Related papers: Optimal Hamiltonian for a quantum state with finit…
The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian. First, we show the existence of a good product-state approximation for the ground-state energy of…
Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy…
We present exact results for the periodic Anderson model for finite Hubbard interaction 0 <= U < +infinity on certain restricted domains of the model's phase diagram, in d=1 dimension. Decomposing the Hamiltonian into positive semidefinite…
Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…
The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE…
We study the problem of learning a Hamiltonian $H$ to precision $\varepsilon$, supposing we are given copies of its Gibbs state $\rho=\exp(-\beta H)/\operatorname{Tr}(\exp(-\beta H))$ at a known inverse temperature $\beta$. Anshu,…
In this paper, we find the necessary and sufficient condition for the maximal entanglement of the state, $ |\psi>=\mu|\alpha>|\beta>+\lambda|\alpha>|\delta>+ \rho|\gamma>|\beta>+\nu|\gamma>|\delta>,$ constructed by linearly independent…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detail…
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy, and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies.…
In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure…
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the…
We consider a system of a quantum particle interacting with a quantum field and an external potential $V(\bx)$. The Hamiltonian is defined by a quadratic form $H^V = H^0 + V(\bx)$, where $H^0$ is a quadratic form which preserves the total…
We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest…
Understanding the entanglement structure of local Hamiltonian ground spaces is a physically motivated problem, with applications ranging from tensor network design to quantum error-correcting codes. To this end, we study the complexity of…
We observe that the many-body eigenstates of any quadratic, fermionic Hamiltonian with sublattice symmetry have quantized entanglement entropies between the sublattices: the entanglement comes in multiple singlets. Moreover, such systems…
We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using…
We study the simple Hamiltonian, $H=-K(S_{1z}^2 +S_{2z}^2)+ \lambda\vec S_1\cdot\vec S_2$, of two, large, coupled spins which are taken equal, each of total spin $s$ with $\lambda$ the exchange coupling constant. The exact ground state of…
Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N)…
We analyze the possibility of modifying the original Farhi-Gutmann Hamiltonian algorithm in order to speed up the procedure for producing a suitably distributed unknown normalized quantum mechanical state. Such a modification is feasible…