# Suppressing Decoherence in Quantum State Transfer with Unitary Operations

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## Abstract

**:**

## 1. Introduction

## 2. Error Suppression Using Unitary Operations

## 3. Demonstrating Error Suppression with a Quantum Emulator

`AerSimulator`emulator provided as part of the

`qiskit`package [83]. We consider a simplified error model, where the decoherence channel is taken as a tensor power of a single-qubit channel ${\mathcal{E}}^{\left(1\right)}$, namely,

## 4. Validating Error Suppression with a Cloud-Based Quantum Processor

`ibmq_manila`. To access the decoherence process on the real device, we utilize the

`Delay`instructions in the natural time units (

`dt`). Delay time can be seen as the strength of the decoherence distortion of the input state on the real device.

## 5. Error Suppression in a State Transfer

`ibm_oslo`quantum processor (see Figure 9). This can be considered as a prototype experiment for realizing quantum state transfer between distinct quantum information processing devices connected via a quantum interface [1].

## 6. Conclusions

`ibmq_manila`, where the strength of the decoherence is controlled by the delay. We have observed the results of increasing the fidelity value both in the case of two-qubit decoherence and in the case of four-qubit decoherence for all types of schemes. We also have demonstrated the real-world example of quantum state transfer with a cloud-accessible, seven-qubit quantum processor

`ibm_oslo`. We have observed the increase in fidelity for optimized state transfer protocol up to $10\%$. We expect our findings to be useful for increasing the performance of current NISQ devices.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Quantum circuit of error suppression based on pre-processing and post-processing unitary operations.

**Figure 2.**Schemes for protecting a pure state $|{\Psi}_{\mathrm{in}}\rangle $ from the decoherence channel $\mathcal{E}$: individual–individual (

**a**), individual–collective (

**b**), collective–individual scheme (

**c**), and collective–collective (

**d**). Note that single-qubit U and V can be different for different qubits.

**Figure 3.**Quantum circuit for the unitary operator performing preparation of the n-qubit input state $|{\Psi}_{\mathrm{in}}\left(\theta \right)\rangle $.

**Figure 5.**Circuit for the measurement of the resulting fidelity. Parameter $\theta $ for the ${\mathcal{U}}_{\mathrm{prep}}$ is taken to be equal to $2\pi /3$.

**Figure 6.**Simulation results for $n=2$ qubit (

**a**–

**c**) and $n=4$ qubit (

**d**–

**f**) cases. The amplitude damping (

**a**,

**d**), dephasing (

**b**,

**e**), and depolarizing (

**c**,

**f**) channels are considered.

**Figure 7.**Experimental results of $\xi $ angle calibration from IBMQ quantum processor for (

**a**) two-qubit experiment and (

**b**) four-qubit experiment. Solid and dashed lines stand for collective–individual and individual–collective schemes, respectively.

**Figure 8.**Experimental results from IBMQ quantum processor for (

**a**) two-qubit experiment and (

**b**) four-qubit experiment.

**Figure 9.**Scheme of the

`ibm_oslo`quantum processor experiment (inset is from quantum-computing.ibm.com, accessed on 26 December 2022).

**Figure 10.**Quantum circuits of state transfer experiments with (

**a**) individual–individual protection scheme and (

**b**) collective–individual protection scheme.

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**MDPI and ACS Style**

Gavreev, M.A.; Kiktenko, E.O.; Mastiukova, A.S.; Fedorov, A.K.
Suppressing Decoherence in Quantum State Transfer with Unitary Operations. *Entropy* **2023**, *25*, 67.
https://doi.org/10.3390/e25010067

**AMA Style**

Gavreev MA, Kiktenko EO, Mastiukova AS, Fedorov AK.
Suppressing Decoherence in Quantum State Transfer with Unitary Operations. *Entropy*. 2023; 25(1):67.
https://doi.org/10.3390/e25010067

**Chicago/Turabian Style**

Gavreev, Maxim A., Evgeniy O. Kiktenko, Alena S. Mastiukova, and Aleksey K. Fedorov.
2023. "Suppressing Decoherence in Quantum State Transfer with Unitary Operations" *Entropy* 25, no. 1: 67.
https://doi.org/10.3390/e25010067