Quantum Routing with Teleportation

Abstract

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation - showing an $O(\sqrt{N\log N})$ upper bound on the separation in routing time for any interaction graph - and give tighter bounds for some common classes of graphs.

12 pages, 7 figures

References in corpus (19)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Teleportation is a Universal Computational Primitive
• Topological quantum memory
• Quantum Communication Through an Unmodulated Spin Chain
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Quantum Low-Density Parity-Check Codes
• Quantum LDPC Codes with Almost Linear Minimum Distance
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Long-range entanglement from measuring symmetry-protected topological phases
• A Quantum Router Architecture for High-Fidelity Entanglement Flows in Quantum Networks
• Surface code compilation via edge-disjoint paths
• Entanglement generation in a quantum network at distance-independent rate
• Dual-Species, Multi-Qubit Logic Primitives for Ca+/Sr+ Trapped-Ion Crystals
• Advantages and limitations of quantum routing
• Long-range-enhanced surface codes
• Quantum routing with fast reversals
• Quantum linear network coding for entanglement distribution in restricted architectures
• Entanglement bounds on the performance of quantum computing architectures

Cited by in corpus (4)

• Toward a 2D Local Implementation of Quantum LDPC Codes
• High-precision and low-depth quantum algorithm design for eigenstate problems
• Quantum Routing and Entanglement Dynamics Through Bottlenecks
• Basic entanglement distillation with realistic noise