A polynomial-time algorithm for the ground state of one-dimensional gapped Hamiltonians

Abstract

A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon ,n,\eta$ be the energy gap, the system size, and the desired precision, respectively. Neglecting $\epsilon$-dependent subpolynomial (in $n$) and constant factors, the running time of the algorithm is $n^{O(1)}$ for $\eta =n^{-O(1)}$.

References in corpus (9)

• Matrix product states represent ground states faithfully
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• The power of quantum systems on a line
• Powers of Tensors and Fast Matrix Multiplication
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Stochastic Error Cancellation in Analog Quantum Simulation
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Cited by in corpus (8)

• Adiabatic Quantum Computing
• Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
• Computing the Degenerate Ground Space of Gapped Spin Chains in Polynomial Time
• Computing energy density in one dimension
• Approximating local properties by tensor network states with constant bond dimension
• Two-dimensional local Hamiltonian problem with area laws is QMA-complete
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
• Computing local properties in the trivial phase