The Quantum Torpedo is the first of probably many efforts by Starfleet to come up new weaponry to replace those that they have relied on for inordinately long periods of time. As its name implies the Quantum Torpedo relies on releasing what is known as a Quantum Energy Reaction.
Theoretically a Quantum Energy Reaction is something that by virtue of its existence would disprove the old theory that mass and energy can be neither created nor destroyed. In the most basic description, a Quantum Torpedo works by folding and compressing the fabric of space until such time that it collapses into itself and forms a new particle. This process could be likened to a miniature "big bang" as the as the sudden release of these new particles generates an inordinate amount of energy. The location in which space collapses into this new particle is called the "Zero Point" hence the name zero point energy. The subspace disruption located in the Zero Point is what gives the Quantum Torpedo such lethality against energy shielding. The fact a Quantum Reaction relies on folding space to create new particles has lead some other brands to utilize the term "Creation Energy" in exchange for Quantum Reaction. The fact that current science believes matter can be broken down into single dimensional matter streams lends credence to the possibility of a Quantum Reaction.
It has been conjectured that the Quantum Torpedo; like its older brother the Photon Torpedo utilizes a magnetically contained antimatter stream. This does not seem unreasonable as a reaction such as this would take a "kickstarting" energy source. Much in the same way the Hydrogen Bomb utilizes a plutonium warhead to ignite its deuterium supply.
On a side note, Quantum Torpedoes seem much more adept then their predecessors at penetrating a ships hull. In Star Trek First Contact we bare witness as the Enterprise destroys an unshielded Borg Sphere with four quantum torpedoes. if one pays close attention they will note that the four torpedoes disappear into the hull of the ship before exploding. Indicating they have burrowed deep in the hull prior to detonation. This is a certain improvement over the photon torpedo which only penetrated a hull if it was successful in completely breaching a hull. (Star Trek XI: The Undiscovered Country)