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Related papers: Solving Gapped Hamiltonians Locally

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Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…

Quantum Physics · Physics 2020-12-16 Lin Lin , Yu Tong

Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be…

Quantum Physics · Physics 2013-05-29 Xie Chen , Bei Zeng , Zhengcheng Gu , Beni Yoshida , Isaac L. Chuang

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…

Quantum Physics · Physics 2023-01-12 Karen J. Morenz Korol , Kenny Choo , Antonio Mezzacapo

A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the…

Quantum Physics · Physics 2023-08-14 P. Jouzdani , S. Bringuier , M. Kostuk

Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from…

Strongly Correlated Electrons · Physics 2026-05-28 Denise Cocchiarella , Mingru Yang , Yueshui Zhang , Mari Carmen Bañuls , Hong-Hao Tu , Yuhan Liu

We prove that ground states of gapped local Hamiltonians on an infinite spin chain can be efficiently approximated by matrix product states with a bond dimension which scales as D~(L-1)/epsilon, where any local quantity on L consecutive…

Strongly Correlated Electrons · Physics 2017-11-27 Norbert Schuch , Frank Verstraete

The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area…

Quantum Physics · Physics 2017-01-18 Tomotaka Kuwahara , Itai Arad , Luigi Amico , Vlatko Vedral

By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by…

Disordered Systems and Neural Networks · Physics 2007-05-23 Massimo Ostilli , Carlo Presilla

We consider free-fermion chains in the ground state and the entanglement Hamiltonian for a subsystem consisting of two separated intervals. In this case, one has a peculiar long-range hopping between the intervals in addition to the…

Statistical Mechanics · Physics 2022-08-18 Viktor Eisler , Erik Tonni , Ingo Peschel

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…

Quantum Physics · Physics 2020-08-26 William J. Huggins , Joonho Lee , Unpil Baek , Bryan O'Gorman , K. Birgitta Whaley

We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state,…

Mathematical Physics · Physics 2025-11-19 Wojciech De Roeck , Martin Fraas , Bruno de O. Carvalho

We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…

Quantum Physics · Physics 2025-04-17 Taehee Ko , Hyowon Park , Sangkook Choi

In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value…

Quantum Physics · Physics 2025-01-16 Štěpán Šmíd , Roberto Bondesan

In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of…

Strongly Correlated Electrons · Physics 2008-11-27 Michael Freedman , Chetan Nayak , Kirill Shtengel

Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…

We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…

Quantum Physics · Physics 2012-03-05 W. Dür , M. Van den Nest

We show how local bounded interactions in an unbounded Hamiltonian lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglement of multi-particle spin systems. We begin by analyzing the…

Functional Analysis · Mathematics 2022-01-12 Mazen Ali

The characterization of ground states among all quantum states is an important problem in quantum many-body physics. For example, the celebrated entanglement area law for gapped Hamiltonians has allowed for efficient simulation of 1d and…

Strongly Correlated Electrons · Physics 2024-03-18 Lei Gioia , Ryan Thorngren

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main…

Quantum Physics · Physics 2024-11-08 Adam Bouland , Chenyi Zhang , Zixin Zhou

Here we present a problem related to the local Hamiltonian problem (identifying whether the ground state energy falls within one of two ranges) which is restricted to being translationally invariant. We prove that for problems with a fixed…

Quantum Physics · Physics 2011-11-09 Alastair Kay