Related papers: An Efficient Algorithm for approximating 1D Ground…
The Density Matrix Renormalization Group (DMRG) is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC) from the…
We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) has emerged as a promising approach for this task. However, many KQD methods…
We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…
Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound…
We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure…
In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pad\'e and Arnoldi approximations to the evolution operator. By…
Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their…
We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired…
Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, [Huang et…
Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting…
We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states…
The infinite Density Matrix Renormalisation Group (iDMRG) algorithm is a highly successful numerical algorithm for the study of low-dimensional quantum systems, and is also frequently used to initialise the more popular finite DMRG…
We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic,…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
A key property of many-body localization, the localization of quantum particles in systems with both quenched disorder and interactions, is the area law entanglement of even highly excited eigenstates of many-body localized Hamiltonians.…