What are the bare minimum nutrients required to survive as a human?
Essential nutrients include (NutrientsReview):


Water
9 amino acids: histidine, isoleucine, leucine, lysine, methionine,
phenylalanine, tryptophan, threonine, valine
2 fatty acids (alpha linolenic and linoleic acid)
Vitamins: A, B1, B2, B3, B5, B6, folic acid, biotin, B12, C,
D, E and K (and choline, which is considered a vitamin-like substance)
Minerals: calcium, chromium, chloride, copper, iodine, iron,
manganese, molybdenum, phosphorus, potassium, selenium, sodium, zinc


The "bare minimum" intakes of most nutrients needed for survival are not known, because they could be determined only by studies in which participants would be given various low amounts of nutrients and observed for how long they can survive. The following are estimations of the lowest intakes of some nutrients needed to remain healthy.. Note, that this are not "recommended" or "optimal" intakes.

Protein = 35 grams per day (Metabolic Basis of Obesity) 

Fat = 20% of total calorie intake, that is 44 g per day in a 2,000 Calorie diet (PubMed, 2017)

Carbohydrates = zero (National Academic Press)

Only 2 fatty acids and 9 amino acids are essential, so theoretically, you could consume only those and would be fine. In foods, these acids usually do not appear individually but as part of fats and proteins, so the recommendation is given for fats and proteins - if you meet that, you will likely consume enough of the essential acids. Theoretically, you can survive without consuming any carbohydrates, because all of them you need can be synthesized in your body. People have survived and remained healthy without consuming carbohydrates for a year or more (National Academic Press).

Sodium = 200 mg per day (Recommended Dietary Allowances: 10th Edition)

Water = 1 liter per day (only in ideal circumstances with minimal sweating; in the table, water requirement = "net water loss") (National Academic Press)



Here's a table with dietary reference intakes for vitamins, minerals, carbohydrates, fats (and separately for the 2 essential fatty acids), proteins and water (Nationalacademics.org), which should be sufficient for most individuals in a given sex/age group to remain healthy long-term. These amounts can be considerably greater than what is needed just for survival.

In Recommended Dietary Allowances: 10th Edition, in the Table 6-1, there are "estimates of amino acid requirements" for all 9 essential amino acids. 

There was a man who was fasting for more than a year, drinking only water and getting potassium supplements, and the concentrations of most nutrients in his blood remained normal and he had no health issues (Postgraduate Medical Journal, 1973). This shows how difficult is to find "bare minimal" amounts of nutrients.

Yes, it is possible to make a "pill" with only essential nutrients in required amounts included. Such products already exist, but I don't want to promote them, because there is no evidence of their long-term health benefits and safety.