Evolution of Quantum Programs

Shangzhou Xia, Junjie Luo, Jianjun Zhao

Quantum program analysis remains challenging due to the exponentially large state space of quantum programs and the difficulty of precisely characterizing their execution behavior. In particular, non-Clifford operations introduce additional complexity that limits the applicability of stabilizer-based techniques. Although stabilizer representations provide compact descriptions for Clifford circuits, their limited expressiveness prevents them from directly supporting general quantum program analysis. In this work, we propose StabQ, a symbolic execution framework for quantum program analysis based on stabilizer representations. StabQ extends stabilizer-based symbolic execution beyond Clifford-only programs by introducing a symbolic state representation that captures and propagates quantum state evolution while preserving execution semantics. Based on this representation, StabQ constructs a Tableau Chain that represents the evolution of intermediate symbolic states throughout program execution and enables reusable analysis of quantum program executions. Furthermore, StabQ incorporates tableau consolidation and global-phase recovery mechanisms to mitigate symbolic state growth during execution. Building upon the Tableau Chain, StabQ supports multiple quantum program analysis tasks, including quantum state reconstruction, entanglement analysis, and Clifford-property detection. We evaluate StabQ on three benchmark suites---Algorithms, MQT Bench, and QASMBench. The results demonstrate that StabQ constructs semantically consistent symbolic models, accurately preserves quantum state evolution, and effectively supports downstream analysis tasks across diverse quantum programs.

André Leier, Wolfgang Banzhaf

This work is a first study of search spaces and fitness landscapes in the context of quantum program evolution. Considering small instances of the Deutsch-Josza problem as a staring point for explorations of quantum program search spaces, we analyze the structure of mutation landscapes using autocorrelation characteristics and information measures. Our motivation is to obtain insights into the relationship between landscape characteristic and quantum circuit evolution with the aim to improve the efficiency of evolutionary search.

Duncan MacKinnon

In this thesis we present a genetic programming scheme for evolving quantum programs in the form of arbitrary unitary operators. Expanding on the work done by Hutsell and Greenwood, and later by Krawec in developing unitary operator evolution schemes, we present an alternative representation for unitary operators which has a better search topology than the representations used in these previous implementations. This alternative representation is tested on a general unitary evolution problem, and displays better convergence than previously implemented representations.