Can the next U.S. President undo the current President's pardons?
No. There are few if any checks on any President for any Pardons issued (a general Impeachment may be the only check but there has never been a strong call for impeachment for a pardon.). Further more, the protection against Double Jeopardy is in effect meaning future Presidents cannot prosecute the pardon recipient for any crimes that were pardoned by a previous president, though they may prosecute any future criminal incidents perpetrated by the pardoned person that are not related to the events surrounding the pardoned crime.
"The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to Grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment." U.S. Const. Art. I, sec. II, cl. I (emphasis added).
Just thought that we should at least get that part out of the way. I would -- if I had a client and they were pardoned by the President, and the next President reversed his pardon -- argue first that no "person be subject for the same offence to be twice put in jeopardy of life or limb" under the Eighth Amendment, and that perhaps the res judicata doctrine would apply since a pardon ends imprisonment, or sometimes, like in the case of Joe Arpaio, when he was held and convicted in/of Contempt of Court, prevents sentencing from occuring at all after a conviction. See https://www.justice.gov/pardon/file/993586/download.