5 citations · 9 across the 4 of their papers we have counts for
4 papers
Depth-1 expanders on the unitary group and applications
Anurag Anshu, Shankar Balasubramanian, Jonas Haferkamp +2
We construct a constant-degree and constant-gap quantum expander on qubits where each unitary can be implemented by a depth- and 1D circuit of Pauli or CNOT gates. We provid…
Random dimension reduction and learning symmetric properties of quantum states
Angus Lowe, Xinyu Tan
We describe a procedure that simultaneously reduces the dimensions of many, potentially distinct quantum states while preserving properties invariant under the tensor power action…
Incompressibility and spectral gaps of random circuits
Chi-Fang Chen, Jeongwan Haah, Jonas Haferkamp +3
Random reversible and quantum circuits form random walks on the alternating group and unitary group , respectively. Known bounds on the spectr…
Efficient approximate unitary designs from random Pauli rotations
Jeongwan Haah, Yunchao Liu, Xinyu Tan
We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order . Specifically, a step of the walk on the unitary or orthogn…