Quantum computing topological invariants of two-dimensional quantum matter

• URL: http://arxiv.org/abs/2404.06048v2
• Date: Wed, 10 Apr 2024 11:28:16 GMT
• Title: Quantum computing topological invariants of two-dimensional quantum matter
• Authors: Marcel Niedermeier, Marc Nairn, Christian Flindt, Jose L. Lado,
• Abstract summary: We present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. First algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. Second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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