# A Coherent LQG approach to Quantum Equalization

**Authors:** Rebbecca TY Thien, Shanon L. Vuglar, Ian R. Petersen  
**arXiv:** [2304.01413](https://arxiv.org/abs/2304.01413)  
**Date:** 2023-04-03  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.01413v1/

## Key points

- The paper proposes a method for designing a suboptimal, coherent quantum LQG controller to solve a quantum equalization problem.
- The authors use the Linear Quadratic Gaussian (LQG) control theory to design controllers for quantum systems.
- This method allows for the design of suboptimal controllers that are easier to implement than optimal ones while still achieving good performance.
- The proposed algorithm is applicable to both active and passive systems with dynamics described in terms of either position and momentum operators or annihilation operators only.
- The authors demonstrate their algorithm on two examples: one involving an active system with dynamics described in terms of position and momentum operators, and another involving a passive system with dynamics described in terms of annihilation operators only.
- Overall, this paper presents an innovative approach to solving quantum equalization problems using classical LQG controllers implemented as quantum systems.

## Summary

In their paper titled "A Coherent LQG approach to Quantum Equalization," Rebecca TY Thien, Shanon L. Vuglar, and Ian R. Petersen propose a method for designing a suboptimal, coherent quantum LQG controller to solve a quantum equalization problem. The authors begin by reformulating the problem as a control problem and then designing a classical LQG controller that can be implemented as a quantum system. The proposed algorithm is demonstrated through illustrative examples for both active and passive systems with dynamics described in terms of both position and momentum operators or annihilation operators only. The authors' approach involves using the Linear Quadratic Gaussian (LQG) control theory, which is widely used in classical control systems, to design controllers for quantum systems. This method allows for the design of suboptimal controllers that are easier to implement than optimal ones while still achieving good performance. The proposed algorithm is applicable to both active and passive systems with dynamics described in terms of either position and momentum operators or annihilation operators only. The authors demonstrate their algorithm on two examples: one involving an active system with dynamics described in terms of position and momentum operators, and another involving a passive system with dynamics described in terms of annihilation operators only. Overall, this paper presents an innovative approach to solving quantum equalization problems using classical LQG controllers implemented as quantum systems. The proposed method has the potential to be useful in various applications where precise control over quantum states is required.