Some of these proposals involve using superconducting qubits, trapped ions, liquid and solid state nuclear magnetic resonance, or optical cluster states, all of which show good prospects but also have issues that prevent their practical implementation.
According to DiVincenzo's criteria, constructing a quantum computer requires that the experimental setup meet seven conditions.
Currently, one of the biggest problems being faced is that we require exponentially larger experimental setups to accommodate a greater number of qubits.
In the case of using liquid-state nuclear magnetic resonance (NMR), it was found that increased macroscopic size led to system initialisation that left computational qubits in a highly mixed state.
One could say that as the number of computational qubits increases they become less well characterised until a threshold is reached at which they are no longer useful.
In particular, the unitarity nature of quantum mechanics makes initialisation of the qubits extremely important.
This is of particular importance when you consider quantum error correction, a procedure to perform quantum processes that are robust against certain types of noise and that require a large supply of freshly initialised qubits, which places restrictions on how fast the initialisation can be.
An example of annealing is described in a 2005 paper by Petta, et al., where a Bell pair of electrons is prepared in quantum dots.
[5] Alternate approaches (usually involving optical pumping[6]) have been developed to reduce the initialisation time and improve the fidelity of the procedure.
In solid-state NMR using nitrogen-vacancy centers, the orbital electron experiences short decoherence times, making computations problematic; the proposed solution has been to encode the qubit in the nuclear spin of the nitrogen atom, thus increasing the decoherence time.
In other systems, such as the quantum dot, issues with strong environmental effects limit the T2 decoherence time.
Any experimental setup that manages to have well-characterised qubits; quick, faithful initialisation; and long decoherence times must also be capable of influencing the Hamiltonian (total energy) of the system, in order to effect coherent changes capable of implementing a universal set of gates.
[7] Liquid-state NMR was one of the first setups capable of implementing a universal set of gates, through the use of precise timing and magnetic field pulses.
The main issue now is the decoherence the photon experiences whilst interacting with particles in the atmosphere.