Work

The Power of the Lorentz Quantum Computer

Year: 2026

Type: article

Abstract: We analyze the power of the recently proposed Lorentz quantum computer (LQC), a theoretical model leveraging hyperbolic bits (hybits) governed by complex Lorentz transformations. We define the complexity class BLQP (bounded-error Lorentz quantum polynomial-time) and demonstrate its equivalence to the complexity class P♯P (the class of problems solvable by a deterministic polynomial-time Turing machine with access to a ♯P oracle). LQC algorithms are shown to solve NP-hard problems, such as the maximum independent set (MIS), in polynomial time, thereby placing NP and co-NP within BLQP. Furthermore, we establish that LQC can efficiently simulate quantum computing with postselection (PostBQP), while the reverse is not possible, highlighting LQC's unique "super-postselection" capability. By proving BLQP =P♯P, we situate the entire polynomial hierarchy (PH) within BLQP and reveal profound connections between computational complexity and physical frameworks like Lorentz quantum mechanics. These results underscore LQC's theoretical superiority over conventional quantum computing models and its potential to redefine boundaries in complexity theory.

Source: Entropy

DOI: 10.3390/e28030266

Authors: Qi Zhang, Biao Wu

Institutions: Liaoning Shihua University, University of Science and Technology of China, Peking University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China