Simulating spin systems with Majorana networks

Abstract

With the discovery of Majorana quasiparticles in semiconductor-superconductor hybrid structures, topologically protected qubits have emerged as a promising contender for quantum information processing. While the construction of a universal quantum computer with topological protection likely requires significant advances in materials science, intermediate-scale devices are nearly within the reach of current technology. As a near-term milestone for topological qubits, we propose a network of topological superconductors as a simulator of a large variety of quantum spin systems, including those with frustration. Our proposal is founded on existing technology, combining advantages of semiconducting and superconducting qubits. We identify local measurement protocols that give access to information about ground and excited states as well as dynamic correlations. The topological protection of the qubits results in longer coherence times, and relaxation to the groundstate can be controlled by coupling the network an external bath. We conclude by pointing out specific applications of the quantum simulator, e.g., spin liquids, quantum criticality, and thermalization.

arXiv comment27 pages, 10 figures

References in corpus (114)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Charge insensitive qubit design derived from the Cooper pair box
• Chaos and Quantum Thermalization
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Quantum Simulation
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Entanglement entropy and conformal field theory
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Quantum Spin Liquid States
• "Deconfined" quantum critical points
• Coupling Superconducting Qubits via a Cavity Bus
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Exponential Protection of Zero Modes in Majorana Islands
• Unbounded growth of entanglement in models of many-body localization
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Exploring the many-body localization transition in two dimensions
• Effective quantum spin systems with ion traps
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Spin-orbit qubit in a semiconductor nanowire
• Lieb-Schultz-Mattis in Higher Dimensions
• Identifying Topological Order by Entanglement Entropy
• Many-body localization: an introduction and selected topics
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Roads towards fault-tolerant universal quantum computation
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Universal dynamics and renormalization in many body localized systems
• Experimental Comparison of Two Quantum Computing Architectures
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Quantized Majorana conductance
• Measuring the scrambling of quantum information
• Scaling of Majorana Zero-Bias Conductance Peaks
• Non-Fermi liquid behavior and Griffiths phase in {\it f}-electron compounds
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Quantum quenches in 1+1 dimensional conformal field theories
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Induced Superconductivity in the Quantum Spin Hall Edge
• An exact chiral spin liquid with non-Abelian anyons
• Simulating chemistry using quantum computers
• End states and subgap structure in proximity-coupled chains of magnetic adatoms
• Dipole coupling of a double quantum dot to a microwave resonator
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Observation of Entangled States of a Fully Controlled 20-Qubit System
• Flux-controlled quantum computation with Majorana fermions
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks
• Properties of an algebraic spin liquid on the kagome lattice
• Quantum control and process tomography of a semiconductor quantum dot hybrid qubit
• Topological Superconductivity in a Planar Josephson Junction
• Crystal field splitting and correlation effect on the electronic structure of A2IrO3
• Two universality classes for the many-body localization transition
• Two-dimensional platform for networks of Majorana bound states
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Dirac, Anderson, and Goldstone on the Kagome
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• Many-body Localization and Symmetry Protected Topological Order
• Topological Kondo effect with Majorana fermions
• Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
• Parity lifetime of bound states in a proximitized semiconductor nanowire
• Inducing Superconducting Correlation in Quantum Hall Edge States
• Effective Spin Quantum Phases in Systems of Trapped Ions
• Ground-State Phase Diagram of Quantum Heisenberg Antiferromagnets on the Anisotropic Dimerized Square Lattice
• Thermal and Residual Excited-State Population in a 3D Transmon Qubit
• Entanglement Scrambling in 2d Conformal Field Theory
• Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Measurement of many-body chaos using a quantum clock
• Correlated impurities and intrinsic spin liquid physics in the kagome material Herbertsmithite
• Microwave-driven coherent operations of a semiconductor quantum dot charge qubit
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Towards realistic implementations of a Majorana surface code
• Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Transport signatures of quasiparticle poisoning in a Majorana island
• Quantum Phase Transition in Heisenberg-Kitaev Model
• 1 minute parity lifetime of a NbTiN Cooper-pair transistor
• Critical behavior of O(2)xO(N) symmetric models
• Valence Bond Glass Phase in the Diluted Kagome Antiferromagnets
• Mosaic spin models with topological order
• Quantum spin-liquid behavior in the spin-1/2 random-bond Heisenberg antiferromagnet on the kagome lattice
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
• Phase transitions in an Ising chain interacting with a single mode cavity field
• The mother of all states of the kagome quantum antiferromagnet
• Eigenstate phase transitions and the emergence of universal dynamics in highly excited states
• Statistics of fractionalized excitations through threshold spectroscopy
• Hybridization of sub-gap states in one-dimensional superconductor/semiconductor Coulomb islands
• Quantum spin metal state on a decorated honeycomb lattice
• Interferometric Approach to Probing Fast Scrambling
• Quantum simulator for the Hubbard model with long-range Coulomb interactions using surface acoustic waves
• Quantum kagome antiferromagnet: ZnCu3(OH)6Cl2
• QED${}_3$ with quenched disorder: quantum critical states with interactions and disorder
• Hidden Quasiparticles and Incoherent Photoemission Spectra in Na2IrO3
• The renormalization group flow in field theories with quenched disorder
• Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance
• Two dimensional metallic phases from disordered QED${}_3$
• Spin liquids from Majorana Zero Modes in a Cooper Box
• Field theory for generalized Shastry-Sutherland models
• Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana Nanowires
• The renormalization group in quantum quenched disorder
• Energy protection arguments fail in the interaction picture
• Simulating the Quantum Magnet

Cited by in corpus (4)

• Majorana Quantum Lego, a Route Towards Fracton Matter
• Simulating topological tensor networks with Majorana qubits
• Designing ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ topological orders in networks of Majorana bound states
• Simulating exotic phases of matter with bond-directed interactions with arrays of Majorana-Cooper pair boxes