Robust measurement of wave function topology on NISQ quantum computers

Xiao Xiao1, J. K. Freericks2, and A. F. Kemper1

1Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
2Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057 USA

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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.

Calculations on current noisy intermediate-scale quantum (NISQ) hardware are susceptible to operation errors during the implementations of quantum circuits. Therefore, it is challenging to identify useful applications on which the present quantum hardware can be used. Here we provide a systematical strategy, which can be easily integrated with variational quantum algorithms, to characterize a key property of quantum matter: the wave function. Strikingly, we demonstrated that one important quantity that characterizes the wave function topology, the Chern number, can be calculated accurately on present quantum hardware without any error mitigation or error correction. Our work is an appealing demonstration that NISQ hardware might be a good platform to study quantum topological states and topological phenomena.

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Cited by

[1] Emiel Koridon, Joana Fraxanet, Alexandre Dauphin, Lucas Visscher, Thomas E. O'Brien, and Stefano Polla, "A hybrid quantum algorithm to detect conical intersections", Quantum 8, 1259 (2024).

[2] Efekan Kökcü, Daan Camps, Lindsay Bassman, J. K. Freericks, Wibe A. de Jong, Roel Van Beeumen, and Alexander F. Kemper, "Algebraic compression of quantum circuits for Hamiltonian evolution", Physical Review A 105 3, 032420 (2022).

[3] Huai-Chun Chang and Hsiu-Chuan Hsu, "Digital quantum simulation of dynamical topological invariants on near-term quantum computers", Quantum Information Processing 21 1, 41 (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 20:42:07) and SAO/NASA ADS (last updated successfully 2024-05-24 20:42:08). The list may be incomplete as not all publishers provide suitable and complete citation data.