The quantum circuit model of computation uses wires and gates. The information flows along the wires and gates attached to the wires modify the information and pass it further down the wires.
In quantum computing, people often talk about circuit depth and circuit connectivity. While I have an intuitive understanding of both, I cannot find the formal definitions of these concepts. Does anyone know the formal definition of circuit depth and connectivity?
Below is a handwavy explanation of depth given in the book "An Introduction to Quantum Computing" by Kaye, Laflamme and Mosca:
If we visualize the circuit as being divided into a sequence of discrete time-slices, where the application of a single gate requires a single time-slice, the depth of a circuit is its total number of time- slices. Note that this is not necessarily the same as the total number of gates in the circuit, since gates that act on disjoint bits can often be applied in parallel.
While it is somewhat clear what they mean here it is not the definition. One of my colleagues casually mentioned the "longest path" in the circuit as a measure of depth, though they did not attempt to give a formal definition. The connectivity in the circuit is even less clear to me, let alone trying to come up with a formal definition of the concept.
Just to summarize. I would like to know if the notion of circuit depth and connectivity were ever formally defined in some literature.
Edit: Niel de Beaudrap gave the definition of the circuit depth
The circuit depth is the length of the longest path from the input (or from a preparation) to the output (or a measurement gate), moving forward in time along qubit wires. The stopping points on the path are the gates, the allowed paths that must be considered can enter and exit those gates on any input / output, and the length is the number of jumps from each gate to the next gates along the path.
No luck with the definition of the circuit connectivity , so far.