The paper presents a novel construction for generating random unitaries in extremely low circuit depths, demonstrating that random quantum circuits can approximate Haar-random unitaries with optimal scaling. Specifically, the authors show that random unitary designs and pseudorandom unitaries can be formed in $\log n$ and $\text{poly log } n$ depth, respectively, on any geometry, including a 1D line. This is achieved by gluing small random unitaries on patches of $\log n$ or $\text{poly log } n$ qubits to form a global random unitary. The construction is versatile and can be applied to various quantum applications, such as classical shadow tomography, quantum hardness of recognizing topological order, and quantum advantages in learning low-complexity physical systems. The results improve upon existing constructions by achieving exponential reductions in circuit depth, which is crucial for practical quantum technologies and theoretical analyses.The paper presents a novel construction for generating random unitaries in extremely low circuit depths, demonstrating that random quantum circuits can approximate Haar-random unitaries with optimal scaling. Specifically, the authors show that random unitary designs and pseudorandom unitaries can be formed in $\log n$ and $\text{poly log } n$ depth, respectively, on any geometry, including a 1D line. This is achieved by gluing small random unitaries on patches of $\log n$ or $\text{poly log } n$ qubits to form a global random unitary. The construction is versatile and can be applied to various quantum applications, such as classical shadow tomography, quantum hardness of recognizing topological order, and quantum advantages in learning low-complexity physical systems. The results improve upon existing constructions by achieving exponential reductions in circuit depth, which is crucial for practical quantum technologies and theoretical analyses.