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arXiv:1909.03646 · Physical Review A

High-fidelity and long-distance entangled-state transfer with Floquet topological edge modes

S. G. Tan, Raditya Weda Bomantara, Jiangbin Gong

Published Aug 10, 2020• 21 citations
arXivHTMLPDF

Abstract

We propose the generation of entangled qubits by utilizing the properties of edge states appearing at one end of a periodically driven (Floquet) superconducting qubit chain. Such qubits are naturally protected by the system's topology and their manipulation is possible through adiabatic control of the system parameters. By utilizing a Y-junction geometry, we then develop a protocol to perform high-fidelity transfer of entangled qubits from one end to another end of a qubit chain. Our quantum state transfer protocol is found to be robust against disorder and imperfection in the system parameters. More importantly, our proposed protocol also performs remarkably well at larger system sizes due to nonvanishing gaps between the involved edge states and the bulk states, thus allowing us in principle to transfer entangled states over an arbitrarily large distance. This work hence indicates that Floquet topological edge states are not only resourceful for implementing quantum gate operations, but also useful for high-fidelity and long-distance transfer of entangled states along solid-state qubit chains.

DOI
10.1103/physreva.102.022608

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We propose the generation of entangled qubits by utilizing the properties of edge states appearing at one end of a periodically driven (Floquet) superconducting qubit chain. Such qubits are naturally protected by the system's topology and their manipulation is possible through adiabatic control of the system parameters. By utilizing a Y-junction geometry, we then develop a protocol to perform high-fidelity transfer of entangled qubits from one end to another end of a qubit chain. Our quantum state transfer protocol is found to be robust against disorder and imperfection in the system parameters. More importantly, our proposed protocol also performs remarkably well at larger system sizes due to nonvanishing gaps between the involved edge states and the bulk states, thus allowing us in principle to transfer entangled states over an arbitrarily large distance. This work hence indicates that Floquet topological edge states are not only resourceful for implementing quantum gate operations, but also useful for high-fidelity and long-distance transfer of entangled states along solid-state qubit chains.
We develop a theoretical framework for fast, robust and high-fidelity topological quantum state transfer in one-dimensional systems with long-range couplings, motivated by chains of Rydberg atoms with dipole-dipole interactions. Such long-range interactions naturally give rise to extended Su-Schrieffer-Heeger and Rice-Mele models supporting topologically protected edge states. We show that these edge states enable high-fidelity edge-to-edge excitation transfer using both time-independent protocols, based on coherent edge state dynamics, and time-dependent protocols, based on adiabatic modulation of system parameters. Long-range couplings play a central role by enhancing the relevant energy gaps, leading to a substantial improvement in transfer efficiency compared to nearest neighbour models. The resulting transfer is robust against positional disorder, reflecting its topological origin and highlighting the potential of long-range interacting platforms for reliable quantum state transfer.
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.
Floquet topological matter has emerged as one exciting platform to explore rich physics and game-changing applications of topological phases. As one remarkable and recently discovered feature of Floquet symmetry protected topological (SPT) phases, in principle, a simple periodically driven system can host an arbitrary number of topological protected zero edge modes and $\ensuremath{\pi}$ edge modes, with Majorana zero modes and Majorana $\ensuremath{\pi}$ modes as examples protected by the particle-hole symmetry. This work advocates a new route to holonomic quantum computation by exploiting the co-existence of many Floquet SPT edge modes, all of which have trivial dynamical phases during a computation protocol. As compelling evidence supporting this ambitious goal, three pairs of Majorana edge modes, hosted by a periodically driven one-dimensional (1D) superconducting superlattice, are shown to suffice to encode two logical qubits, realize quantum gate operations, and execute two simple quantum algorithms through adiabatic lattice deformation. When compared with early studies on quantum computation based on Majorana zero modes of topological quantum wires, significant resource saving is now made possible by use of Floquet SPT phases.
Topologically protected edge states exactly at topological phase boundaries challenge the conventional belief that topological states must be associated with a bulk energy gap. Because periodically driven (Floquet) systems host unusually intricate topological phase boundaries, topological edge states can be prolific at such Floquet quantum criticality. Working on a class of chiral-symmetric, Floquet-driven Majorana fermion chains, we analytically and computationally show that the precise boundaries between different Floquet topological gapped phases can accommodate topological edge modes, including the so-called critical Majorana π modes. We also identify a general bulk-edge correspondence formula to predict and understand the emergence of topological edge modes at Floquet quantum criticality. Of direct interest to quantum simulation experiments, our work opens an avenue for exploring topological physics intrinsic to nonequilibrium phase boundaries. The authors develop a theoretical framework to characterize the topology and edge states at the nonequilibrium critical points of periodically driven (Floquet) quantum systems. The rule of bulk-edge correspondence applicable to both gapped and gapless Floquet topological phases in 1D chiral symmetric driven systems is proposed.
Robust quantum state transfer (QST) is the foundation for information exchange among nodes in quantum networks. In this paper, we propose a robust QST protocol that utilizes topological edge modes in the qubit chains to encode (decode) quantum states (flying qubits). By employing qubits with tunable couplings, we construct Su-Schrieffer-Heeger (SSH) chains as the nodes of a quantum network. The end qubit of each SSH chain is dissipatively coupled to a chiral waveguide, and the dissipative strength is a constant. We refer to the SSH chain with a dissipation channel at the end qubit as the non-Hermitian SSH chain. Comparing the symmetry and energy spectra of the non-Hermitian SSH chain with those of the SSH chain, our analysis reveals that the dissipative dynamics of the topological edge state in the non-Hermitian SSH chain are governed by its imaginary spectra. The edge mode with the imaginary spectrum can be used to encode (decode) quantum states (flying qubits), thereby enabling robust QST between two remote mirrored non-Hermitian SSH chains. Our numerical simulations demonstrate that high-fidelity QST can be achieved even in the presence of coupling errors. Furthermore, we extend our analysis to consider QST in imperfect chiral waveguides, providing insights into the robustness of our protocol under realistic conditions. Our discussion is applicable to various quantum platforms and holds significant implications for constructing large-scale quantum networks.