Superconducting Quantum Simulator for Topological Order and the Toric Code

TL;DR

This paper proposes a superconducting circuit-based analog quantum simulator for the Toric Code, enabling the study of topological order, quantum excitations, and fractional statistics in a controllable, scalable platform.

Contribution

It introduces a novel implementation of the Toric Code Hamiltonian using superconducting circuits with high control, facilitating the exploration of topological quantum phenomena.

Findings

Implementation of four-body interactions via SQUIDs

Preparation of topologically ordered states through adiabatic ramp

Verification of fractional statistics of excitations

Abstract

Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations and prospects for protecting stored quantum information against errors. Here we show that the Hamiltonian of the central model of this class of systems, the Toric Code, can be directly implemented as an analog quantum simulator in lattices of superconducting circuits. The four-body interactions, which lie at its heart, are in our concept realized via Superconducting Quantum Interference Devices (SQUIDs) that are driven by a suitably oscillating flux bias. All physical qubits and coupling SQUIDs can be individually controlled with high precision. Topologically ordered states can be prepared via an adiabatic ramp of the stabilizer interactions. Strings of qubit operators, including the stabilizers and correlations along non-contractible loops, can be read out via a capacitive coupling to read-out resonators. Moreover, the available single qubit operations allow to create and propagate elementary excitations of the Toric Code and to verify their fractional statistics. The architecture we propose allows to implement a large variety of many-body interactions and thus provides a versatile analog quantum simulator for topological order and lattice gauge theories.