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A Numerically Exact Method for Dissipative Dynamics of Qubits^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Hamiltonian

#### 2.2. Short-Iterative Lanczos

## 3. Results

#### 3.1. Spin-Boson Model

#### 3.2. Quantum Annealing

## 4. Discussion

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Results for SBM. (

**a**) Time evolution of $\langle {\sigma}_{z}\left(t\right)\rangle $ for an unbiased qubit in an Ohmic bath ($s=1$), having chosen $\eta =7.5\times {10}^{-2}$, ${\omega}_{\mathrm{c}}=10\mathsf{\Gamma}$ and $T=0$, for ${N}_{\mathrm{ph}}=\{1,2,3\}$, respectively. SIL results are plotted against the Lindblad curve (solid black curve); (

**b**) Numerical results for quality factor $\mathsf{\Omega}/\gamma $ of the underdamped oscillations of $\langle {\sigma}_{z}\left(t\right)\rangle $ in time as a function of the coupling strength $\eta $, compared with NIBA theoretical results (solid yellow curve) [1]. Parameter values of qubit and dissipation are the same as (

**a**) and ${N}_{\mathrm{ph}}=\{2,3\}$.

**Figure 2.**Results of quantum annealing. (

**a**) SIL results for residual energy as a function of the annealing time ${t}_{f}$ for different values of the coupling strength $\eta $; (

**b**) Analogous curves computed using the adiabatic Lindblad equation.

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## Share and Cite

**MDPI and ACS Style**

Cangemi, L.M.; Passarelli, G.; Cataudella, V.; Lucignano, P.; Filippis, G.D.
A Numerically Exact Method for Dissipative Dynamics of Qubits. *Proceedings* **2019**, *12*, 59.
https://doi.org/10.3390/proceedings2019012059

**AMA Style**

Cangemi LM, Passarelli G, Cataudella V, Lucignano P, Filippis GD.
A Numerically Exact Method for Dissipative Dynamics of Qubits. *Proceedings*. 2019; 12(1):59.
https://doi.org/10.3390/proceedings2019012059

**Chicago/Turabian Style**

Cangemi, L. M., G. Passarelli, V. Cataudella, P. Lucignano, and G. De Filippis.
2019. "A Numerically Exact Method for Dissipative Dynamics of Qubits" *Proceedings* 12, no. 1: 59.
https://doi.org/10.3390/proceedings2019012059