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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Efficient quantum circuits for dense circulant and circulant like operators.

S S Zhou^1,2,3, J B Wang⁴

¹Kuang Yaming Honors School, Nanjing University, Nanjing 210093, People's Republic of China.

Royal Society Open Science

|June 3, 2017

Summary

This summary is machine-generated.

This study introduces efficient quantum circuits for implementing circulant operators, reducing resource usage and complexity. These methods also extend to other matrix types and enable efficient inverse and product calculations.

Keywords:

Toeplitz and Hankel matrices block circulant operator dense circulant operator quantum circuit quantum computation

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Area of Science:

Quantum computing
Linear algebra
Scientific computing

Background:

Circulant matrices are fundamental operators with broad applications in science and engineering.
Existing methods for implementing circulant operators on quantum computers can be resource-intensive and complex.

Purpose of the Study:

To develop efficient quantum circuits for implementing circulant operators.
To reduce the resource requirements and computational complexity of quantum circulant matrix implementation.
To extend these methods to related matrix types and enable efficient inverse and product computations.

Main Methods:

Design and implementation of novel quantum circuits for circulant operators.
Adaptation of circuits for Toeplitz, Hankel, and block circulant matrices.
Development of quantum algorithms for matrix inversion and multiplication.

Main Results:

Demonstrated efficient quantum circuits for circulant operators with lower complexity.
Showcased the scalability of the circuits for related matrix structures.
Provided efficient quantum algorithms for inverse and product operations.

Conclusions:

The proposed quantum circuits offer a significant improvement for implementing circulant operators.
The developed methods are versatile and applicable to a broader class of matrices.
These advancements facilitate applications in areas like solving equations of motion for cyclic systems.