We extend the circuit model of quantum computation so that wiring between gates is soft-coded within registers inside gates. The addresses in these can be manipulated and put into superpositions. This aims at capturing indefinite causal orders making their geometrical layout explicit: we express switch polarizing beam-splitter model. In this context, our main contribution a full characterizatio...

Due to its fault-tolerant gates, the Clifford+T library consisting of Hadamard (denoted by H), T , and CNOT gates has attracted interest in the synthesis of quantum circuits. Since the implementation of T gates is expensive, recent research is aiming at minimizing the use of such gates. It has been shown that T -depth optimizations can be implemented efficiently for circuits consisting only of ...

Agrawal and Vinay [AV08] have recently shown that an exponential lower bound for depth four homogeneous circuits with bottom layer of × gates having sublinear fanin translates to an exponential lower bound for a general arithmetic circuit computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via homogeneous depth four circuits with boun...