Can anyone please point me to the current state of the art way to do Quantum Computing in Mathematica?
As Mathematica has most necessary matrix algebra functions (crucially the matrix exponential) built in natively (both for symbolic and numerics) it is quite simple to roll most things yourself. For more complicated manipulations QuantumUtils is useful (disclaimer this was made by some colleagues).
I should point out that the focus of this library is not on building and simulating algorithms (although possible) but the description and manipulation of quantum channels and hamiltonians. Hamiltonian simulation and GRAPE pulse design is also baked in.
Completely out of my domain of expertise, however I stumbled across the "Live CEOing" videos Wolfram is doing on YouTube. Quantum computing seems to be a focus. For example:
Looks to be destined for the Wolfram Language and Mathematica in the future. Not sure if it is of interest to you, but thought I would mention it. Clearly not something available now though.
Yes, there is the Wolfram Quantum Framework, here are some useful links.
"The Wolfram Quantum Framework brings a broad, coherent design for quantum computation, together with a host of leading-edge capabilities and full integration into Mathematica and Wolfram Language. Starting from discrete quantum mechanics, the Framework provides a high-level symbolic representation of quantum bases, states and operators. The Framework can perform measurements and is equipped with various well-known states and operators, such as Bell states and Pauli operators. Using such simulation capabilities as a foundation, one can use the Framework to model and simulate quantum circuits and algorithms.
All functions and objects in the Wolfram Quantum Framework work seamlessly with the 5,000+ built-in functions made available through Wolfram Language. The immediate availability of such functions allows one to study a full range of questions around quantum computation and can serve as a helpful resource for teaching."