Quantum computing topological invariants of two-dimensional quantum matter

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 (14)

• Non-Abelian Anyons and Topological Quantum Computation
• The density-matrix renormalization group in the age of matrix product states
• The Variational Quantum Eigensolver: a review of methods and best practices
• Computing topological invariants without inversion symmetry
• Colloquium: Quantum anomalous Hall effect
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Observation of topological transitions in interacting quantum circuits
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Electric polarization in a Chern insulator
• A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity
• Opening the Black Box Inside Grover's Algorithm
• Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation
• Efficient variational quantum circuit structure for correlated topological phases
• Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks

Cited by in corpus (2)

• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach