Universal quantum computing with a single arbitrary gate

• URL: http://arxiv.org/abs/2409.20025v1
• Date: Mon, 30 Sep 2024 07:30:57 GMT
• Title: Universal quantum computing with a single arbitrary gate
• Authors: Zhong-Yi Ni, Yu-Sheng Zhao, Jin-Guo Liu,
• Abstract summary: We show almost any target gate can be compiled to precision $epsilon$ with a circuit depth of approximately $log(epsilon-1)$. Under the assumption of reasonable classical resource, we show the gate imperfection can be lowered to $10-3$. By treating the imperfection as coherent error, we show that the error can be further reduced by roughly two orders of magnitude.
• Score: 1.1246601908663711
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing a single arbitrary gate for compiling is beneficial for systems with limited degrees of freedom, e.g. the scattering based quantum computing schemes. However, how to efficiently compile the wanted gate with a single arbitrary gate, and finally achieve fault-tolerant quantum computing is unknown. In this work, we show almost any target gate can be compiled to precision $\epsilon$ with a circuit depth of approximately $\log(\epsilon^{-1})$ with an improved brute-force compiling method. Under the assumption of reasonable classical resource, we show the gate imperfection can be lowered to $10^{-3}$. By treating the imperfection as coherent error, we show that the error can be further reduced by roughly two orders of magnitude with a measurement-free quantum error correction method.

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