Many-body Chern number from statistical correlations of randomized measurements

Abstract

One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant is conventionally based on the linear-response techniques which require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction. Remarkably, our results apply to disk-like geometries that are more amenable to current quantum simulator architectures.

arXiv comment8 pages, 4 figures

References in corpus (43)

• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Non-Abelian Anyons and Topological Quantum Computation
• Topological Photonics
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Measuring entanglement entropy through the interference of quantum many-body twins
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum thermalization through entanglement in an isolated many-body system
• Topological Bands for Ultracold Atoms
• Zoo of quantum-topological phases of matter
• The Quantum-Mechanical Position Operator in Extended Systems
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Chiral groundstate currents of interacting photons in a synthetic magnetic field
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Detection of Symmetry Protected Topological Phases in 1D
• Fractional Quantum Hall Effect in Optical Lattices
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• Measuring quantized circular dichroism in ultracold topological matter
• Probing topology by "heating": Quantized circular dichroism in ultracold atoms
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Probing scrambling using statistical correlations between randomized measurements
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Induced self-stabilization in fractional quantum Hall states of light
• An order parameter for symmetry-protected phases in one dimension
• Many-body topological invariants from randomized measurements
• Interferometric Measurements of Many-body Topological Invariants using Mobile Impurities
• Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices
• Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices
• Symbolic integration with respect to the Haar measure on the unitary group
• Detecting fractional Chern insulators through circular dichroism
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Extraction of many-body Chern number from a single wave function
• Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
• Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
• Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement
• Optical Lattice with Torus Topology
• Local order parameters for symmetry fractionalization

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• Probing many-body quantum chaos with quantum simulators
• Chiral central charge from a single bulk wave function
• Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors
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• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
• Topological photonics: fundamental concepts, recent developments, and future directions
• Quantum scrambling with classical shadows
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Modular commutator in gapped quantum many-body systems
• Measuring Arbitrary Physical Properties in Analog Quantum Simulation
• Extraction of many-body Chern number from a single wave function
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• Recent Developments in Fractional Chern Insulators
• Robust estimation of the Quantum Fisher Information on a quantum processor
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Characterizing correlation within multipartite quantum systems via local randomized measurements
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• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
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• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
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• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Extracting higher central charge from a single wave function
• Detecting Quantum Anomalies in Open Systems
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
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• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Localized Virtual Purification
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Learning topological states from randomized measurements using variational tensor network tomography
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Crystalline invariants of fractional Chern insulators
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• Measurable fractional spin for quantum Hall quasiparticles on the disk
• Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)D topological order
• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Unsupervised Learning of Symmetry Protected Topological Phase Transitions
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