Physics and computation: An insight from non-Hermitian quantum computing

TL;DR

This paper introduces a non-Hermitian quantum computing model that can solve complex problems efficiently, highlighting the deep link between physics and computation.

Contribution

It proposes a non-Hermitian quantum computer model with a non-unitary gate, demonstrating its ability to solve NP and P^#P problems efficiently.

Findings

NQC can solve all NP problems in polynomial time.

NQC can solve all P^#P problems in polynomial time.

The computational power stems from exponentially large physical resources.

Abstract

We elucidate the profound connection between physics and computation by proposing and examining the model of the non-Hermitian quantum computer (NQC). In addition to conventional quantum gates such as the Hadamard, phase, and CNOT gates, this model incorporates a non-unitary quantum gate $G$. We show that NQC is extraordinarily powerful, capable of solving not only all NP problems but also all problems within the complexity class $\text{P}^{\sharp\text{P}}$ in polynomial time. We investigate two physical schemes for implementing the non-unitary gate $G$ and find that the remarkable computational power of NQC originates from the exponentially large physical resources required.