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+0.4993⋅log2(n)+3.0191⋅log(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+1.9496⋅log2(n)+3.5075⋅log(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+2.9487⋅log2(n)+8.4909⋅log(n)−44.4798⌋ for Clifford circuits, offering an improvement by a factor of roughly 5/3 .
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