相关论文: Hamiltonian Purification
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…
A given Hamiltonian matrix H with real spectrum is assumed tridiagonal and non-Hermitian. Its possible Hermitizations via an amended, ad hoc inner-product metric are studied. Under certain reasonable assumptions, all of these metrics are…
We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
We consider quantum Hamiltonians of the form $H = H_0 - U \sum_j \cos(C_j)$ where $H_0$ is a quadratic function of position and momentum variables $\{x_1, p_1, x_2, p_2,...\}$ and the $C_j$'s are linear in these variables. We allow $H_0$…
Solvability of the rational quantum integrable systems related to exceptional root spaces $G_2, F_4$ is re-examined and for $E_{6,7,8}$ is established in the framework of a unified approach. It is shown the Hamiltonians take algebraic form…
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few…
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential…
Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
We propose a simple idea to construct 1D integrable models with impurities. We illustrate the strategy for a supersymmetric $t-J$ Hamiltonian in considerable detail. The impurity comprises the local deformation of the hopping and exchange…
We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the…
Non-Hermitian but P(phi)T(phi)-symmetrized spherically-separable Dirac and Schrodinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H(r), H(theta), and H(phi) play essential roles and offer some…
Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
Density matrix embedding theory (Phys. Rev. Lett. 109, 186404 (2012)) and density embedding theory ((Phys. Rev. B 89, 035140 (2014)) have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work,…
Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…
We study a deformation of the counterdiabatic-driving Hamiltonian as a systematic strategy for an adiabatic control of quantum states. Using a unitary transformation, we design a convenient form of the driver Hamiltonian. We apply the…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
First order Hamiltonian operators of differential-geometric type were introduced by Dubrovin and Novikov in 1983, and thoroughly investigated by Mokhov. In 2D, they are generated by a pair of compatible flat metrics $g$ and $\tilde g$ which…