Quantum simulation of the spin-boson model: monitoring the bath

Silvia Kleff, Stefan K. Kehrein, Jan von Delft

Reinhold Egger, U. Weiss

Mischa P. Woods, M. Cramer, Martin Bodo Plenio

We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths, the truncation of both the number of modes and the local Hilbert-space dimensions is necessary. We derive superexponential Lieb-Robinson-type bounds on the error when restricting the bath to finitely many modes and show how the error introduced by truncating the local Hilbert spaces may be efficiently monitored numerically. In this way we give error bounds for approximating the infinite system by a finite-dimensional one. As a consequence, numerical simulations such as the time-evolving density with orthogonal polynomials algorithm (TEDOPA) now allow for the fully certified treatment of the system-environment interaction.

Juha Leppäkangas, Jochen Braumüller, Melanie Hauck +7 more

We consider superconducting circuits for the purpose of simulating the spin-boson model. The spin-boson model consists of a single two-level system coupled to bosonic modes. In most cases, the model is considered in a limit where the bosonic modes are sufficiently dense to form a continuous spectral bath. A very well known case is the Ohmic bath, where the density of states grows linearly with the frequency. In the limit of weak coupling or large temperature, this problem can be solved numerically. If the coupling is strong, the bosonic modes can become sufficiently excited to make a classical simulation impossible. Here we discuss how a quantum simulation of this problem can be performed by coupling a superconducting qubit to a set of microwave resonators. We demonstrate a possible implementation of a continuous spectral bath with individual bath resonators coupling strongly to the qubit. Applying a microwave drive scheme potentially allows us to access the strong-coupling regime of the spin-boson model. We discuss how the resulting spin relaxation dynamics with different initialization conditions can be probed by standard qubit-readout techniques from circuit quantum electrodynamics.

Ulrich Weiß, Maura Sassetti

Olga Goulko, Guy Cohen, Moshe Goldstein +1 more