Abstract
In this study, building on the 1D topological Su–Schrieffer–Heeger (SSH) model, we propose a model of quantum dot arrays with odd and even parity and variable on-site local potentials to examine topological edge states and a possible quantum information encoding, using these states. We first investigate the SSH model with alternating tunneling amplitudes t1 and t2. We study the model in a ring-like structure and then proceed to minimal open-end chains with even (N=4) and odd (N=5) number of dots. Furthermore, we depart from the basic SSH model by introducing local potentials μi, which offer additional control at the cost of breaking the chiral symmetry of the Hamiltonian and study the implications. Then, we propose an idealized “static” charge qubit design, based on encoding the topological invariant ν as qubit states, that exploits the topological nature of the edge states and their collective character. We introduce perturbing noise δtij(t) into the system and demonstrate the robustness of the states for some range of the ratio ξ=t1/t2. Moreover, we show a possible way to detect the presence of topological order in the system using equilibrium dynamics for both even and odd chains. We utilize the quantum informatic measure of bipartite mutual information I{b:e}(2)(t) as a measure of bulk-edge quantum correlations and a quantitative indicator for the manifestation of bulk-edge correspondence; here, we also propose a dynamical qubit encoding with ν for specific quantum chain parity. Finally, we offer a few remarks on potential future explorations.
Highlights
Quantum computers[1,2] are a promising upcoming technology that will revolutionize computation and, as a consequence, many other fields such as quantum chemistry,[3,4] pharmaceutical drug design,[5,6] finance,[7,8] quantum machine learning, and AI.[9,10] They are a new generation of computers, which take advantage of “spooky” laws that reside in the quantum realm, such as superposition and entanglement, in order to encode, decode, and process information
In this study, building on the 1D topological Su–Schrieffer–Heeger (SSH) model, we propose a model of quantum dot arrays with odd and even parity and variable on-site local potentials to examine topological edge states and a possible quantum information encoding, using these states
These logical processes are done in a parallel manner,[11,12] which results in an exponential speedup in computational time and reduction of computational resources needed
Summary
Quantum computers[1,2] are a promising upcoming technology that will revolutionize computation and, as a consequence, many other fields such as quantum chemistry,[3,4] pharmaceutical drug design,[5,6] finance,[7,8] quantum machine learning, and AI.[9,10] They are a new generation of computers, which take advantage of “spooky” laws that reside in the quantum realm, such as superposition and entanglement, in order to encode, decode, and process information. It exhibits the existence of topologically protected states, whose topological character is quantified by a nontrivial topological invariant, namely the winding number ν This corresponds to the Zak phase,[32,37] which is a geometric phase picked up by the electron during its motion in the periodic structure; we define it later on. The topological phase is protected and in order to go from the nontrivial insulating topological phase (ν 1⁄4 1) to the trivial one (ν 1⁄4 0), the system needs to undergo a topological phase transition.[31,36,39] That is, it goes first through a metallic phase (ν 1⁄4 ?) or breaks somehow the chiral symmetry (e.g., if we include a nonuniform local chemical potential term) and the winding number ν “jumps” from 0 to 1 and vice versa; this is depicted in Fig. 3(f ) as a function of both t1 and t2.
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