  We demonstrate the superior capabilities of the recently proposed Lorentz
quantum computer (LQC) compared to conventional quantum computers. We introduce
an associated computational complexity class, bounded-error Lorentz quantum
polynomial-time (BLQP), and prove that the complexity class ${\text P}^{\sharp
\text{P}}$ is contained within BLQP. We present LQC algorithms that solve in
polynomial time the problem of maximum independent set and the problems in the
classes of NP, co-NP, PH (polynomial hierarchy), PP (probabilistic
polynomial-time), and ${\text P}^{\sharp \text{P}}$. We show that the quantum
computing with postselection proposed by Aaronson can be simulated efficiently
by LQC, but not vice versa.
