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arXiv:1901.03220 · Physical Review A

Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains

Feng Mei, Gang Chen, Lin Tian, Shi-Liang Zhu, Suotang Jia

Published Sep 21, 2018• 20 citations
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Abstract

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.

DOI
10.1103/physreva.98.032323

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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.
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.
Identifying and measuring topological invariants remains a fundamental challenge due to the non-local nature of momentum eigenstates in real space. Established approaches based on Bloch oscillations, quantum walks, charge pumping and quench dynamics, typically fail to provide direct momentum-dependent geometric information of each Bloch state. Here, we propose a novel framework for implementing direct band-topology tomography via momentum-selective measurements, and experimentally demonstrate it on a superconducting processor featuring a highly connected coupling architecture. Utilizing a ``star-like" geometry in which an auxiliary probe couples to a one-dimensional topological chain with spatially modulated coupling strengths, we selectively address the desired momentum states of the chain. This approach enables the direct and robust extraction of the winding phase that contributes to the associated topological invariant. Leveraging non-local couplers bridged by long tantalum airbridges, we realize an extended Su-Schrieffer-Heeger (SSH) model and map its full topological phase diagram. Through a nested Fourier analysis over time and space, we directly extract the winding phase across Brillouin zone and resolve quantized winding numbers of ν={0,±1,2}ν=\{0,\pm1,2\}ν={0,±1,2} characterized by phase winding {0,±2π,4π}\{0, \pm 2π,4π\}{0,±2π,4π}. Our work establishes a versatile tool for probing topological characteristics and opens a new avenue for robust quantum computing architectures based on topological protection.
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.
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.
Abstract The Su–Schrieffer–Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer trans -polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically protected, dispersionless boundary states. Here, using 87 Rb atoms in a momentum-space lattice, we realize fully tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation.