A superconducting circuit realization of combinatorial gauge symmetry

Abstract

We propose a superconducting quantum circuit based on a general symmetry principle -- combinatorial gauge symmetry -- designed to emulate topologically-ordered quantum liquids and serve as a foundation for the construction of topological qubits. The proposed circuit exhibits rich features: in the classical limit of large capacitances its ground state consists of two superimposed loop structures; one is a crystal of small loops containing disordered $U(1)$ degrees of freedom, and the other is a gas of loops of all sizes associated to ${\mathbb{Z}}_2$ topological order. We show that these classical results carry over to the quantum case, where phase fluctuations arise from the presence of finite capacitances, yielding ${\mathbb{Z}}_2$ quantum topological order. A key feature of the exact gauge symmetry is that amplitudes connecting different ${\mathbb{Z}}_2$ loop states arise from paths having zero classical energy cost. As a result, these amplitudes are controlled by dimensional confinement rather than tunneling through energy barriers. We argue that this effect may lead to larger energy gaps than previous proposals which are limited by such barriers, potentially making it more likely for a topological phase to be experimentally observable. Finally, we discuss how our superconducting circuit realization of combinatorial gauge symmetry can be implemented in practice.

arXiv commentJoined by new author. Added section on experimental realization. Added analytical results

References in corpus (26)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Superconducting Qubits: Current State of Play
• Randomized Benchmarking of Quantum Gates
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Decoherence in a superconducting quantum bit circuit
• The Flux Qubit Revisited to Enhance Coherence and Reproducibility
• Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
• Decoherence of flux qubits due to 1/f flux noise
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• Implementation of superconductor-ferromagnet-superconductor pi-shifters in superconducting digital and quantum circuits
• Topologically protected quantum bits from Josephson junction arrays
• Superconducting Nanocircuits for Topologically Protected Qubits
• Protected Qubits and Chern Simons theories in Josephson Junction Arrays
• Superconducting pi qubit with a ferromagnetic Josephson junction
• Possible realization of an ideal quantum computer in Josephson junction array
• Solid-state qubits integrated with superconducting through-silicon vias
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• Topological order in the insulating Josephson junction array
• Topological order and topological entropy in classical systems
• Loop models with crossings
• Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Intersecting Loop Models on Z^D: Rigorous Results
• Superconducting tetrahedral quantum bits

Cited by in corpus (5)

• $U(1)$ symmetry-enriched toric code
• Fracton and topological order in the XY checkerboard toric code
• Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Absence of topological order in the $U(1)$ checkerboard toric code
• Nonequilibrium plasmon liquid in a Josephson junction chain