Dissipative mean-field theory of IBM utility experiment

In spite of remarkable recent advances, quantum computers have not yet found any useful applications. A promising direction for such utility is offered by the simulation of the dynamics of many-body quantum systems, which cannot be efficiently computed classically. Recently, IBM used a superconducting quantum computer to simulate a kicked quantum Ising model for large numbers of qubits and time steps. By employing powerful error mitigation techniques, they were able to obtain an excellent agreement with the exact solution of the model. This result is very surprising, considering that the total error accumulated by the circuit is prohibitively large. In this letter, we address this paradox by introducing a dissipative mean-field approximation based on Kraus operators. Our effective theory reproduces the many-body unitary dynamics and matches quantitatively local and non-local observables. These findings demonstrate that the observed dynamics is equivalent to a single qubit undergoing rotations and dephasing. Our emergent description can explain the success of the quantum computer in solving this specific problem.Comment: 4 pages, 2 figure

Introduction to the Dicke model : from equilibrium to nonequilibrium, and vice versa

P.K. acknowledges support from EPSRC (EP/M010910/1) and the Austrian Academy of Sciences (ÖAW). P.K. and J.K. acknowledge support from EPSRC program “Hybrid Polaritonics” (EP/M025330/1).The Dicke model describes the coupling between a quantized cavity field and a large ensemble of two-level atoms. When the number of atoms tends to infinity, this model can undergo a transition to a superradiant phase, belonging to the mean-field Ising universality class. The superradiant transition was first predicted for atoms in thermal equilibrium, but its experimental realizations required driven-dissipative systems. In this Progress Report, we offer an introduction to some theoretical concepts relevant to the Dicke model, reviewing the critical properties of the superradiant phase transition, and the distinction between equilibrium and nonequilibrium conditions. In addition, we explain the fundamental difference between the superradiant phase transition and the more common lasing transition. Our report mostly focuses on the steady states of single-mode optical cavities, but we also mention some aspects of real-time dynamics, as well as applications to multimode cavities, superconducting circuits, and trapped ions.PostprintPeer reviewe

Dicke model.

The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes