A Symbolic Approach to Quantum Computation Simulation

Meghana Aparna Sistla, Swarat Chaudhuri, Thomas Reps

Abstract The simulation of quantum circuits on classical computers is an important problem in quantum computing. Such simulation requires representations of distributions over very large sets of basis vectors, and recent work has used symbolic data-structures such as Binary Decision Diagrams (BDDs) for this purpose. In this tool paper, we present Quasimodo, an extensible, open-source Python library for symbolic simulation of quantum circuits. Quasimodo is specifically designed for easy extensibility to other backends. Quasimodo allows simulations of quantum circuits, checking properties of the outputs of quantum circuits, and debugging quantum circuits. It also allows the user to choose from among several symbolic data-structures—both unweighted and weighted BDDs, and a recent structure called Context-Free-Language Ordered Binary Decision Diagrams (CFLOBDDs)—and can be easily extended to support other symbolic data-structures.

Tzvetan S. Metodi, Frederic T. Chong

Tzvetan S. Metodi, Arvin I. Faruque, Frederic T. Chong

Alexandre de A. Barbosa, Bernardo Lula, Aércio Ferreira de Lima

Simulation fulfills an important mechanism for the study and the development of many areas. Quantum computation simulation tools have become essential, because no effective quantum hardware has been implemented yet. However, the currently available simulators have serious deficiencies, which makes the description of this new computational paradigm incomplete. This article presents a universal quantum circuit simulator, called Zeno, and the symbolic extension that is being developed to it. The extension will allow a symbolic description of the system's state allied to the graphical representation of the circuit to be visualized together. Users will be able to work in a faster and more efficient way than making this calculations by hand. The extension will make possible a faithful description of the system computation like the descriptions observed in related literature.

Yongshan Ding, Frederic T. Chong

Jincheng Zhang

Symbolic regression is a powerful technique for uncovering hidden mathematical relationships within data. However, its computational complexity grows dramatically with dataset size and the desired expression complexity. This work proposes a novel approach combining symbolic regression with evolutionary algorithms executed on a quantum computer. The core idea is to exploit the inherent parallelism of quantum computation to accelerate the exploration of the vast solution space, while leveraging an evolutionary algorithm to refine and optimize the generated symbolic expressions. We hypothesize that this hybrid approach will significantly outperform traditional symbolic regression methods, particularly for challenging datasets. The system is designed to iteratively generate symbolic expressions through quantum computation and then refine them using an evolutionary strategy. This process aims to find an expression that best represents the data while maintaining a desired level of complexity and accuracy. The effectiveness of this approach is evaluated theoretically and through simulation, demonstrating its potential for tackling complex symbolic regression problems.