Simulating infinite systems

Heiner Muller-Krumbhaar

Guifré Vidal

Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.

Ernst Hairer, Gerhard Wanner

Jacob Jordan, Román Orús, Guifré Vidal +2 more

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Hemant Kumar Balasaheb Jadhav, Dinesh Goyal, Tanya Singh +3 more

There is a powerful mathematical method for simulating quantum dynamics that goes beyond finite qubit representations called infinite-dimensional Hamiltonian systems. These systems make it possible to describe quantum fields, open quantum systems, and hybrid designs more accurately by simulating unbounded operators, spectral decompositions, and continuous-variable interactions. Quantum algorithms for partial differential equations, many-body physics, and error-tolerant models of infinite Hilbert spaces are all areas where they are useful. Adding Hamiltonians with infinite dimensions to computer systems makes it possible to use both classical approximation and quantum hardware. This method makes it easier to scale up, improves accuracy when dynamics aren’t simple, and sets the stage for more advanced robust quantum computing models in chemistry, information sciences, and physics.

Joshua Jortner, Alberte Pullman, Bernard Pullman