Quanz, M. (2023):

Efficient Parallel Quantum Circuit Optimization using the ZX Calculus

Through the quantum effects of the so-called `qubit', quantum computers are potentially able to solve a larger problem class than classical computers in polynomial time, called bounded-error quantum polynomial time (BQP). However, the practicality of scaling quantum computers to tackle larger problems comes with formidable challenges – increased costs, reduced accuracy, as well as longer design and construction times. These challenges can render a quantum computing design infeasible, emphasizing the critical need to ensure quantum circuits are only as large as they are required to be. In order to reduce the size of the circuit, various optimization techniques can be employed. Current quantum circuit optimization algorithms transform circuits into a more general representation in the ZX-calculus, perform various simplification operations on it, and then extract a reduced, but equivalent quantum circuit. Out of these, the simplification and extraction require the greatest amount of time, potentially even outclassing the computational class of BQP. Our research explores methods to parallelize the quantum circuit extraction process, rendering it suitable for high-performance systems. We present our implementation of a parallelized quantum circuit extraction algorithm, alongside surprising findings that have emerged during our work and evaluation, offering avenues for further investigation and refinement.

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