量子纠错码中的测量与前馈电路

中文摘要 AI 辅助

测量和前馈增强了浅层量子电路的能力，使得全局幺正操作的确定性实现和长程纠缠态的制备成为可能。我们在所有此类协议与量子纠错码之间建立了一种一般性的对应关系：测量之前的电路充当编码器，并且当且仅当测量投影算符是码空间上的可检测错误时，幺正前馈可以消除后选择。这种对应关系为利用测量和前馈进行态制备和全局幺正操作的实现提供了一个通用框架，将两者都转化为码设计问题。对于具有泡利测量的稳定子码，尽管所得操作可以是非克利福德的，我们证明其非稳定子性完全源于编码器。我们利用非泡利测量或非加性码克服了这一限制，构造了仅需单量子比特幺正校正即可产生长程非稳定子性的协议。

英文摘要

Measurements and feedforward enhance the power of shallow quantum circuits, enabling the deterministic implementation of global unitary operations and the preparation of long-range entangled states. We establish a general correspondence between all such protocols and quantum error-correcting codes: the circuit preceding the measurements acts as an encoder, and unitary feedforward can eliminate post-selection if and only if the measurement projectors are detectable errors on the codespace. This correspondence provides a common framework for state preparation and implementation of global unitaries with measurements and feedforward, turning both into a code-design problem. For stabilizer codes with Pauli measurements, although the resulting operation can be non-Clifford, we show that its nonstabilizerness originates entirely from the encoder. We overcome this restriction using non-Pauli measurements or non-additive codes, constructing protocols that generate long-range nonstabilizerness while requiring only single-qubit unitary corrections.

发表机构

• Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
• Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）

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