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Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are particularly promising for a large-scale quantum computer due to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent due to the slow operation.Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the condition of qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate the universal gate fidelity beyond the fault-tolerance threshold and pave the way for scalable silicon quantum computers.
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured err
In this paper we introduce a universal operator theoretic framework for quantum fault tolerance. This incorporates a top-down approach that implements a system-level criterion based on specification of the full system dynamics, applied at every level
We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the information remains protected.
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivale
We extensively test a recent protocol to demonstrate quantum fault tolerance on three systems: (1) a real-time simulation of five spin qubits coupled to an environment with two-level defects, (2) a real-time simulation of transmon quantum computers,