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The multiplicative depth of a logic network over the gate basis $\{\land,\oplus, \neg\}$ is the largest number of $\land$ gates on any path from aprimary input to a primary output in the network. We describe a dynamicprogramming based logic synthesis algorithm to reduce the multiplicative depthin logic networks. It makes use of cut enumeration, tree balancing, andexclusive sum-of-products (ESOP) representations. Our algorithm hasapplications to cryptography and quantum computing, as a reduction in themultiplicative depth directly translates to a lower $T$-depth of thecorresponding quantum circuit. Our experimental results show improvements in$T$-depth over state-of-the-art methods and over several hand-optimized quantumcircuits for instances of AES, SHA, and floating-point arithmetic.

Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks