Curator's Take
This article challenges a fundamental assumption in quantum computing by demonstrating that non-Hermitian quantum computers can achieve their full computational power using only real numbers, eliminating the need for complex arithmetic that has long been considered essential to quantum mechanics. The researchers show that a surprisingly minimal set of real gates can solve problems in the complexity class P^#P, which includes notoriously difficult counting problems, suggesting that the non-unitary nature of these systems rather than mathematical complexity drives their computational advantage. This finding could significantly simplify the theoretical framework for non-Hermitian quantum computing and potentially lead to more practical implementations, since real number operations are generally easier to control and less prone to certain types of errors than complex number manipulations. The work represents an important step toward understanding what mathematical resources are truly necessary for quantum computational speedups beyond classical computers.
— Mark Eatherly
Summary
In traditional quantum computing, it has been established that real quantum computation augmented with non-Clifford gates is as powerful as universal quantum computation. Here we investigate this phenomenon in the non-Hermitian setting. We show that a non-Hermitian quantum computer equipped with the real gate set ${H, \text{CCNOT}, G}$, where $G = \operatorname{diag}(g^{-1}, g)$ with $g > 0$ and $g \neq 1$, can solve problems in $\text{P}^{\sharp\text{P}}$ in polynomial time, matching the capability of its universal non-Hermitian counterpart ${H, T, \text{CNOT}, G}$. This demonstrates that non-unitarity, rather than universality, is the essential resource, and that complex numbers are unnecessary.