Quantum computing topological invariants of two-dimensional quantum matter
arXiv:2404.06048 · doi:10.1103/PhysRevResearch.6.043288
Abstract
Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time-evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers.
11 pages, 7 figures
References in corpus (41)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Effect in Graphene
- Non-Abelian Anyons and Topological Quantum Computation
- Berry Phase Effects on Electronic Properties
- The density-matrix renormalization group in the age of matrix product states
- New directions in the pursuit of Majorana fermions in solid state systems
- WannierTools: An open-source software package for novel topological materials
- Non-Abelian statistics and topological quantum information processing in 1D wire networks
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- The Variational Quantum Eigensolver: a review of methods and best practices
- The ITensor Software Library for Tensor Network Calculations
- An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
- Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Computing topological invariants without inversion symmetry
- Topological Phases in Two-Dimensional Materials: A Brief Review
- Colloquium: Quantum anomalous Hall effect
- Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
- A Short Introduction to Topological Quantum Computation
- Observation of topological transitions in interacting quantum circuits
- Detecting topological invariants in nonunitary discrete-time quantum walks
- What limits the simulation of quantum computers?
- 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
- Electric polarization in a Chern insulator
- Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
- A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity
- 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
- Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems
- Optimising Matrix Product State Simulations of Shor's Algorithm
- Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
- Calculating nonadiabatic couplings and Berry's phase by variational quantum eigensolvers
- Opening the Black Box Inside Grover's Algorithm
- Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation
- Robust measurement of wave function topology on NISQ quantum computers
- Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks
- Efficient variational quantum circuit structure for correlated topological phases