自主量子纠错方案的自动发现
Automated discovery of autonomous quantum error correction schemes
摘要：
我们可以在量子系统的能级中对量子比特进行编码。弛豫和其他耗散过程导致这种存储信息的保真度衰减。是否有可能通过引入额外的驱动和耗散来更长时间地保存量子信息？自治量子纠错码的存在肯定地回答了这个问题。尽管如此，为真实的物理系统发现这些代码，找到编码和相关的驱动场和浴耦合仍然是一个挑战，需要直觉和灵感来克服。在这项工作中，我们开发和展示了一种计算方法的基础上，伴随优化发现自治量子纠错码给定的描述的物理系统。我们实现了一个优化器，搜索一个逻辑子空间和控制参数，以更好地保存量子信息。我们证明了我们的方法耦合到一个有损量子比特的谐振子系统，并发现，在福克空间中的不同的哈密顿距离-控制硬件复杂性的代理-导致发现不同的和新的纠错方案。我们发现我们所谓的$\sqrt{3}$代码，实现与哈密顿距离$d=2$，并提出了一个硬件高效的实现超导电路的基础上。
英文摘要：
We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by introducing additional drives and dissipation? The existence of autonomous quantum error correcting codes answers this question in the positive. Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overcome. In this work, we develop and demonstrate a computational approach based on adjoint optimization for discovering autonomous quantum error correcting codes given a description of a physical system. We implement an optimizer that searches for a logical subspace and control parameters to better preserve quantum information. We demonstrate our method on a system of a harmonic oscillator coupled to a lossy qubit, and find that varying the Hamiltonian distance in Fock space -- a proxy for the control hardware complexity -- leads to discovery of different and new error correcting schemes. We discover what we call the $\sqrt{3}$ code, realizable with a Hamiltonian distance $d=2$, and propose a hardware-efficient implementation based on superconducting circuits.
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