Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine learning algorithms. We describe a generic mathematical model to leverage quantum…
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48 results for “quantum parallelism”
Quantum computing improves Monte Carlo option pricing for complex derivatives.
problem Complex financial derivatives require extensive computations in high-dimensional spaces.
method Developed a quantum algorithm for simulating many potential asset paths in parallel.
result Quantum algorithm provides highly accurate option pricing and risk analysis.
TQFTs and quantum computingquant-ph
Program connects quantum computing and topological field theories.
problem Connecting quantum computing and topological field theories.
method Formalizes the connection using cobordisms and parallel transport.
result Realizes quantum circuits as cobordisms in a double category.
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges. A principal opportunity is that a large number of computations can be carried ou…
Quantum connections replace metrics with operator inner products.
problem Quantifying geometric properties in quantum systems.
method Defining quantum connections and duals using operator fields and inner products.
result Holonomy and dual connections are equivalent in quantum geometry.
We explain how the kind of ``parallel transport'' of a wavefunction used in discussing the Berry or Geometrical phase induces the conventional parallel transport of certain real vectors. These real vectors are associated with operators whose commutators yield diagonal operators; or in Lie algebras those operators whose…
Study of bound states in quantum layers with confining potentials.
problem Investigating bound states in quantum layers with confining potentials.
method Developed a general approach using parallel coordinates based on the surface but outside its cut locus.
result Discrete eigenvalues exist for certain quantum layers with positive total Gauss curvature.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…
Quantum variational circuits improve reinforcement learning efficiency.
problem Improving reinforcement learning algorithms using quantum computing.
method Investigation of quantum variational circuits for DQN and Double DQN, encoding classical data for quantum circuits.
result Quantum variational circuits can solve reinforcement learning tasks with a smaller parameter space.
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 …
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is studied as an example of bundle-like objects with discordant (sogo) transition functi…
New method combines QQA and gradient-based sampling for combinatorial optimization.
problem Scalability challenges in learning-based solvers for combinatorial optimization.
method Integrates gradient-based update through continuous relaxation with Quasi-Quantum Annealing (QQA) and parallel communication.
result Achieves superior speed-quality trade-offs for large-scale instances.
Unified framework for robust causal directionality in quantum systems under MNAR observation.
problem Determining causal directionality in quantum systems under MNAR observation.
method Integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization.
result Achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics.
TQFT's and gerbesmath.DG
We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a one-to-one correspondence between their local des…
We give a direct proof for the asymptotic faithfulness of the quantum representations of the mapping class groups using peak sections in Kodaira embedding. We give also estimates on the norm of the parallell transport of the projective connection on the Verlinde bundle. The faithfulness has been proved earlier …
Quantum models face barren plateaus, but specific losses can be trainable.
problem Barren plateaus and loss concentration in quantum generative models.
method Investigated explicit and implicit losses, and their interplay.
result Explicit losses lead to new barren plateaus, while implicit losses can be trainable.
Quantum probability theory reveals hidden structure in joint probability distributions.
problem Understanding hidden structure in joint probability distributions.
method Modeling joint probability distributions as density operators and applying partial trace.
result Decoding extra information in reduced density operators that captures subsystem interactions.
Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.
problem Computing heat kernel traces for Ricci flat manifolds.
method Quantum stochastic differential equation (qsde) on Fock space over differential 1-forms, adapted flow construction.
result Trace of the connection Laplacian heat kernel can be computed over any compact Ricci-flat Riemannian manifold.
We give parallel constructions of an invariant R(W,f), based on the classical Rogers dilogarithm, and of quantum hyperbolic invariants (QHI), based on the Faddeev-Kashaev quantum dilogarithms, for flat PSL(2,C)-bundles f over closed oriented 3-manifolds W. All these invariants are explicitely computed as a sum or state…
Quantum algorithms accelerate financial risk computation.
problem Accelerating the computation of financial market risk.
method Quantum gradient estimation algorithms for market sensitivities.
result Significant reduction in resource requirements for financial quantum advantage.
Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learningquant-ph
Quantum circuits explained using Shapley values for better understanding.
problem Improving the explainability of quantum machine learning circuits.
method Applying Shapley values to quantify gate importance in quantum circuits.
result Quantum circuits can be explained by their gate importance, enhancing understanding and interpretability.
Quantum computing poses a threat to Bitcoin and Ethereum, but only to spending and not mining.
problem Quantum computing threat to Bitcoin and Ethereum
method Separation of Shor's and Grover's quantum algorithms
result Quantum algorithms' impact on Bitcoin and Ethereum
Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a first order transversally elliptic operator with the (classical) evolution of it…
New smooth 2-group extensions from bundle gerbes on manifolds.
problem Classifying equivariant structures on bundle gerbes.
method Global approach to parallel transport, homotopy-coherent associated bundle construction.
result New models for the string group of compact simply-connected Lie groups.
