Custom Optimizations of Quantum Gate Reductions with ZX-Calculus
Session Number
Project ID: CMPS 32
Advisor(s)
Dr. Robert Rand, University of Chicago
Discipline
Computer Science
Start Date
17-4-2024 9:20 AM
End Date
17-4-2024 9:35 AM
Abstract
Quantum circuit gate and depth optimization is important for improving accuracy and reducing errors when running quantum computations on quantum computers. Current quantum optimization uses a number of algorithms, and heuristic brute force methods to find equivalent circuits for quantum gates Gate reduction minimizes the chance of quantum states deteriorating into mixed states, leading to better performance and fidelities. ZX-calculus is a graphical language that utilizes linear maps to represent circuits. ZX Calculus has applications in surface codes, quantum verification, and graph state descriptions. ZX-calculus includes rewrite rules that cause gate decompositions, leading to further optimization.
This research aims to benchmark and analyze the differences in quantum gate reduction for different ZX Calculus optimization algorithms and implement custom ZH rules for Toffoli decomposition. ZH-calculus is similar to ZX-calculus, and focuses on the Z and the H gates. In ZH-calculus, Z and H gates are represented as graphical elements with specific rules that describe how they can be combined and manipulated. The circuits analyzed are classical circuits. These optimizations are meant to characterize the performance of ZX rewrite rules, for quantum and classical.
Custom Optimizations of Quantum Gate Reductions with ZX-Calculus
Quantum circuit gate and depth optimization is important for improving accuracy and reducing errors when running quantum computations on quantum computers. Current quantum optimization uses a number of algorithms, and heuristic brute force methods to find equivalent circuits for quantum gates Gate reduction minimizes the chance of quantum states deteriorating into mixed states, leading to better performance and fidelities. ZX-calculus is a graphical language that utilizes linear maps to represent circuits. ZX Calculus has applications in surface codes, quantum verification, and graph state descriptions. ZX-calculus includes rewrite rules that cause gate decompositions, leading to further optimization.
This research aims to benchmark and analyze the differences in quantum gate reduction for different ZX Calculus optimization algorithms and implement custom ZH rules for Toffoli decomposition. ZH-calculus is similar to ZX-calculus, and focuses on the Z and the H gates. In ZH-calculus, Z and H gates are represented as graphical elements with specific rules that describe how they can be combined and manipulated. The circuits analyzed are classical circuits. These optimizations are meant to characterize the performance of ZX rewrite rules, for quantum and classical.