相关论文: Constructing Fermionic Hamiltonians with Non-Gauss…

QMA and QCMA are possible quantum analogues of the complexity class NP. In QCMA the verifier is a quantum program and the proof is classical. In contrast, in QMA the proof is also a quantum state. We show that two known QMA-complete…

The pairing interaction is one of the most important contribution of the residual interaction and then, it is of major importance for the study of many-body systems. One can get solutions of the pairing Hamiltonian throught the…

We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample…

In this letter we investigate a class of Hamiltonians which, in addition to the usual center-of-mass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy…

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin…

We identify the the ground-state of a truncated version of Haldane's pseudo-potential Hamiltonian in a thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice…

A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…

The relative entropy between two states is a key concept in quantum information theory and quantum field theory. In the setting of quantum field theory, its computation requires the handling of relative modular Hamiltonians, which are…

A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in closed form. An entirely new class of QES Hamiltonians having sextic polynomial…

We provide a completely self-contained construction of a family of NLTS Hamiltonians [Freedman and Hastings, 2014] based on ideas from [Anshu, Breuckmann, and Nirkhe, 2022], [Cross, He, Natarajan, Szegedy, and Zhu, 2022] and [Eldar and…

The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…

Conformal field theory has recently been applied to derive few-body Hamiltonians whose ground states are lattice versions of fractional quantum Hall states. The exact lattice models involve interactions over long distances, which is…

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…

Some theorems on derivatives of the Coulomb density functional with respect to the coupling constant $\lambda$ are given. Consider an electron density $n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the reduced…

A novel hierarchy of fractional quantum Hall (FQH) states in the lowest Landau level (LL) is proposed to explain recently observed FQH fractions such as nu=5/13, 3/8, or 4/11. Based on the analysis of their interaction pseudopotentials, it…

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high…

It is shown that four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock (HF) equations can be implemented in an unified manner, by making use of the atomic nature of the small components of…

The quantum analogue of a constraint satisfaction problem is a sum of local Hamiltonians - each local Hamiltonian specifies a local constraint whose violation contributes to the energy of the given quantum state. Formalizing the intuitive…

We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…