There is another route to become a Quant, similar to become a start-up founder in software/internet industry. You can just learn to trade by yourself with some simple trading strategy. One popular strategy is "High Frequency" automatic or semi-automatic trading. A friend of mine has achieved such a good result which allows him quit his day job. I'm not saying this route is for everyone or easier than learning at hedge funds or investment banks though.
The high frequency trading is a term used to denote automated trading in intervals of tenths to hundredths of second, in volumes of even hundreds to millions $ in one transaction, so that is not something an individual would do. Automated trading by itself is of course feasible for almost anyone determined enough.
Automated trading by itself is of course feasible for almost anyone determined enough.
...as well as a healthy bankroll to start with. If you can't maintain at least $25,000 in your trading account, you can't day-trade anything but currencies, so you can't really bootstrap from nothing. And if you don't have a lot more money than that to play with, you're never going to make enough to replace a salary. Even if you're actually able to beat the market.
Which brings me to: don't underestimate the market. That doesn't mean it's efficient, but it's very difficult to beat it by a large margin or without considerable risk. A 51/49 edge can be very good if you can get enough trades that offer those odds (forgive my putting it in those terms, I know it's not completely accurate), but that's still going to mean that you can have huge swings either way, even over a large number of trades.
And please, please, PLEASE don't assume that because something worked on historical data it will necessarily work in the live market. There are so many ways to arrive at faulty conclusions here, not the least of which is bad data or analysis (no, your vanilla backprop network is not predicting daily S&P 500 returns, even if it looks like it when you compare it to the training data...), so even if you've got a rock solid strategy that you're sure will continue to work, make sure you could actually make the trades before you get too excited. Don't assume highs, lows, or opens mean anything, pretty much ever, because weird trades that you couldn't have made sometimes show up in those. If you can, deal with bid/ask data (tick by tick, ideally) instead, and make sure the things you want to trade are actually there long enough to get them given your latency.
Needless to say, use a decent broker that charges low fees and lets you have programmatic access to their trading platform. Most fail on both counts, so beware.
I know that some of the larger operations get live market data from Bloomberg and Reuters. You may want to take a look at https://loginabout.reuters.com/Home/RMDS.aspx although I have no idea how much it costs.