Thermalization in the quantum Ising model—approximations, limits, and beyond

Abstract

We present quantitative predictions for quantum simulator experiments on Ising models from trapped ions to Rydberg chains and show how the thermalization, and thus decoherence times, can be controlled by considering common, independent, and end-cap couplings to the bath. We find (i) independent baths enable more rapid thermalization in comparison to a common one; (ii) the thermalization timescale depends strongly on the position in the Ising phase diagram; (iii) for a common bath larger system sizes show a significant slow down in the thermalization process; and (iv) finite-size scaling indicates a subradiance effect slowing thermalization rates toward the infinite spin chain limit. We find it is necessary to treat the full multi-channel Lindblad master equation rather than the commonly used single-channel local Lindblad approximation to make accurate predictions on a classical computer. This method reduces the number of qubits one can practically classical simulate by at least a factor of 4, in turn showing a quantum advantage for such thermalization problems at a factor of 4 smaller qubit number for open quantum systems as opposed to closed ones. Thus, our results encourage open quantum system exploration in noisy intermediate-scale quantum technologies. arXiv:1805.04934v2 [cond-mat.quant-gas]

Nonreciprocal quantum transport at junctions of structured leads

“…Hence, the phenomenological Lindblad approach described in (11) is only accurate when the system frequencies are not spread in comparison to the bath spec-tral function, in such a way that the decay rates corresponding to each system decay channel Γ α,α (ω = 0). Taking into account the multiple decay channels of the system appears to be crucial not only to describe transport properties, as described here, but also to describe thermalization [51][52][53][54].…”

“…Computing the long time evolution of the system state via (5) can still be time consuming due to the integral-differential nature of the equation of motion and the power-law slowly decaying bath correlations. In the appendix we present a Redfield master equation directly targeting the Born steady state and an approximate approach that leads to a Lindblad form [51][52][53][54].…”

Classical critical dynamics in quadratically driven Kerr resonators

“…This could be useful to speed up or slow down relaxation to the same steady state numerically or experimentally. A possibility would be exploiting the difference between one common bath or independent baths, which has shown to reflect at least on the decoherence time of an open quantum system [32] It would also be interesting to see how the dynamical criticality behaves in the quantum regime, where Kibble-Zurek effect can exhibit richer behavior [60], as has also been suggested to study experimentally with For the fastest quenches (v/J 2 ≥ 10 −2 ), 10 3 trajectories were used, and 10 2 trajectories for the slower quenches. The yellow vertical lines denote approximate values for vKZ and va, marking the edges of regime where power-law scaling is valid.…”

“…In particular, the system was found to belong to the universality class of the quantum or thermal Ising model respectively [29,30]. The crossover between these two spin models has also been subject to more general recent studies on the dynamics [31] and thermalization mechanism [32].…”

Open source matrix product states: exact diagonalization and other entanglement-accurate methods revisited in quantum systems

“…We skip details of the complete derivation of the structure of the resulting Lindblad equation; corresponding details can be found in the original study of the quantum Ising model [46] or the references [44,45]. The Lindblad equation following the full-spectrum then readsρ…”