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Quantum simulation of DIII class topological superconductors using superconducting quantum circuits

Yong Hu, Zheng‐Yuan Xue, Zhongdong Wang, Yaqin Zhao

Published Jul 23, 2014• 0 citations
OpenAlex

Abstract

An exotic DIII model of one-dimensional p-wave spin-triplet superconductors with the $\mathbb{Z}_{2}$ topological phase protected by the time-reversal symmetry is simulated by an array of inductively coupled transmon qubits with tunable nearest-neighbor couplings and scalability. The anti-commutation relation between opposite spin components in the DIII model is realized by a novel dispersive dynamic modulation approach, while previous schemes consider only spinless fermions. Our detailed analysis reveals that distinctive topological phenomena can be visualized with the state-of-the-art technology in this superconducting-circuit array.

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An exotic DIII model of one-dimensional p-wave spin-triplet superconductors with the Z2\mathbb{Z}_{2}Z2​ topological phase protected by the time-reversal symmetry is simulated by an array of inductively coupled transmon qubits with tunable nearest-neighbor couplings and scalability. The anti-commutation relation between opposite spin components in the DIII model is realized by a novel dispersive dynamic modulation approach, while previous schemes consider only spinless fermions. Our detailed analysis reveals that distinctive topological phenomena can be visualized with the state-of-the-art technology in this superconducting-circuit array.
Abstract One-dimensional time-reversal invariant topological superconducting wires of the symmetry class DIII exhibit exotic physics which can be exploited to realize the set of universal operations in topological quantum computing. However, the verification of DIII-class physics in conventional condensed matter materials is highly nontrivial due to realistic constraints. Here we propose a symmetry-protected hard-core boson simulator of the one-dimensional DIII topological superconductor. By using the developed dispersive dynamic modulation approach, not only the faithful simulation of this new type of spinful superconducting chains is achieved, but also a set of universal quantum gates can be realized with the computational basis formed by the degenerate ground states that are topologically protected against random local perturbations. Physical implementation of our scheme based on a Josephson quantum circuit is presented, where our detailed analysis pinpoints that this scheme is experimentally feasible with the state-of-the-art technology.
A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z2{\mathbb{Z}}_{2}Z2​ gauge fields. The Majorana fermion model can be viewed as a model of time-reversal-invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z2{\mathbb{Z}}_{2}Z2​ topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the $\ensuremath{\pi}$-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z2{\mathbb{Z}}_{2}Z2​ trivial and nontrivial phases.
Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional superconductor model where Majorana end states can appear. Combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. We further show that in a similar way, a controlled-not gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations.
The recent experimental realization of a programmable two-dimensional square superconducting qubit array opens a new avenue for quantum simulation with qubits [Science 372, 948 (2021)]. Here, we present an experimentally feasible method to achieve two-dimensional superconducting qubit lattice with tunable coupling strengths. A configuration with higher-order topological phases is constructed, featuring topologically protected boundary states in lower dimension (corner states). We show that the quadrupole topological phases can be effectively characterized by the dynamics of the single-excitation quantum state. Moreover, we also explore the detection and dynamics of the corner modes in our qubit lattice system. Particularly, we propose an effective scheme to realize quantum information transfer via the corner states. Our work suggests that superconducting circuits systems are a fertile platform to study novel topological quantum phases and may shed light on the ongoing exploration of topologically protected quantum information processing.
We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that, despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.
We propose a platform for quantum many body simulations of dipolar spin models using current circuit QED technology. Our basic building blocks are 3D transmon qubits where we use the naturally occurring dipolar interactions to realize interacting spin systems. This opens the way toward the realization of a broad class of tunable spin models in both two- and one-dimensional geometries. We illustrate the potential offered by these systems in the context of dimerized Majumdar-Ghosh-type phases, archetypical examples of quantum magnetism, showing how such phases are robust against disorder and decoherence and could be observed within state-of-the-art experiments.