相关论文: The Complexity of Stoquastic Local Hamiltonian Pro…

The quantum k-Local Hamiltonian problem is a natural generalization of classical constraint satisfaction problems (k-CSP) and is complete for QMA, a quantum analog of NP. Although the complexity of k-Local Hamiltonian problems has been well…

The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behavior of various problems at the forefront of physics. Focusing on an important sub-class of such problems, bosonic $(2+1)$-dimensional…

We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…

This work extends weak KAM theory to the case of a nonsmooth Lagrangian satisfying a superlinear growth condition. Using the solution of a weak KAM equation that is a stationary Hamilton-Jacobi equation and the proximal aiming method, we…

The problem of estimating the spectral gap of a local Hamiltonian is known to be contained in the class $P^{QMA[log]}$: polynomial time with access to a logarithmic number of QMA queries. The problem was shown to be hard for…

Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…

We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and…

A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…

Solutions of the Hamilton-Jacobi equation $H(x,-Du(x))=1$, with $H(\cdot,p)$ H\"older continuous and $H(x,\cdot)$ convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential…

The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…

$\mathsf{StoqMA}$ captures the computational hardness of approximating the ground energy of local Hamiltonians that do not suffer the so-called sign problem. We provide a novel connection between $\mathsf{StoqMA}$ and distribution testing…

This paper is concerned with the computational complexity of learning the Hidden Markov Model (HMM). Although HMMs are some of the most widely used tools in sequential and time series modeling, they are cryptographically hard to learn in…

In this work, we give a polynomial-time quantum algorithm for solving the ground states of a class of classically hard Hamiltonians. The mechanism of the exponential speedup that appeared in our algorithm comes from dissipation in open…

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of…

Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC…

The stochastic partial differential equation analyzed in this work is the Cahn-Hilliard equation perturbed by an additive fractional white noise (fractional in time and white in space). We work in the case of one spatial dimension and apply…

The negativity Hamiltonian, defined as the logarithm of a partially transposed density matrix, provides an operatorial characterisation of mixed-state entanglement. However, so far, it has only been studied for the mixed-state density…

Although the post-Newtonian Lagrangian formalism is widely used in relativistic dynamical and statistical studies of test bodies moving around arbitrary mass distributions, the corresponding general Hamiltonian formalism is still relatively…

We consider a stochastic boundary value elliptic problem on a bounded domain $D\subset \mathbb{R}^k$, driven by a fractional Brownian field with Hurst parameter $H=(H_1,...,H_k)\in[{1/2},1[^k$. First we define the stochastic convolution…

Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…