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If the QI drive actually works (I'm skeptical), it would be pushing against the mass of the Universe or the local area in the galaxy/solar system, without touching said mass. Vastly more efficient (understated) than using on board propellant to push against.

Of course, "dark matter" could just be rogue planets, black dwarfs, cold neutron stars, near absolute zero, or just small black holes with no accretion.