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Although CO_{2} and SiO_{2} both belong to group-IV oxides, they exhibit remarkably different bonding characteristics and phase behavior at ambient conditions. At room temperature, CO_{2} is a gas, whereas SiO_{2} is a covalent solid with rich polymorphs. A recent successful synthesis of the silicon-carbonate solid from the reaction between CO_{2} and SiO_{2} under high pressure [M. Santoro et al., Proc. Natl. Acad. Sci. U.S.A. 108, 7689 (2011)] has resolved a long-standing puzzle regarding whether a Si_{x}C_{1−x}O_{2} compound between CO_{2} and SiO_{2} exists in nature. Nevertheless, the detailed atomic structure of the Si_{x}C_{1−x}O_{2} crystal is still unknown. Here, we report an extensive search for the high-pressure crystalline structures of the Si_{x}C_{1−x}O_{2} compound with various stoichiometric ratios (SiO_{2}:CO_{2}) using an evolutionary algorithm. Based on the low-enthalpy structures obtained for each given stoichiometric ratio, several generic structural features and bonding characteristics of Si and C in the high-pressure phases are identified. The computed formation enthalpies show that the SiC_{2}O_{6} compound with a multislab three-dimensional (3D) structure is energetically the most favorable at 20 GPa. Hence, a stable crystalline structure of the elusive Si_{x}C_{1−x}O_{2} compound under high pressure is predicted and awaiting future experimental confirmation. The SiC_{2}O_{6} crystal is an insulator with elastic constants comparable to typical hard solids, and it possesses nearly isotropic tensile strength as well as extremely low shear strength in the 2D plane, suggesting that the multislab 3D crystal is a promising solid lubricant. These valuable mechanical and electronic properties endow the SiC_{2}O_{6} crystal for potential applications in tribology and nanoelectronic devices, or as a stable solid-state form for CO_{2} sequestration.