Since you want to limit the question to the Enterprise D; the "main computer" (which is actually a system of 2 redundant cores) uses isolinear chips and circuits to carry out the bulk of its tasks.

  These seem to conform to a traditional Turing machine, altough they are much faster than previous systems (such as duotronics). The greatest argument against the Enterprise D using only turing machine computing would be the gel packs.

Gel packs were mostly used in Voyager, but do make up a part of the Enterpise D's systems. They are organic, and use what appear to be neural networks to carry out fuzzy logic.

EDIT: A non-cannon argument for quantum computers (which would not be Turing machines) is found in the ST:TNG Technical Manual. It says that "Each main core incorporates a series of miniature subspace field generators, which creates a symmetrical (nonpropulsive) field distortion of 3350 millicochranes within the faster-than-light (FTL) core elements."

I don't recall what the current knowledge of quantum computing at the time of TNG being produced was, so this might have been the writers trying to create a quantum computer without knowing what one was (which can be hinted at by the FTL processing).

Since you want to limit the question to the Enterprise D; the "main computer" (which is actually a system of 2 redundant cores) uses isolinear chips and circuits to carry out the bulk of its tasks. These seem to conform to a traditional Turing machine, altough they are much faster than previous systems (such as duotronics).

In Voyager, we have gel packs, which are organic, and use what appear to be neural networks to carry out fuzzy logic.

EDIT: A non-cannon argument for quantum computers (which would not be Turing machines) is found in the ST:TNG Technical Manual. It says that "Each main core incorporates a series of miniature subspace field generators, which creates a symmetrical (nonpropulsive) field distortion of 3350 millicochranes within the faster-than-light (FTL) core elements."

I don't recall what the current knowledge of quantum computing at the time of TNG being produced was, so this might have been the writers trying to create a quantum computer without knowing what one was (which can be hinted at by the FTL processing).

Since you want to limit the question to the Enterprise D; the "main computer" (which is actually a system of 2 redundant cores) uses isolinear chips and circuits to carry out the bulk of its tasks.

These seem to conform to a traditional Turing machine, altough they are much faster than previous systems (such as duotronics). The greatest argument against the Enterprise D using only turing machine computing would be the gel packs.

Gel packs were mostly used in Voyager, but do make up a part of the Enterpise D's systems. They are organic, and use what appear to be neural networks to carry out fuzzy logic.

Since you want to limit the question to the Enterprise D; the "main computer" (which is actually a system of 2 redundant cores) uses isolinear chips and circuits to carry out the bulk of its tasks.

These seem to conform to a traditional Turing machine, altough they are much faster than previous systems (such as duotronics). The greatest argument against the Enterprise D using only turing machine computing would be the gel packs.

Gel packs were mostly used in Voyager, but do make up a part of the Enterpise D's systems. They are organic, and use what appear to be neural networks to carry out fuzzy logic.

EDIT: A non-cannon argument for quantum computers (which would not be Turing machines) is found in the ST:TNG Technical Manual. It says that "Each main core incorporates a series of miniature subspace field generators, which creates a symmetrical (nonpropulsive) field distortion of 3350 millicochranes within the faster-than-light (FTL) core elements."

I don't recall what the current knowledge of quantum computing at the time of TNG being produced was, so this might have been the writers trying to create a quantum computer without knowing what one was (which can be hinted at by the FTL processing).