Non-perturbative gadget for topological quantum codes

Abstract

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly non-local interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. Here, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians non-perturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasi-particle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other non-local spin Hamiltonians may be possible.

13 pages, 8 figures, PRL Accepted

References in corpus (12)

• Detecting topological order in a ground state wave function
• A toolbox for lattice spin models with polar molecules
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• A Rydberg Quantum Simulator
• Topological quantum order: stability under local perturbations
• An exact chiral spin liquid with non-Abelian anyons
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Perturbative Gadgets at Arbitrary Orders
• Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Toric codes and quantum doubles from two-body Hamiltonians
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians

Cited by in corpus (17)

• Exotic topological order in fractal spin liquids
• Optical Abelian Lattice Gauge Theories
• Induced self-stabilization in fractional quantum Hall states of light
• Permutation-invariant quantum codes
• Renormalization group constructions of topological quantum liquids and beyond
• The upside of noise: engineered dissipation as a resource in superconducting circuits
• Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric
• Quantum storage in quantum ferromagnets
• Can long-range interactions stabilize quantum memory at nonzero temperature?
• Quadratization in discrete optimization and quantum mechanics
• Information storage capacity of discrete spin systems
• Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians
• Exponential Lifetime Improvement in Topological Quantum Memories
• Perturbative gadgets without strong interactions
• Efficient optimization of perturbative gadgets
• Perturbative gadgets for gate-based quantum computing: Non-recursive constructions without subspace restrictions
• Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry