Interplay between lattice gauge theory and subsystem codes

Abstract

It is now widely recognized that the toric code is a pure gauge-theory model governed by a projective Hamiltonian with topological orders. In this work, we extend the interplay between quantum information system and gauge-theory model from the view point of subsystem code, which is suitable for \textit{gauge systems including matter fields}. As an example, we show that $Z_2$ lattice gauge-Higgs model in (2+1)-dimensions with specific open boundary conditions is noting but a kind of subsystem code. In the system, Gauss-law constraints are stabilizers, and order parameters identifying Higgs and confinement phases exist and they are nothing but logical operators in subsystem codes residing on the boundaries. Mixed anomaly of them dictates the existence of boundary zero modes, which is a direct consequence of symmetry-protected topological order in Higgs and confinement phases. After identifying phase diagram, subsystem codes are embedded in the Higgs and confinement phases. As our main findings, we give an explicit description of the code (encoded qubit) in the Higgs and confinement phases, which clarifies duality between Higgs and confinement phases. The degenerate structure of subsystem code in the Higgs and confinement phases remains even in very high-energy levels, which is analogous to notion of strong-zero modes observed in some interesting condensed-matter systems. Numerical methods are used to corroborate analytically-obtained results and the obtained spectrum structure supports the analytical description of various subsystem codes in the gauge theory phases.

arXiv comment14 pages, 8 figures, accepted for publication from Phys. Rev. B

References in corpus (38)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Generalized Global Symmetries
• Many-body localization in a disordered quantum Ising chain
• Area laws in a many-body localized state and its implications for topological order
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Localization protected quantum order
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Stabilizer Formalism for Operator Quantum Error Correction
• Generalized Symmetries in Condensed Matter
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Entanglement phase transitions in measurement-only dynamics
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Robustness of a perturbed topological phase
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
• Quantum phase transition between cluster and antiferromagnetic states
• Topological order and criticality in (2+1)D monitored random quantum circuits
• Long coherence times for edge spins
• Topological order in 1D Cluster state protected by symmetry
• Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
• Prethermal Strong Zero Modes and Topological Qubits
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• Gauging the Kitaev chain
• Stabilizing lattice gauge theories through simplified local pseudo generators
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• CP^1+U(1) Lattice Gauge Theory in Three Dimensions: Phase Structure, Spins, Gauge Bosons, and Instantons
• Universality Classes of Stabilizer Code Hamiltonians
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Lattice Gauge Theory for Condensed Matter Physics: Ferromagnetic Superconductivity as its Example
• Production of lattice gauge-Higgs topological states in measurement-only quantum circuit
• Z_N Gauge Theories on a Lattice and Quantum Memory
• Entanglement and spectra in topological many-body localized phases

Cited by in corpus (5)

• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits