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We develop genetic algorithms for searching quantum circuits, in particular stabilizer quantum error correction codes. Quantum codes equivalent to notable examples such as the 5-qubit perfect code, Shor's code, and the 7-qubit color code are evolved out of initially random quantum circuits. We anticipate evolution as a promising tool in the NISQ era, with applications such as the search for novel topological ordered states, quantum compiling, and hardware optimization.
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Tandeitnik et al. (2022) studied this question.