients of Verma modules over quotient rings.
result Maximal universal invariants for prime N, interpolating Jones and ADO polynomials.
New basis for quantum gl_N invariants derived from Macdonald polynomials.
problem Constructing new bases for quantum gl_N invariants.
method Using interpolation Macdonald polynomials and Okounkov's results.
result Cyclotomic expansions for gl_N invariants and knot invariants.
We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth ro…
We derive the quantum Teichmüller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the decomposition of the tensor square, the quantum…
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
problem Classifying homogeneous metrics on group manifolds by long-distance properties.
method Apply universality concept to geometry, focusing on metrics on Lie groups.
result Many metrics on low-dimensional Lie groups have similar long-distance properties despite differing short-distance properties.
In this work, the Z3-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algeb…
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 shows limitations and universality of equivariant QNNs with Sn-equivariant gates.
problem Understanding the expressiveness of Sn-equivariant QNNs with k-body gates. method Investigated the interplay between symmetry and k-bodyness in Sn-equivariant QNN generators. result QNNs are semi-universal but not universal with one- and two-body Sn-equivariant gates. Quantum optimization aids in financial crash prediction and portfolio management.
problem Hard financial optimization problems.
method Quantum algorithms for financial crashes and portfolio optimization.
result Quantum strategies improve financial prediction and portfolio management.
Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by …
Quantum kernels show no advantage in stock return prediction, but differ in stability metrics.
problem Determining if quantum kernels improve stock return prediction.
method Controlled horse race on Chinese A-share market with identical training subsamples and tuning budgets.
result Quantum kernels do not outperform classical RBF controls in cross-sectional stock return prediction.
New non-semisimple Ising anyons enable robust universal quantum computation.
problem Limitation of semisimple theories in universal topological quantum computation.
method Developed non-semisimple Ising anyon model with new anyon types indexed by α. result Robust universality of braiding persists over an open interval of α. Quantum models can approximate any function if data encoding allows for a rich enough frequency spectrum.
problem Theoretical properties of quantum machine learning models, particularly their expressive power.
method Investigated how data encoding affects the expressive power of parametrized quantum circuits.
result Quantum models can access increasingly rich frequency spectra by repeating data encoding gates, potentially making them universal function approximators.
The paper shows instability in Minkowski spacetime for a quantum system.
problem Linear instability of the semiclassical Einstein-Klein-Gordon system in Minkowski spacetime.
method Formulated a forcing problem for metric and state perturbations, used tensor decomposition and quantum Møller operator.
result Metric perturbations grow exponentially, bounded by a universal scale H, indicating quantum backreaction.
Quantum algorithm speeds up MIP solving by a near-quadratic factor.
problem Solving Mixed Integer Programs (MIPs) efficiently.
method Incremental-Quantum-Branch-and-Bound algorithm combining quantum speedup with classical search heuristics.
result Universal near-quadratic speedup over classical Branch-and-Bound algorithms.
We show that the perturbative g invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra g, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate …
A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S3. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-value…
New model suggests universe emerges from single particle quantum mechanics.
problem Exploring how the universe might arise from a single particle in quantum mechanics.
method Novel spontaneous symmetry breaking acting on probability distributions of Hamiltonians.
result Evidence supports the hypothesis that nature seeks tensor decompositions.
New approach to quantum knot invariants using perturbed Gaussian generating functions.
problem Developing universal quantum knot invariants.
method Introducing generating functions of the form PeG where G is quadratic and P is a perturbation, and developing a calculus for such functions. result The rank one invariant ZD dominates sl2-colored Jones polynomials and relates to knot genus and Whitehead doubling. Develops quantum circuits for faster learning with symmetry considerations.
problem Speeding up learning quantum states with symmetry considerations.
method Utilizes Okounkov-Vershik approach and Young-Jucys-Murphy elements to develop Sn-equivariant convolutional quantum circuits. result Proves Sn-CQA generates any unitary in any given Sn irrep sector, universal for SU(d) symmetry. Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
Quantum machine learning model for binary classification.
problem Efficiency in high-dimensional binary classification tasks.
method Quantum-classical hybrid algorithm and quantum computer for inference.
result Quantum discriminator achieves 99% accuracy on Iris dataset.
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in p…
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…
A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrari…
We construct a cohomology theory for oriented links using singular cobordisms and a special type of 2-dimensional Topological Quantum Field Theory (TQFT), categorifying the quantum sl(2) invariant. In particular, we give a description of the universal dot-free sl(2) foam cohomology for links via a TQFT.
Quantum polynomials are derived from a specific tribracket structure.
problem Quantum enhancement polynomials for oriented links.
method Defined using a canonical two-element tribracket, proving polynomials can be derived from five specific ones.
result Universal quantum enhancement polynomials are strictly stronger than the Jones polynomial.
This text explains how fiber bundle structure is fundamental for classical physics.
problem None explicitly stated, but implied as understanding fiber bundles is crucial for physics.
method Explains the fiber bundle structure and its universality for physics laws.
result Fiber bundle structure is fundamental for classical physics laws.
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which accommodates the KdV equation and other well known integrable systems. In the case of qua…
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
problem Understanding the underlying mechanism of distribution formation in complex quantum entanglement.
method Exploring the logical relationship between Schrödinger's wave equation and Shi's trading volume-price wave equation in finance.
result A non-localized wave equation in quantum mechanics reveals the invariance of interaction as a universal law.
Quantum theory constructs a group and skein module for knot complements.
problem Understanding the fundamental group of knot complements using quantum methods.
method Using bottom tangles, the universal space of quantum representations is constructed, then factored by the skein relation to get the skein module.
result Derives recurrence relation for the colored Jones polynomial, known as Aq polynomial. We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime, the existence, the signature and a specific form of a metric on it, and certain na…
Investigates quantum vs classical portfolio optimization of 60 stocks.
problem Optimizing risk vs return portfolios of 60 stocks using quantum and classical methods.
method Classical and quantum annealing approaches applied to historical data.
result Quantum and classical methods yield similar optimal portfolios.
Develops a new geometric framework for quantum metrics.
problem Quantum metric generalization for pure two-qubit states.
method Support-projected Petz monotone geometry for pure two-qubit families.
result Strictly generalizes SLD/Bures case and includes other metrics.
The paper defines cyclic sets from ribbon string links and connects them to quantum invariants.
problem Defining and relating cyclic sets from ribbon string links.
method Endowing ribbon string links with cyclic and cocyclic structures, relating to coend of a ribbon category via quantum invariants.
result Established a relationship between ribbon string links and quantum invariants.
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 quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the…
Algorithm designs neural group actions for symmetric transformations.
problem Designing neural networks for symmetric transformations.
method Develops Neural Group Actions (NGAs) for finite groups, enforcing volume-preserving constraints.
result Demonstrates NGAs for the quaternion group Q8 can learn quantum gate transformations. The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry''. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohom…
New universal automorphic functions capture monstrous moonshine.
problem Developing a universal framework for automorphic functions.
method Reformulating old results, constructing new coordinates, and defining central extensions.
result New invariant 1-forms and representations for universal Teichmüller space.
Quantum isometry groups extend to all countable metric spaces, and loose embeddings help understand metric space relationships.
problem Understanding the quantum isometry groups of all countable metric spaces.
method Defining and studying loose embeddability, showing that 0-dimensional compact metric spaces are generically loosely embeddable into the real line.
result 0-dimensional compact metric spaces are generically loosely embeddable into the real line.