# Towards Quantum Control with Advanced Quantum Computing: A Perspective

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Data Encoding and State Preparation

#### 2.2. Quantum Simulation

#### 2.3. Measurement and Evaluation of the Quantum Function

#### 2.4. Classical Optimization

## 3. Examples

#### 3.1. Quantum Approximate Optimization Algorithm

#### 3.2. Digital Adiabatic Quantum Computing

#### 3.3. Quantum Optimal Control

## 4. Discussion and Outlooks

## 5. Concluding Remarks

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram of using a quantum computer to solve a general quantum control problem numerically. Here, we briefly explain the workflow by starting from the box on the top left. One usually formulates a quantum control problem by minimizing or maximizing a cost functional $J\left[\mathit{u}\left(t\right),\mathit{x}\left(t\right),T\right]$ in a continuous operation time interval $t\in \left[0,T\right]$, where $\mathit{u}\left(t\right)$ and $\mathit{x}\left(t\right)$ are the controller and state, respectively. Our protocol encodes the initial state $\mathit{x}\left(0\right)$ into a qubit wave function $|\Psi \u27e9$, which is prepared in a quantum computer. Following the Suzuki-Trotter decomposition, we discretize the continuous time into time steps of length $\mathsf{\Delta}t$, simulating the quantum dynamics with blocks of quantum circuits, which the controller $\mathit{u}\left(t\right)$ is also discretized and mapped into gate parameters ${\theta}_{i}$. After the digital quantum simulation, we measure the qubits to retrieve the classical final state $\mathit{x}\left(T\right)$, which allows the evaluation of the cost function. A classical optimizer tunes the gate parameters iteratively until the convergence criteria are satisfied, and outputs the controller $\mathit{u}\left(t\right)$ at the end.

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**MDPI and ACS Style**

Ding, Y.; Ban, Y.; Chen, X.
Towards Quantum Control with Advanced Quantum Computing: A Perspective. *Entropy* **2022**, *24*, 1743.
https://doi.org/10.3390/e24121743

**AMA Style**

Ding Y, Ban Y, Chen X.
Towards Quantum Control with Advanced Quantum Computing: A Perspective. *Entropy*. 2022; 24(12):1743.
https://doi.org/10.3390/e24121743

**Chicago/Turabian Style**

Ding, Yongcheng, Yue Ban, and Xi Chen.
2022. "Towards Quantum Control with Advanced Quantum Computing: A Perspective" *Entropy* 24, no. 12: 1743.
https://doi.org/10.3390/e24121743