Lowering the T-depth of Quantum Circuits via Logic Network Optimization

The multiplicative depth of a logic network over the gate basis {∧ , ⊕ , ¬} is the largest number of ∧ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based logic synthesis algorithm to reduce the multiplicative depth of logic networks. It makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations. Our algorithm has applications to cryptography and quantum computing, as a reduction in the multiplicative depth directly translates to a lower T-depth of the corresponding quantum circuit. Our experimental results show improvements in T-depth over state-of-the-art methods and over several hand-optimized quantum circuits, for instance, of AES, SHA, and floating-point arithmetic.