A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New algorithms improve MCMC efficiency for complex distributions.
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of q…
New method uses quantum computing to process classical data efficiently.
New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the standard technique for mapping the quantum spin systems to the classical ones. In this…
Characterizes optimal-speed quantum state evolution Hamiltonians.
Hamiltonian method applied to floating barrier options pricing.
Paper bridges quantum and classical mechanics for open systems.
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation tech…
Quantum computers can simulate flow models efficiently.
Quantum algorithm solves financial option pricing using Hamiltonian simulation.
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorph…
Unified geometric framework for adiabatic quantum mechanics.
Quantum computer method for pricing lookback options with jumps.
In this paper we introduce the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.
New algorithm improves efficiency of quantum system modeling.
Let M be a real 2m-torus equipped with a translation-invariant metric h and a translation-invariant symplectic form w; the latter we interpret as a magnetic field on M. The Hamiltonian flow of half the norm-squared function induced by h on T^*M (the "kinetic energy") with respect to the twisted symplectic form w_{T^*M}…
This work explores using deep NNs to learn quantum systems from probability distributions.
The paper uses a Hamiltonian method to price barrier options under Vasicek interest rate model.
Quantum propagation studied for Berezin-Toeplitz operators.
We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes the quantization of Hamiltonian -spaces to quasi-Hamiltonian…
This paper studies the question of when a loop in the group Symp of symplectomorphisms of a symplectic manifold is isotopic to a loop that is generated by a time-dependent Hamiltonian function. (Loops with this property are said to be Hamiltonian.) Our main result is that Hamiltonian loops are rigid …
The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.
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…
Method learns molecular Hamiltonian for accurate electron dynamics predictions.
New pseudo-Hermitian models from non-semisimple TQFTs.
We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Foc…
In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, firstly when volatility is taken to be a function of the forward rates…
Quantum model generates complex time series data with preserved temporal dynamics.
Improves VQAs by balancing classical and quantum training resources.
Evolutionary strategy optimizes quantum circuit design and parameters.
We study quantum moment maps of -invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a -invariant star product is differentiable. This property gives us a new method for the class…
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
Hybrid quantum algorithm tackles binary optimization problems with multiple constraints.
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of a geometric cobordism bicategory which incorporates general backgro…
Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the …
New features for quantum calculations learn N-center Hamiltonian matrix elements.
Develops Hamiltonian quantization for complex Chern-Simons theory at even level k.
In this paper, we use Floer theory to study the Hofer length functional for paths of Hamiltonian diffeomorphisms which are sufficiently short. In particular, the length minimizing properties of a short Hamiltonian path are related to the properties and number of its periodic orbits.
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
We use virtual neighborhood technique to establish GW-invariants, Quantum cohomology, equivariant GW-invariants, equivariant quantum cohomology and Floer cohomology for general symplectic manifold. We also establish GW-invariants for a family of symplectic manifolds. As a consequence, we prove Arnold conjecture for non…
Meta-learning algorithms prepare quantum Gibbs states efficiently for NISQ devices.
ECD algorithm speeds up non-convex optimization, offering quantum and stochastic enhancements.
The paper calculates quantum cohomology for coadjoint orbits and Hamiltonian groups.
Study symmetry breaking in quantum mechanics to understand many-body physics.
We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing t…
We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdière and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quan…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical" Poisson bracket and "quantum" one takes place.