Robust measurement of wave function topology on NISQ quantum computers
arXiv:2101.07283 · doi:10.22331/q-2023-04-27-987
Abstract
Topological quantum phases of quantum materials are defined through their topological invariants. These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are immune to local noise. Here, we present a strategy to measure topological invariants on quantum computers. We show that our strategy can be easily integrated with the variational quantum eigensolver (VQE) so that the topological properties of generic quantum many-body states can be characterized on current quantum hardware. We demonstrate the robust nature of the method by measuring topological invariants for both non-interacting and interacting models, and map out interacting quantum phase diagrams on quantum simulators and IBM quantum hardware.
arXiv comment21 pages, 14 figures, 4 tables
References in corpus (53)
- Quantum Computing in the NISQ era and beyond
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Quantum Computing with Very Noisy Devices
- An adaptive variational algorithm for exact molecular simulations on a quantum computer
- Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
- Extending the computational reach of a noisy superconducting quantum processor
- Scalable Quantum Simulation of Molecular Energies
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Topological Anderson Insulator
- Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
- Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states
- Fermion zero modes on vortices in chiral superconductors
- Theory of variational quantum simulation
- Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
- Observation of the topological Anderson insulator in disordered atomic wires
- Photonic Topological Anderson Insulators
- Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
- Observation of topological transitions in interacting quantum circuits
- Detecting topological invariants in nonunitary discrete-time quantum walks
- Disordered Topological Insulators: A Non-Commutative Geometry Perspective
- Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
- Interplay of disorder and interaction in Majorana quantum wires
- Methodology for replacing indirect measurements with direct measurements
- Universal Scaling of Quantum Anomalous Hall Plateau Transition
- Exact Ising model simulation on a quantum computer
- Crossing a topological phase transition with a quantum computer
- Identification of symmetry-protected topological states on noisy quantum computers
- Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
- Probing the topology of density matrices
- Quantum criticality of quasi one-dimensional topological Anderson insulators
- AIII and BDI Topological Systems at Strong Disorder
- Exact Superconducting Instability in a Doped Mott Insulator
- Many-body topological invariants from randomized measurements
- Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
- Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
- Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
- Many-body Chern number from statistical correlations of randomized measurements
- Measuring the winding number in a large-scale chiral quantum walk
- Many-body Chern number without integration
- Digital Simulation of Topological Matter on Programmable Quantum Processors
- Diagnosis of interaction-driven topological phase via exact diagonalization
- Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
- Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
- Interaction and disorder effects in 3D topological insulator thin films
- Stability of Periodically Driven Topological Phases against Disorder
- Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation
- VQE Method: A Short Survey and Recent Developments
- Topological Phase Transitions Induced by Disorder in Magnetically Doped (Bi, Sb)Te Thin Films
- Spin quantum Hall effect and plateau transitions in multilayer network models
- A comparative code study for quantum fault-tolerance
- Stability of Kramers Majorana doublets: the effects of interactions and disorders
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- Noise-Robust Detection of Quantum Phase Transitions
- Quantum computing topological invariants of two-dimensional quantum matter
- Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
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