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Can a polynomial-sized superposition of computational basis states be prepared with a polynomial-sized quantum circuit?

I think so. Let me rephrase what you're asking and hopefully it captures what you want: Suppose you have $N$ distinct circuits $U_i$ such that $U_i|0\rangle = |\psi_i\rangle$, each with complexity $O(...
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Definitions of a quantum circuit's depth and connectivity

I would like to give explicit definitions of the circuit depth and connectivity. I assume that the meaning of terms like vector state, quantum circuit, wires, and 1- and 2-qubit gates is understood. I'...
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Definitions of a quantum circuit's depth and connectivity

The traditional definitions of classical Boolean circuits work perfectly well here: https://en.wikipedia.org/wiki/Boolean_circuit. This is the definition that gives you Niel de Beaudrap's definition. ...
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Definitions of a quantum circuit's depth and connectivity

Let me try to provide a more precise definition of connectivity in a quantum circuit. Every quantum circuit defines a graph (network), with vertices (nodes) given by qubits. There is an edge $q_1 q_2$ ...
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