TL/DR: it depends how one defines "omniscient".
The properties of the tri-omni God (omnipotent, omniscient, omnibenevolent) have given rise to many paradoxes that have been addressed by theologians and apologists. OP's problem is akin to the famous "Can God create a rock so big He can't lift it ?" paradox about God's omnipotence. The classical response is to redefine "omnipotent" as "can do everything that is logically possible".
The same response can be applied to OP's "can God know the result of a single quantic experiment?" and has indeed been applied to similar questions like the problem of free will: "if we have free will how can God know what we are going to do ?". The answer would be "God knows everything that is logically possible to know", and if one insists that God must know things that are impossible to known then the objection formally makes no sense and is not receivable as an argument.
If we go this way, in the case of physics God might not know the result of a singular quantic experiment but can make predictions at the macro level, in the same way we do (except God knows the exact model to apply and the initial conditions with perfect precision). In the same way, God would be able to know our state of mind better than us but be unable to know our next decision because we have free will. If we consider that even I, mere human, can predict with very high certainty my kid is not going to answer "no" if i say "do you want to have cake?", God who knows everything there is to know about psychology and our state of mind at any time could still be able to make very accurate predictions of our behavior without violating free will.