# Engineering Four-Qubit Fuel States for Protecting Quantum Thermalization Machine from Decoherence

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Working Basis

#### 2.2. Quantum Thermalization Machine

#### 2.3. Decoherence Channel

#### 2.4. Realistic Parameter Space

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Four-atom ensembles are injected to the cavity in Poisson distribution. During the flight time, ${t}_{tr}$, atoms are subject to decoherence due to ambient temperature. Atoms interact with the cavity field during the transition time, $\tau $. As shown in Figure 2, specific coherences of the atomic system might lead to pure thermalization of the cavity field, controlling its effective temperature.

**Figure 2.**Heat exchange coherences of the density matrix of (

**a**) three- and (

**b**) four-qubit ensembles in the energy basis leading to pure thermalization of the cavity field.

**Figure 3.**Effective temperature of the cavity ${T}_{cav}$ in Kelvin as the KPI of the quantum thermalization machine performance due to repeated interactions with the injected four-qubit atomic ensembles. Atoms are subjected to generalized amplitude damping decoherence due to ambient temperature during their flight to the cavity. The strength of the decoherence increases with the flight time ${t}_{tr}$. However, tuning the control parameter $\u03f5$ of the state we design in Equation (28) according to the expected flight time, the effect of the decoherence on the quantum thermalization machine performance can almost be reset.

**Figure 4.**Quantum machine performance versus the flight time if the atomic system is prepared in the F or in the ${\rho}_{\u03f5}^{0}$ state. While the decoherence on the F state significantly degrading the machine performance, tuning the control parameter $\u03f5$ protects the machine performance from the impact of the decoherence.

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**MDPI and ACS Style**

Ozaydin, F.; Sarkar, R.; Bayrakci, V.; Bayındır, C.; Altintas, A.A.; Müstecaplıoğlu, Ö.E.
Engineering Four-Qubit Fuel States for Protecting Quantum Thermalization Machine from Decoherence. *Information* **2024**, *15*, 35.
https://doi.org/10.3390/info15010035

**AMA Style**

Ozaydin F, Sarkar R, Bayrakci V, Bayındır C, Altintas AA, Müstecaplıoğlu ÖE.
Engineering Four-Qubit Fuel States for Protecting Quantum Thermalization Machine from Decoherence. *Information*. 2024; 15(1):35.
https://doi.org/10.3390/info15010035

**Chicago/Turabian Style**

Ozaydin, Fatih, Ramita Sarkar, Veysel Bayrakci, Cihan Bayındır, Azmi Ali Altintas, and Özgür E. Müstecaplıoğlu.
2024. "Engineering Four-Qubit Fuel States for Protecting Quantum Thermalization Machine from Decoherence" *Information* 15, no. 1: 35.
https://doi.org/10.3390/info15010035