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arXiv:2111.05561 · Physical Review A

Arbitrary entangled state transfer via a topological qubit chain

Chong Wang, Linhu Li, Jiangbin Gong, Yu-xi Liu

Published Nov 10, 2022• 35 citations
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Abstract

Quantum state transfer is one of the basic tasks in quantum information processing. We here propose a theoretical approach to realize arbitrary entangled state transfer through a qubit chain, which is a class of extended Su-Schrieffer-Heeger models and accommodates multiple topological edge states separated from the bulk states. We show that an arbitrary entangled state, from two qubits to $\mathcal{N}$ qubits, can be encoded in the corresponding edge states, and then adiabatically transferred from one end to the other of the chain. The dynamical phase differences resulting from the time evolutions of different edge states can be eliminated by properly choosing evolution time. Our approach is robust against both the qubit-qubit coupling disorder and the evolution time disorder. For concreteness of discussions, we assume that such a chain is constructed by an experimentally feasible superconducting qubit system, but our proposal can also be applied to other systems.

DOI
10.1103/physreva.106.052411

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Quantum state transfer is one of the basic tasks in quantum information processing. We here propose a theoretical approach to realize arbitrary entangled state transfer through a qubit chain, which is a class of extended Su-Schrieffer-Heeger models and accommodates multiple topological edge states separated from the bulk states. We show that an arbitrary entangled state, from two qubits to N\mathcal{N}N qubits, can be encoded in the corresponding edge states, and then adiabatically transferred from one end to the other of the chain. The dynamical phase differences resulting from the time evolutions of different edge states can be eliminated by properly choosing evolution time. Our approach is robust against both the qubit-qubit coupling disorder and the evolution time disorder. For concreteness of discussions, we assume that such a chain is constructed by an experimentally feasible superconducting qubit system, but our proposal can also be applied to other systems.
Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.
Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible scheme for robust QST via topologically protected edge states in superconducting circuits. Using superconducting X-mon qubits with tunable couplings, the generalized Su-Schrieffer-Heeger models with topological magnon bands can be constructed. A novel entanglement-dependent topological Thouless pumping can be directly observed in this system. More importantly, we show that single-qubit states and entanglement can be robustly transferred with high fidelity in the presence of qubit-coupling imperfection, which is a hallmark of topological protection. This approach is experimentally applicable to a variety of quantum systems.
We propose a protocol using a tunable Xmon qubit chain to construct generalized Su-Schrieffer-Heeger (SSH) models that support various topological phases. We study the time evolution of a single-excitation quantum state in a SSH-type qubit chain and find that such dynamics is linked to the topological winding number. We also investigate the adiabatic transfer of a single-excitation quantum state in a generalized SSH-type qubit chain and show that this process can be connected with the topological Chern number and be used to generate an entanglement-dependent topological pumping. All results have been demonstrated to be robust against qubit coupling imperfections and can be observed in a short Xmon qubit chain. Our study provides a simple method to directly measure topological invariants rooted in momentum space using quantum dynamics in real space.
As is well known, within the single-excitation subspace, the Su-Schrieffer-Heeger (SSH) model exhibits a remarkable ability to transfer an excitation from one end of the lattice to the other. In this work, by relaxing the restriction of the single excitation, we find that a topological channel formed by the topological edge modes of the SSH model can also realize the transfer of arbitrary Gaussian states. Specifically, we investigate the state transfer process within a one-dimensional (1D) optomechanical lattice, which can be mapped to the SSH model with tunable coupling strength. By initially preparing the first optical mode in a squeezed vacuum state and adiabatically varying the system parameters over a full cycle, the squeezed vacuum state can be transferred to the NthN\mathrm{th}Nth mechanical mode. Furthermore, we extend our investigation to the transfer of arbitrary Gaussian states. Since Gaussian states can be described by the covariance matrix of the system, we reformulate the evolution equation of the covariance matrix in a Schr\"odinger-type equation. This reformulation provides us with an intuitive way to show how an arbitrary Gaussian state is transferred. Our work broadens the application of topological systems for quantum state transfer, demonstrating that not only single-excitation states but also arbitrary Gaussian states, which include multiple excitations and quantum coherence, can be efficiently transferred, with potential implications for quantum information processing.
We present a fast and robust protocol for realizing topological quantum state transfer in a dimeric Su-Schrieffer-Heeger spin chain. By giving a more general condition sufficient for the resonant adiabatic evolution, we develop a method of constructing time-driving functions for topological quantum state transfer, which makes it possible to shorten the needed operation time via resonant adiabatic passage between topologically protected edge states. Compared with previous protocols, our protocol can shorten the operation time appreciably while maintaining robustness against disorder in the spin chain, thereby avoiding decoherence resulting from long-running evolution and increasing transmission efficiency. Numerical simulations demonstrate that our protocol possesses excellent robustness and scalability. Our results provide a promising route for the realization of fast and robust quantum state transfer in spin chain systems.
Topological insulators have inspired the study with various quantum simulators. Exploiting the tunability of the qubit frequency and qubit-qubit coupling, we show that a superconducting qubit chain can simulate various topological band models. When the system is restricted to the single-spin excitation subspace, the Su-Schrieffer-Heeger (SSH) model can be equivalently simulated by alternating the coupling strength between neighboring qubits. The existence of topological edge states in this qubit chain is demonstrated in the quench dynamics after the first qubit is excited. This excitation propagates along the chain where the qubit-qubit coupling is homogeneous. In contrast, in our qubit chain, the spin-up state localizes at the first qubit and the rest qubits remain in the spin-down state. We further show that the spin-up state can be transported along the chain by modulating the coupling strengths and the qubit frequencies. This demonstrates adiabatic pumping based on the Rice-Mele model. Moreover, we also discuss possible ways to construct other topological models with different topological phenomena within the current technology of superconducting qubits.