1st & 2nd quantization from TCS Last year I attended Scott Aaronson's talk Hawking Quantum Wares at the Classical Complexity Bazaar. Being intrigued by his argument that "[e]ven if quantum mechanics hadn't existed, theoretical computer scientists would eventually have had to invent it", I have been thinking about how we can derive the first and second quantization in quantum mechanics from theoretical computer science.

First quantization is basically the quantization of properties of a unit quantum system and second quantization is the quantization of the electromagnetic field. Is there some way that theoretical computer science could entail these two ideas? I can recognize some "quantumnesses" in theoretical computer science, including


enumeration of set elements,
enumeration of interactions with oracles, and
discrete states of Turing machine,


but I am having a hard time relating them to first and second quantization.
I would amend your definition of second quantization.  It is not a procedure that is applied only to the electromagnetic field.  It is more properly a process in which something like the Schrodinger equation is re-interpreted as a classical field, which is then quantized.  This is the standard old-fashioned way to move from single-particle quantum systems to multi-particle quantum systems in which particle creation and annihilation can be described via unitary operators.

I'm not sure that the paradigm of second-quantization makes sense in the context of quantum computation.  To do so, one would need to interpret the "first-quantized" theory as a system which conserves something like particle number.  The "second-quantized" theory allows for a description of systems with different particle numbers.  Qubits obey neither Bose-Einstein nor Fermi-Dirac statistics and thus there is nothing analogous to "particle-number" in a qubit system.  From this point of view it is hard to see that "second-quantizing" a qubit system would lead to something sensible.