Computing energy density in one dimension
arXiv:1505.00772
Abstract
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 precision if the ground state satisfies area laws for the Renyi entanglement entropy (this is the first rigorous formulation of the folklore that area laws imply efficient matrix-product-state algorithms); (ii) independent of the system size and polynomial in the desired precision if the system is gapped. As a by-product, we prove that in the presence of area laws (or even an energy gap) the ground state can be approximated by a positive semidefinite matrix product operator of bond dimension independent of the system size and subpolynomial in the desired precision of local properties.
References in corpus (12)
- Matrix product states represent ground states faithfully
- Entropy scaling and simulability by Matrix Product States
- The power of quantum systems on a line
- Hamiltonian complexity
- The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
- Stochastic Error Cancellation in Analog Quantum Simulation
- A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians
- Area law in one dimension: Degenerate ground states and Renyi entanglement entropy
- Quantum Adiabatic Computation With a Constant Gap is Not Useful in One Dimension
- An Efficient Algorithm for approximating 1D Ground States
- Computing the Degenerate Ground Space of Gapped Spin Chains in Polynomial Time
- A polynomial-time algorithm for the ground state of one-dimensional gapped Hamiltonians
Cited by in corpus (9)
- Mathematical open problems in Projected Entangled Pair States
- Relativistic continuous matrix product states for quantum fields without cutoff
- Approximating local properties by tensor network states with constant bond dimension
- Rényi free energy and variational approximations to thermal states
- Variational method in relativistic quantum field theory without cutoff
- Two-dimensional local Hamiltonian problem with area laws is QMA-complete
- Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
- Generation of photonic tensor network states with Circuit QED
- Computing local properties in the trivial phase