Preparing topological PEPS on a quantum computer

Abstract

Simulating of exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states -- the G-injective Projected Entangled Pair States (PEPS) -- on a quantum computer. Important examples include the resonant valence bond (RVB) states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors, and inverse-polynomially in the spectral gap of the PEPS parent Hamiltonian.

7 pages, 2 figures, REVTeX format

References in corpus (6)

• Quantum algorithm for solving linear systems of equations
• Valence Bond Solids for Quantum Computation
• Optimal Quantum Measurements of Expectation Values of Observables
• Entanglement renormalization and topological order
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Spectral Gap Amplification

Cited by in corpus (19)

• Towards Practical Quantum Variational Algorithms
• Towards Quantum Machine Learning with Tensor Networks
• Challenges and Opportunities of Near-Term Quantum Computing Systems
• Quantum Machine Learning for Chemistry and Physics
• Rapid adiabatic preparation of injective PEPS and Gibbs states
• Twisted Injectivity in PEPS and the Classification of Quantum Phases
• Probabilistic Nonunitary Gate in Imaginary Time Evolution
• Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
• Resource theory of quantum uncomplexity
• Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS
• Approximating local observables on projected entangled pair states
• Divide and conquer method for proving gaps of frustration free Hamiltonians
• Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories
• Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions
• Complexity-constrained quantum thermodynamics
• Variational adiabatic transport of tensor networks
• An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma
• Preparing topologically ordered states by Hamiltonian interpolation
• Attention to Quantum Complexity