Click here to flash read.
We design algorithms for computing expectation values of observables in the
equilibrium states of local quantum Hamiltonians, both at zero and positive
temperature. The algorithms are based on hierarchies of convex relaxations over
the positive semidefinite cone and the matrix relative entropy cone, and give
certified and converging upper and lower bounds on the desired expectation
value. In the thermodynamic limit of infinite lattices, this shows that
expectation values of local observables can be approximated in finite time,
which contrasts with recent undecidability results about properties of infinite
quantum lattice systems. In addition, when the Hamiltonian is commuting on a
2-dimensional lattice, we prove fast convergence of the hierarchy at high
temperature leading to a runtime guarantee for the algorithm that is polynomial
in the desired error.
No creative common's license