Journal
PHYSICAL REVIEW B
Volume 104, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.104.085138
Keywords
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Funding
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [FOR 2414, 277974659, EXC-2111-390814868]
- Max Weber Program
- European Union [754388]
- LMUexcellent
- Federal Ministry of Education and Research (BMBF)
- State of Bavaria under the Excellence Strategy of the German Federal Government
- European Research Council (ERC) under the European Union [803047]
- Australian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS) [CE170100009]
- European Research Council (ERC) [803047] Funding Source: European Research Council (ERC)
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This work presents a building block for Z(2) lattice gauge theories coupled to dynamical matter, enabling the implementation of the toric code ground state and its topological excitations. The proposal is realized in the second-order coupling regime and is well suited for superconducting qubit implementations. The study outlines a pathway for preparing topologically nontrivial initial states and experimental signatures of the ground-state wave function.
Kitaev's toric code is an exactly solvable model with Z(2)-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge. Here, we propose a building block for Z(2) lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically nontrivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wave function and introduce a minimal braiding protocol. Detecting a p-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.
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