Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems

• Published in: Physical review. X Vol. 11; no. 3; p. 031016
• Main Authors: Tran, Minh C, Guo, Andrew Y, Deshpande, Abhinav, Lucas, Andrew, Gorshkov, Alexey V
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 01.07.2021
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Decay rate; Entangled states; entanglement manipulation; entanglement production; Gate counting; Lower bounds; MATHEMATICS AND COMPUTING; Optimization; Particle decay; physics; Polynomials; Power law; Privacy; Quantum computing; Quantum entanglement; Quantum mechanics; Quantum phenomena; quantum state transfer; Qubits (quantum computing); Speed limits; Tightness; Atomic and Molecular Physics; Condensed Matter Physics; Quantum Information
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.11.031016

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law interactions. For all power-law exponents between and , where is the dimension of the system, the protocol yields a polynomial speed-up for and a superpolynomial speed-up for , compared to the state of the art. For all , the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. In addition, the protocol provides a lower bound on the gate count in digital simulations of power-law interacting systems.