Hay from the Haystack: Explicit Examples of Exponential Quantum Circuit Complexity

The vast majority of quantum states and unitaries have circuit complexity exponential in the number qubits. In a similar vein, most them also minimum description length, which makes it difficult to pinpoint examples complexity. this work, we construct constant length but We provide infinite families such that each element requires an two-qubit gates be generated exactly from product where same is true for approximate generation elements family. results are based on sets large transcendence degree discussed tensor networks, diagonal maximally coherent states.