The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit from the circuit's classical description. However, a similar complexity-theoretic lower bound on the computational hardness of cloning a witness is not known. In this note, we derive a conjecture about cloning algorithms for maximally entangled states over hidden subspaces which would imply that no efficient algorithm exists for cloning witnesses (assuming BQP does not contain NP). The conjecture and result follow from connections between quantum computation and representation theory; specifically, the relationship between quantum state complexity and the complexity of computing Kronecker coefficients.

翻译：量子电路所接受的状态被称为该量子电路可满足性的见证态。假设BQP不等于QMA，意味着不存在从量子电路的经典描述高效构造其见证态的有效算法。然而，对于克隆见证态的计算困难性，尚未有类似的复杂性理论下界结果。在本短文中，我们提出了一个关于隐藏子空间上最大纠缠态克隆算法的猜想，该猜想将意味着不存在克隆见证态的高效算法（假设BQP不包含NP）。这一猜想及结果源于量子计算与表示理论之间的联系；具体而言，量子态复杂度与计算克罗内克系数复杂度之间的关系。