While I do know that there is no possible explanation for how we might wake someone up from such a long sleep, I was wondering what food would be edible after one million or so years where the humans on board went into cryosleep.
I have researched long lasting foods that will last indefinitely, and so far I have only come up with oats, sugar, honey, hard liquor and white rice.
Are there any methods for preserving foods other than these that will allow it to last indefinitely?
Put the food into cryosleep as well. If the people don't degrade, neither will the food.
Don't. Your ship will almost certainly need a large amount of food for after they wake up and you don't want to store that much food and take it with you.
Store a few frozen seeds with the frozen people. Defrost them months before and use hydroponics, unless you have the tech to synthesize food from the raw elements on board. PS 1 000 000 years would be a rather large timescale for such things. It would be 60 light years at the speed earth moves round the sun. Such ships would move faster and probably not as far at first.
The ship would need to provide a contained space housing plants and animals that would breed and die over generations. Flora and fauna would evolve and change over a million years, but the food would likely still be edible.
I suspect any contained and artificial ecosystem would need to be highly tuned to prevent its eventual collapse, but it is doable. We're here after all and the Earth has been hurtling through space for billions of years.
Made on demand food. Very stable building blocks like sugars, water, amino acids and the like are stored or harvested and food is assembled on demand. Like 3D printing a steak and potatoes, building the components from simple ingredients.
There are currently no methods for preserving food as long as a million years. If someone claims they have such a method, your correct response to their claim should be "Have you tested it with a million years trial to confirm it works?". Claims of ancient seeds thousands of years old that are still viable have been made, but it looks those claims have not been conclusively proven.
If you are willing to use methods of long term food preservation that don't exist yet (science fiction) you might consider:
Extreme cold tends to really slow down chemical reactions. If you store foods close to absolute zero and hand-wave some technology that prevents the physical damage caused by the freezing process (mostly caused by water expanding into ice crystals, breaking the frozen item's structure), you can say that you use cryofreeze for long term storage. The advantage of using this method in a story is that in deep space keeping things really cold is not difficult.
Long term biospheres to allow food to survive thousands of generations works only if you are able to sustain a biosphere for that long. We know it works in principle, since this is how the Earth works to provide the food we eat. The problem comes in making a much smaller biosphere such as in a spaceship sustainable over long periods of time. One way to explain how your spaceship biosphere remains stable is to create a supervisory computer that regulates problems that will occur in the spaceship biosphere over time.
If you want to go really high tech, you can avoid the preserving/storage problem entirely. Just have your computer build DNA for all the life you want to put into your biosphere from information it has stored and from basic chemicals. If the computer jumpstarts a biosphere when the spaceship gets to its destination a million years later, the only reliable storage needs to be for the data and the ability of the DNA reproduction machinery to last that long.
Preserve the food using the same methods used on the crew. Perhaps that means putting livestock into cryosleep if "dead" things can't work with the same methods.
If the environment is sterilized, food won't decay. Just bathe the whole pantry in radiation, let out the air (you're in space, right?), and it'll last forever. Water will sublimate out of the food though, so you'll want to start with freeze-dried stuff to begin with or it'll taste like bad freezer-burn.
Something to be concerned about: cosmic rays may cause the food molecules to degrade into dust over millions of years. Make sure your pantry is well-shielded. If you're traveling in interstellar space far away from any stars, though, this should be less of an issue.
A million years?! That is a near unsolvable problem. You cannot bring anything that you expect to grow, because growing requires functioning DNA. And DNA degrades over time, with a half-life of only little over 500 years.
You would have to go for really basic substances... almost down to elements, like carbon, nitrogen, oxygen, hydrogen and phosphorous, and then reconstitute those into basic nutrients like vitamins, hydrocarbons and such.
Then there is also the problem of surviving a cryosleep that long. What I said about DNA degrading over time also goes for your travelers. Their DNA will degrade over time. And without functioning DNA, they will not wake up again. Or if they do, they will soon die pretty much as if they has walked into a running nuclear reactor.
However... handwaving away the problem the problem of DNA degradation — maybe by not putting them in actual cryo-sleep but in a form of stasis, where the DNA repair mechanisms of the body can do their work — then it could work. But since foods are "dead" already, DNA repair on things you would want to grow cannot work. So you are stuck with what I said above: reconstitute nutrients from basic elements, because you cannot bring organics and expect them to hold for a million years. You have to bring things that cannot spoil... and only basic substances and elements have that quality.
Hard Scifi Answer
Sorry kind of side stepped the problem but here would by a solution.
Develop nanobots that repair themselves and the spaceship elements and periodically the people in cryo. This can be tested for stability against various challenges (radiation, extreme cold, heat, electrical burnouts, vacuum) before leaving on the voyage. Nanobots would have a swarm intelligence and read molecular layouts so everything is in a sort of stasis. With this tech, some humans could could continue to live on as caretakers as well. With their DNA being continually repaired to that of 20 year olds.
Then for story elements...
Of course after a million years the nanobots have developed sentience and view humans as babies, irrelevant, gods, or raw materials. Take your pick and the human caretakers are no longer human but have changed themselves due to modifying the stasis layouts of their DNA....
For the science http://iopscience.iop.org/article/10.1088/0957-4484/15/11/045/meta
Sterilizing it is an option except that any method we have for that damages the nutrition severely.
Poisoning it (like with liquor or preservatives) also isn't necessarily the best option.
But the other items you listed follow the principle that each of these foods is incomplete... it's a very terrible food on its own, and has to be added to other things to be a proper diet. Microorganisms need to live on top of the thing, not just eat it... they won't take a piece of one and drag it to the other part (like bringing the rice to water or vice versa) so they don't seem to ever touch consume them. Surely in the future you could separate the components from the food without damaging them too badly (eg. condensed milk tastes horrible because it's so damaged, worse than pasteurization).
And one example you didn't list... butter will go bad, but clarified butter takes an extremely long time (not ever scientifically tested to the limit as far as I can tell... maybe forever if produced perfectly and kept out of the sun, cold, etc.). So not just carbs, but fats also can last long. When you clarify the butter, ideally use sour butter which has less/no sugar, and you are removing milk solids, water, etc. so it's the same concept.
Also if you pile enough salt on meat so it soaks right through and sucks out all the moisture (like a whole leg of prosciutto), it lasts enormously long. It only expires quickly after you unbury it or slice it up. And even then, it might just dry up worse and not really rot very fast.
And it'll still break down possibly, but not so much by ordinary life forms. Also as stated in other answers, you still can never be sure since nobody tested such things for a million years. Maybe nothing will be perfect, but a combination of things will be closer than any single method, and close enough for your space voyage.
If you can "store" people for a million years and revive them, then worst case: cannibalism.
Seriously, if you can store human beings and revive them, can't you use exactly the same techniques to store meat?
