Sleep can get pretty disruptive the first few days. Some people will get very little sleep, waking up every hour or not sleeping at all yet not feel tired. Others can sleep 20 hours a day and be exhausted during their waking hours. Whichever way it goes, sleep will adjust itself when you quit and eventually go back to normal.
But there is a catch. You don't know what normal is. Normal is what it was prior to being a smoker with aging thrown in. Some people have not been normal for decades.
Nicotine is a stimulant drug that once it wore off through the smoker into a physiological depressed state. To overcome the smoker would smoke again, thus stimulating him or herself. Which would soon wear off and so on and so on. All the while shooting up blood sugar and hormonal levels and crashing them later. By the end of the day the smoker could be physically exhausted from this chronic stimulant/depressant roller coaster. They had to adjust their sleep around these effects.
Without this chronic abuse, these ex-smokers may find that they can get by on less sleep after they quit smoking, sometimes knocking out hours of what they thought was needed sleep time. Others only minimize sleep by a short time period but it is very obvious when the alarm goes off they can jump out of bed full of energy and ready to go or sometimes even wake up before the alarm with new found energy. When they were smokers they were often exhausted upon waking, hating the alarm and needing cigarettes to wake up and get going.
There are a smaller number of people who need more sleep when they are ex-smokers. These are people who often smoked heavily at the tail end of their days. Their bodies were crying for sleep but they kept pumping nicotine into their system to override the bodies need. Without a constant stimulant they now have to listen to their bodies and go to bed when tired. They could take speed and get the same effects but normally realize that they wouldn't resort to a drug for this effect, yet they can rationalize that smoking was OK for the same purpose. Well it wasn't, it was allowing the smoker to maintain such a schedule at a cost. And the long range cost for this "benefit" could be death.
Anyway, don't panic by the sleep amount the first few days. It is not your normal amount of sleep as an ex-smoker, it is your normal amount of sleep while in drug withdrawal. This is not a normal time or a long lasting time period. Sleep will eventually settle in to a normal pattern for you as an ex-smoker. Then aging will exert its normal adjustments. Whether it turns out to be more sleep or less, you should at least sleep sounder knowing you are no longer under the control of nicotine and no longer posing such a deadly risk to yourself by still smoking. To sleep happier because you know you are staying healthier and likely to live longer, always remember all the times you are awake to never take another puff!