The Power of Lorentz Quantum Computer

Abstract

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 termed bounded-error Lorentz quantum polynomial-time (BLQP), demonstrating its equivalence to the complexity class ${\text{P}}^{♯\text{P}}$. We present LQC algorithms that efficiently solve the problem of maximum independent set, PP (probabilistic polynomial-time), and consequently ${\text{P}}^{♯\text{P}}$, all within polynomial time. Additionally, we show that the quantum computing with postselection proposed by Aaronson can be efficiently simulated by LQC, but not vice versa.

18 pages, 8 figures