Quantum cocycle invariants derived from Yang-Baxter cohomology.
problem Constructing stronger quantum knot invariants.
method Developing quantum cocycle invariants using Yang-Baxter cohomology and deformation theory.
result Quantum cocycle invariants yield stronger invariants in certain examples.
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant and Souriau. We express the associated evolution operators via paral…
A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking into account only the crossing of stocks and fixing a convention defining overcros…
We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previ…
Quantum speedup for Monte Carlo integration reduces integrand calls.
problem Reducing the number of calls to the integrand subroutine in high-dimensional Monte Carlo integration.
method Combining nested quantum amplitude estimation with pseudorandom numbers for separable integrands.
result Significant reduction in the number of integrand calls for high-dimensional integration.
Quantum Annealing for Dirichlet Process Mixture Models with Applications to Network Clusteringcond-mat.dis-nn
We developed a new quantum annealing (QA) algorithm for Dirichlet process mixture (DPM) models based on the Chinese restaurant process (CRP). QA is a parallelized extension of simulated annealing (SA), i.e., it is a parallel stochastic optimization technique. Existing approaches [Kurihara et al. UAI2009, Sato et al. UA…
Quantum annealing improves VB inference, avoiding local minima.
problem Variational Bayes inference stuck in local minima.
method Quantum annealing approach to VB inference.
result Quantum annealing variational Bayes (QAVB) outperforms classical VB.
The colored Jones function of a knot is a sequence of Laurent polynomials that encodes the Jones polynomial of a knot and its parallels. It has been understood in terms of representations of quantum groups and Witten gave an intrinsic quantum field theory interpretation of the colored Jones function as the expectation …
Paper studies non-associativity in quantum systems with magnetic fields.
problem Non-associativity of magnetic translations in quantum systems.
method Quantum field theory approach with -component fermions.
result Non-associativity described by a 3-cocycle of with values in .
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geomet…
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.
We consider the Dirichlet Laplacian in tubular neighbourhoods of complete non-compact Riemannian manifolds immersed in the Euclidean space. We show that the essential spectrum coincides with the spectrum of a planar tube provided that the second fundamental form of the manifold vanishes at infinity and the transport of…
In this paper, we will provide a review of the geometric construction, proposed by Witten, of the SU(n) quantum representations of the mapping class groups which are part of the Reshetikhin-Turaev TQFT for the quantum group U_q(sl(n, C)). In particular, we recall the differential geometric construction of Hitchin's pro…
Jeffreys Flow improves robustness of Boltzmann generators for rare event sampling.
problem Rare events and metastable trapping in sampling physical systems with rough energy landscapes.
method Introduces Jeffreys Flow, a robust generative framework using Parallel Tempering distillation and symmetric Jeffreys divergence to mitigate mode collapse and improve mode coverage.
result Minimizing Jeffreys divergence suppresses mode collapse and corrects inaccuracies in multi-modal distributions.
Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observablesmath.DG
We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel tran…
In this paper we study global properties of the Wigner caustic of parameterized closed planar curves. We find new results on its geometry and singular points. In particular, we consider the Wigner caustic of rosettes, i.e. regular closed parameterized curves with non-vanishing curvature. We present a decomposition of a…
A natural one-parameter family of Kähler quantizations of the cotangent bundle of a compact Lie group , taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the…
The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian converges in a norm-resolvent sense to a Schroedinger operator on the limit…
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…
A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group , we introduce a notion of a modular crossed -category and show that such a category gives rise to a 3-dimensional HQFT with target sp…
Paper proves zero stability for one-row colored sl₃-Jones polynomials.
problem Stability of coefficients in colored Jones polynomials.
method Linear skein theory based on Kuperberg's sl₃-webs.
result Zero stability for B-adequate links with anti-parallel twist regions.
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the spaces of holomorphic sections of a prequantizing line bundle over compact Kähler manifolds under deformations of the complex structure. We show that the parallel transport in the induced vector bundle over the deformation space behaves li…
New fault-tolerant quantum gates for homological LDPC codes with constant or almost-constant rate.
problem Fault-tolerant quantum computing for homological LDPC codes with constant or almost-constant encoding rate.
method Derive generic formula for transversal and logical gates acting on 3-manifolds, using higher symmetries and cup product cohomology.
result Parallelizable logical gates for homological LDPC codes with constant or almost-constant rate.
Study of panhandle polynomials of torus links with geometric applications.
problem Characterizing the HOMFLY-PT polynomial of torus knots and links.
method Utilizing quantum group representations and the Rosso-Jones formula.
result Established panhandle-like structure of HOMFLY-PT polynomials for torus knots and links.