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.

翻译：我们证明了近期提出的洛伦兹量子计算机（LQC）相比传统量子计算机具有更优越的能力。我们引入了一个相关的计算复杂性类——有界误差洛伦兹量子多项式时间（BLQP），并证明了复杂性类${\text P}^{\sharp \text{P}}$包含于BLQP中。我们提出了能在多项式时间内解决最大独立集问题以及NP、co-NP、PH（多项式层级）、PP（概率多项式时间）和${\text P}^{\sharp \text{P}}$等复杂性类中问题的LQC算法。我们还表明，Aaronson提出的带后选择量子计算可被LQC高效模拟，但反之则不然。