Guoding Liu

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this work, we rigorously prove through information-theoretic analysis that one-dimensional logarithmic-depth random Clifford encoding circuits can achieve high quantum error correction performance. We demonstrate that these random codes typically exhibit good approximate quantum error correction capability by proving that their encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors. We show that the error correction inaccuracy decays once a threshold of logarithmic depth is exceeded, resulting in negligible recovery errors. This threshold is shown to be lower than that of the simple separate block encoding, and the decay rate is higher. We further establish that these codes are optimal by proving that logarithmic depth is necessary to maintain a constant encoding rate and high error correction performance. To prove our results, we propose new decoupling theorems for one-dimensional low-depth circuits. These results also imply strong decoupling and rapid thermalization properties in low-depth random circuits and have potential applications in quantum information science and physics.

Efficient entanglement distillation is a central task in quantum information science and future quantum networks. At the core of distillation protocols are the quantum error correction and detection schemes which enhance the fidelity of entangled pairs. Conventional protocols focus on digital systems, which typically require complicated compiled circuits, high-fidelity multi-qubit operations and delicate pulse-level control that impose high demands on near-term hardware. Crucially, the leading physical platforms for quantum networks, trapped ions and neutral atoms, are governed by native many-body Hamiltonians inherently suited for analog, continuous-time evolution. Adopting these natural dynamics is simpler than engineering digital logic via delicate pulse-level control. Motivated by this experimental reality, we seek to leverage the intrinsic analog capabilities for efficient entanglement distillation. In this work, we introduce the Hamiltonian entanglement distillation protocol, which exploits the intrinsic information scrambling generated by random time evolution under native Hamiltonians. We establish a quantitative connection between output fidelity and Out-of-Time-Order Correlators, showing that efficient scrambling directly implies good distillation performance. Since generic Hamiltonians are naturally efficient scramblers, the capability for distillation is ubiquitous: almost all Hamiltonians in the Hilbert space suffice for high-fidelity distillation. Numerical simulations of representative Rydberg-atom and trapped-ion systems further confirm that robust performance could be achieved using only short-range interactions and evolution times feasible in current experiments. By avoiding the complexity of digital circuit control, our approach substantially relaxes experimental requirements, providing a scalable route to entanglement engineering on current analog quantum platforms.

Efficient entanglement distillation is a central task in quantum information science and future quantum networks. At the core of distillation protocols are the quantum error correction and detection schemes which enhance the fidelity of entangled pairs. Conventional protocols focus on digital systems, where good error correction schemes typically require complicated compiled circuits, high-fidelity multi-qubit operations and delicate pulse-level control that impose high demands on near-term hardware. Crucially, the leading physical platforms for quantum networks, trapped ions and neutral atoms, are governed by native many-body Hamiltonians inherently suited for analog, continuous-time evolution. Adopting these natural dynamics is significantly simpler than engineering digital logic via delicate pulse-level control. Motivated by this experimental reality, we seek to leverage the intrinsic analog capabilities for efficient entanglement distillation. In this work, we introduce the Hamiltonian entanglement distillation protocol, which exploits the intrinsic information scrambling generated by random time evolution under native Hamiltonians. We establish a quantitative connection between output fidelity and Out-of-Time-Ordered Correlators, showing that efficient scrambling directly implies good distillation performance. Since generic Hamiltonians are naturally efficient scramblers, the capability for distillation is ubiquitous: almost all Hamiltonians in the Hilbert space suffice for high-fidelity distillation. Numerical simulations of representative Rydberg-atom and trapped-ion systems further confirm that robust performance could be achieved using only short-range interactions and evolution times feasible in current experiments. By avoiding the complexity of digital circuit control, our approach substantially relaxes experimental requirements, providing a scalable route to entanglement engineering on current analog quantum platforms.

Enhancing the performance of quantum key distribution is crucial, driving the exploration of various key distillation techniques to increase the key rate and tolerable error rate. It is imperative to develop a comprehensive framework to encapsulate and enhance the existing methods. In this work, we propose an advantage distillation framework for quantum key distribution. Building on the entanglement distillation protocol, our framework integrates all the existing key distillation methods and offers better generalization and performance. Using classical linear codes, our framework can achieve higher key rates, particularly without one-time pad encryption for postprocessing. Our approach provides insights into existing protocols and offers a systematic way for future enhancements of quantum key distribution protocols.