Related papers: Hamiltonian Locality Testing via Trotterized Posts…
In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz-Thompson empirical process arising from complex sampling designs. Global theorems such as Glivenko-Cantelli and Donsker…
Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…
Commuting local Hamiltonians provide a testing ground for studying many of the most interesting open questions in quantum information theory, including the quantum PCP conjecture and the existence of area laws. Although they are a…
Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
We study a class of time-dependent (TD) non-Hermitian Hamiltonians $H(t)$ that can be transformed into a time-independent pseudo-Hermitian Hamiltonian $\mathcal{H}_{0}^{PH}$ using a suitable TD unitary transformation $F(t)$. The latter can…
Finding a cycle of lowest weight that represents a homology class in a simplicial complex is known as homology localization (HL). Here we address this NP-complete problem using parameterized complexity theory. We show that it is W[1]-hard…
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest…
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the…
Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…
The applicability of the optical theorem in the models with the non-Hermitian Hamiltonian is studied. By way of example we consider the $n\bar{n}$ transition in a medium followed by annihilation. It is shown that an application of optical…
We consider in a Hilbert space a self-adjoint operator H and a family Phi=(Phi_1,...,Phi_d) of mutually commuting self-adjoint operators. Under some regularity properties of H with respect to Phi, we propose two new formulae for a time…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
We study monotonicity testing of functions $f \colon \{0,1\}^d \to \{0,1\}$ using sample-based algorithms, which are only allowed to observe the value of $f$ on points drawn independently from the uniform distribution. A classic result by…
We prove a tight lower bound for the exponent $\rho$ for data-dependent Locality-Sensitive Hashing schemes, recently used to design efficient solutions for the $c$-approximate nearest neighbor search. In particular, our lower bound matches…
We establish local boundedness and local H\"older continuity of weak solutions to the following prototype problem: $$ -\operatorname{div}\left(|x|^{-2 \beta}|\nabla u|^{\mathbf{q}-2} \nabla u\right)+(-\Delta)_{p(\cdot, \cdot),…
A locally threshold testable language L is a language with the property that for some non negative integers k and l and for some word u from L, a word v belongs to L if and only if (1) the prefixes [suffixes] of length k-1 of words u and v…
Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be…