The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale^{1,2,3,4,5,6,7,8,9,10}. However, the operation of the large number of qubits required for advantageous quantum applications^11,12,13 will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher^{14,15,16,17,18}. Here we tune up and operate spin qubits in silicon above 1 K, with fidelities in the range required for fault-tolerant operations at these temperatures^19,20,21. We design an algorithmic initialization protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies and incorporate radiofrequency readout to achieve fidelities up to 99.34% for both readout and initialization. We also demonstrate single-qubit Clifford gate fidelities up to 99.85% and a two-qubit gate fidelity of 98.92%. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for the high-fidelity operation to be possible, surmounting a main obstacle in the pathway to scalable and fault-tolerant quantum computation.

半导体自旋载流子中的量子位编码已被认为是商业量子计算机的一种有前途的方法，可以以光刻方式生产并以^{1,2,3,4,5,6,7,8,9,10}的规模集成。然而，有利的量子应用^11、12、13所需的大量量子位的操作将产生超过毫开温度下低温恒温器的可用冷却能力的热负荷。随着规模扩大的加速，建立 1 K 以上的容错操作变得势在必行，此时冷却功率要高出几个数量级^{14,15,16,17,18}。在这里，我们在 1 K 以上的硅中调整和操作自旋量子位，保真度处于这些温度下容错操作所需的范围内^19,20,21。我们设计了一种算法初始化协议，即使热能远高于量子位能量，也能准备纯双量子位状态，并结合射频读出，以实现读出和初始化高达 99.34% 的保真度。我们还证明了单量子位 Clifford 门保真度高达 99.85%，双量子位门保真度高达 98.92%。这些进步克服了热能必须远低于量子位能量才能实现高保真操作的基本限制，克服了可扩展和容错量子计算途径中的主要障碍。