Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes 10 quantum unitary programs including quantum arithmetic programs, quantum eigenvalue inversion, quantum teleportation and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q#, IBM Qiskit, and AWS Braket.

@article{paperbot2574,
  title = {A Case for Synthesis of Recursive Quantum Unitary Programs},
  author = {Haowei Deng and Runzhou Tao and Yuxiang Peng and Xiaodi Wu},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {8},
  number = {POPL},
  year = {2024},
  doi = {10.1145/3632901}
}