Duality as a Feasible Physical Transformation

Abstract

Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous advantages for the study of many-body physics. In this work, we suggest a method which shall introduce them to the world of quantum simulation too: a feasible scheme for implementing duality transformations as physical operations, mapping between dual quantum states showing the same observable physics, rather than just a mathematical trick. Demonstrating with Abelian lattice models, we show how duality transformations could be implemented in the laboratory as sequences of single- and two-body operations - unitaries and measurements.

arXiv comment16 pages

References in corpus (24)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Anyons in an exactly solved model and beyond
• Quantum Simulation
• Mapping local Hamiltonians of fermions to local Hamiltonians of spins
• Digital lattice gauge theories
• Gauging quantum states: from global to local symmetries in many-body systems
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• Dualities and the phase diagram of the $p$-clock model
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• The Bond-Algebraic Approach to Dualities
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Gauss's Law, Duality, and the Hamiltonian Formulation of U(1) Lattice Gauge Theory
• Fermions without fermi fields
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Unified approach to Quantum and Classical Dualities
• Eliminating fermionic matter fields in lattice gauge theories
• A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations
• Remote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Photon-mediated Stroboscopic Quantum Simulation of a ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Real-time dynamics in 2+1d compact QED using complex periodic Gaussian states
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• Half a state, half an operator: a general formulation of stators

Cited by in corpus (13)

• Measurement as a shortcut to long-range entangled quantum matter
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• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Dualities in one-dimensional quantum lattice models: topological sectors
• Subsystem Non-Invertible Symmetry Operators and Defects
• Non-invertible symmetries act locally by quantum operations
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space