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We report on the fault-tolerant operation of logical qubits on a neutral atom quantum computer, with logical performance surpassing physical performance for multiple circuits including Bell states (12x error reduction), random circuits (15x), and a prototype Anderson Impurity Model ground state solver for materials science applications (up to 6x, non-fault-tolerantly). The logical qubits are implemented via the [[4, 2, 2]] code (C4). Our work constitutes the first complete realization of the benchmarking protocol proposed by Gottesman 2016 [1] demonstrating results consistent with fault-tolerance. In light of recent advances on applying concatenated C4/C6 detection codes to achieve error correction with high code rates and thresholds, our work can be regarded as a building block towards a practical scheme for fault tolerant quantum computation. Our demonstration of a materials science application with logical qubits particularly demonstrates the immediate value of these techniques on current experiments.

Variational algorithms are a representative class of quantum computing workloads that combine quantum and classical computing. This paper presents an LLVM-based C++ compiler toolchain to efficiently execute variational hybrid quantum-classical algorithms on a computational system in which the quantum device acts as an accelerator. We introduce a set of extensions to the C++ language for programming these algorithms. We define a novel Executable and Linking Format (ELF) for Quantum and create a quantum device compiler component in the LLVM framework to compile the quantum part of the C++ source and reuse the host compiler in the LLVM framework to compile the classical computing part of the C++ source. A variational algorithm runs a quantum circuit repeatedly, each time with different gate parameters. We add to the quantum runtime the capability to execute dynamically a quantum circuit with different parameters. Thus, programmers can call quantum routines the same way as classical routines. With these capabilities, a variational hybrid quantum-classical algorithm can be specified in a single-source code and only needs to be compiled once for all iterations. The single compilation significantly reduces the execution latency of variational algorithms. We evaluate the framework's performance by running quantum circuits that prepare Thermofield Double (TFD) states, a quantum-classical variational algorithm., Comment: 13 pages, 10 figures, 1 appendix