The computers we have today help to do logistics to "feed, clothe and house the homeless". They also help you to advocate to do more. How much of that would be comprehensible to someone living in 1900?

I'm not sure that homelessness is a problem quantum computing or AI are suitable for. However, AI has already contributed in helping to solve protein folding problems that are critical in modern medicine.

Solving homelessness and many other problems isn't resource constrained as you think. It's more about the will to solve them, and who profits from leaving them unsolved. We have known for decades that providing homes for the homeless in a large city actually saves the city money, but we're still not doing it. Renewable energy has been cheaper than fossil fuels for almost as long. Medicare for all would cost significantly less than the US private healthcare system, and would lead to better results, but we aren't doing that either.