We seek to develop better upper bound guarantees on the depth of quantum CZ gate, cnot gate, and Clifford circuits than those reported previously. We focus on the number of qubits n 1 345 000 (de Brugière et al. , 2021), which represents the most practical use case. Our upper bound on the depth of CZ circuits is n/2+0.4993log2(n)+3.0191log(n)10.9139 , improving the best-known depth by a factor of roughly 2. We extend the constructions used to prove this upper bound to obtain depth upper bound of n+1.9496log2(n)+3.5075log(n)23.4269 for cnot gate circuits, offering an improvement by a factor of roughly 4/3 over the state of the art, and depth upper bound of 2n+2.9487log2(n)+8.4909log(n)44.4798 for Clifford circuits, offering an improvement by a factor of roughly 5/3 .

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