(This is the most ridiculous thing I've put on the internet, but ah well whatever)
Personally, I feel pretty strongly that consciousness is an emergent property of parallel processing among cooperating agents in a way that is completely at odds with the entire idea of what an "algorithm" is. We feel multiple things at once. Yes there is some research that provides evidence that we can't multi-task for real, that we just switch between tasks, but I am not talking about what we are able to do WITH our consciousness. Our brains are very obviously not firing 1 neuron at a time. Take vision for example. We can focus on one thing at a time, but the image itself is an emergent property in our brains of many different cells firing at the same time. It seems bound to the information feeding it in a way devoid of sequence. I know matrices are used to replicate this, and the input matrix is processed in layers to simulate the parallel processing, but i dont think that really cuts it. Time is still applied in discrete intervals, not continuous. Every algorithm has "steps" like this and I would be surprised if you can ever have enough of them to achieve the real thing. You can probably get infinitely closer from an observational standpoint, but no matter how many edges we give it, it'll still be a polygon instead of a circle so-to-speak. It'll have a rational valued circumference instead of pi, metaphorically speaking.
Whether a Turing machine is sufficient or not to replicate the amount of concurrent processing an actual cell network of millions of Neurons is capable of every moment, I can't know, but today's computers feel way off from even blurring the lines.
A Turing machine seems insufficient to replicate the mechanisms for which our consciousness appears to emerge from - even ignoring the substrate. I don't know much about quantum mechanics or quantum computers but my bet is on the qualities that differentiate them from normal computers to be critical.
Then again we could just define consciousness as a spectrum and then claim everything is on it, so a sufficiently complex loop might be enough for us to categorically claim it as conscious.
For all we know, rocks are conscious. Maybe it isn't an emergent thing at all, and there is only 1 wave of consciousness in the universe for which all matter taps into and our chaotic nature is actually at odds with that comsciousness. Maybe this creates a tension that allows for us to observe it, akin to how we can't look at ourselves but we can see our shadow. In which case we wouldnt have consciousness, consciousness would have us. Maybe we are all the same literal consciousness observing different forms of chaos, and it is the chaos, not the order, which happens to be sufficiently complex enough for us to entertain an identity. /s