Robust teleportation of a surface code and cascade of topological quantum phase transitions

Abstract

Teleportation is a facet where quantum measurements can act as a powerful resource in quantum physics, as local measurements allow to steer quantum information in a non-local way. While this has long been established for a single Bell pair, the teleportation of a many-qubit entangled state using non-maximally entangled resources presents a fundamentally different challenge. Here we investigate a tangible protocol for teleporting a long-range entangled surface code state using elementary Bell measurements and its stability in the presence of coherent errors that weaken the Bell entanglement. We relate the underlying threshold problem to the physics of anyon condensation under weak measurements and map it to a variant of the Ashkin-Teller model of statistical mechanics with Nishimori type disorder, which gives rise to a cascade of phase transitions. Tuning the angle of the local Bell measurements, we find a continuously varying threshold. Notably, the threshold moves to infinity for the $X+Z$ angle along the self-dual line -- indicating that infinitesimally weak entanglement is sufficient in teleporting a self-dual topological surface code. Our teleportation protocol, which can be readily implemented in dynamically configurable Rydberg atom arrays, thereby gives guidance for a practical demonstration of the power of quantum measurements.

7 + 5 pages; 5 + 3 figures

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Cited by in corpus (15)

• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Entanglement swapping in critical quantum spin chains
• Perturbative stability and error correction thresholds of quantum codes
• Coherent information as a mixed-state topological order parameter of fermions
• Playing nonlocal games across a topological phase transition on a quantum computer
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Multipartite entanglement structure of monitored quantum circuits
• Fundamental thresholds for computational and erasure errors via the coherent information
• Mixed-State Topological Order under Coherent Noise
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Revisiting Nishimori multicriticality through the lens of information measures
• GAN decoder on a quantum toric code for noise-robust quantum teleportation
• Noisy Monitored Quantum Circuits
• Holographic duality between bulk topological order and boundary mixed-state order