Abstract: Currently, mainstream quantum computing simulators are generally based on numerical calculations, which suffer from precision loss, lack of intuitive representation of quantum states, and difficulty in supporting parameterized quantum circuits. Although symbolic quantum computing simulators have been proposed, they are limited in describing parameterized quantum states, constructing custom quantum gates, and integrating with quantum programming environments. To address this issue, this paper proposes a symbolic quantum computing simulator, SymQC. SymQC can use either full amplitude vectors or Dirac symbols to represent quantum states, calculate the equivalent matrix of symbolically parameterized quantum circuits, simulate the evolution of quantum states under quantum circuits, and output the execution results of quantum algorithms in different forms. This paper describes the software structure of SymQC and provides a mathematical proof of a commonly used quantum state update algorithm. Algorithm instances including variational quantum eigensolver (VQE) algorithm are used to verify the ability of SymQC.

Key words: quantum computing, simulator, symbolic calculation, quantum state update algorithm