  We improve the Toffoli count of low depth quantum adders, and analyze how
their spacetime cost reacts to having a limited number of magic state
factories. We present a block lookahead adder that parallelizes across blocks
of bits of size $b$, instead of over all bits. The block lookahead adder
achieves a Toffoli count of $3n + 5n/b$ for out of place addition (vs $4n$ in
previous work by Thapliyal et al) and $5n + 8n/b$ for in place addition (vs
$7n$ in previous work by Thapliyal et al). The tradeoff is that the reaction
depth of these circuits depends linearly on $b$, and they use additional
workspace. We estimate the spacetime volume of these adders, and adders from
previous work, for various register sizes and factory counts under plausible
assumptions for a large scale quantum computer based on the surface code and
superconducting qubits.

Quantum Physics