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arXiv · 2506.18012

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

Qi Zhang·Biao Wu
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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.

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Qi Zhang, Biao Wu. 2025-06-22. Physics and computation: An insight from non-Hermitian quantum computing. https://arxiv.org/abs/2506.18012

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