Methods for simulating string-net states and anyons on a digital quantum computer

Abstract

Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to realize a large class of topologically ordered states and simulate their quasiparticle excitations on a digital quantum computer. To achieve this we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with unitary open string operators to simulate the creation and braiding of abelian and non-abelian anyons. We show that the abelian (non-abelian) unitary string operators can be implemented with a constant (linear) depth quantum circuit. Our scheme allows us to directly probe characteristic topological properties, including topological entanglement entropy, braiding statistics, and fusion channels of anyons. Moreover, this set of efficiently prepared topologically ordered states has potential applications in the development of fault-tolerant quantum computers.

A mislabeling in Figure 1 and 2 is corrected

References in corpus (22)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Non-Abelian Anyons and Topological Quantum Computation
• Surface codes: Towards practical large-scale quantum computation
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Efficient quantum state tomography
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Entanglement renormalization and topological order
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Anyonic interferometry and protected memories in atomic spin lattices
• Exact entanglement renormalization for string-net models
• Simulations of quantum double models
• Sequential generation of projected entangled-pair states
• Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
• Quantum Circuits for Measuring Levin-Wen Operators
• Measuring Topological Order
• Tensor-product representations for string-net condensed states
• Generation of photonic tensor network states with Circuit QED

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• Quantum phase transition between symmetry enriched topological phases in tensor-network states
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• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
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• Renormalization of Ising cage-net model and generalized foliation
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• Isolated zero mode in a quantum computer from a duality twist
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• Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Simulating Topological Order on Quantum Processors
• Skeleton of isometric Tensor Network States for Abelian String-Net Models
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
• Holographic duality between bulk topological order and boundary mixed-state order
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes