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Quantum computing topological invariants of two-dimensional quantum matter
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en
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10
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Physical Review Research, Volume 6, issue 4, pp. 1-10
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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Niedermeier, M, Nairn, M & Flindt, C 2024, 'Quantum computing topological invariants of two-dimensional quantum matter', Physical Review Research, vol. 6, no. 4, 043288, pp. 1-10. https://doi.org/10.1103/PhysRevResearch.6.043288