Layden David, Chen Mo, Cappellaro Paola
Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2020 Jan 17;124(2):020504. doi: 10.1103/PhysRevLett.124.020504.
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.
量子纠错预计在大规模量子技术中至关重要。然而，人们认为它所需的大量量子比特开销会极大地限制其在较小的近期设备中的效用。在此，我们引入了一类新的专用量子纠错码，与通常的重复码相比，其开销呈指数级降低。它们是针对当前实验中一种常见且重要的退相干源量身定制的，即量子比特寄存器通过与一个公共涨落器（如谐振器或自旋缺陷）耦合而受到相位噪声影响。最小的实例将一个逻辑量子比特编码到两个物理量子比特中，并使用固定数量的单量子比特和双量子比特操作将退相干校正到主导阶。更一般地说，虽然n个量子比特上的重复码将错误校正到(t^{O(n)})阶，其中t是恢复之间的时间，但我们的码能校正到(t^{O(2^{n})})阶。此外，它们对中小规模设备中的模型缺陷具有鲁棒性，在这些设备中它们已经在错误抑制方面提供了显著的提升。因此，这些硬件高效的码为近期的容错前设备中有用的量子纠错开辟了一条潜在途径。
