Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

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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Abstract

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection $\textit{intrinsic to models being simulated}$, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

It is challenging to achieve high accuracy for programs run on current noisy intermediate-scale quantum (NISQ) hardware. Topological quantum computing has long been thought to be a remedy for handling noise and decoherence, because topological qubits are intrinsically protected from environment. However, the creation of topological qubits is so difficult that we are yet to see topological quantum computers available for use. Here we demonstrate that performing calculations of the topological properties of quantum systems is also intrinsically robust, even if we do so on a conventional quantum computer. We do this in two steps. First, we construct nontrivial topological states by braiding non-Abelian quasi-particles with conventional qubits. Second, we use symmetry-enforced quantum circuits to perform calculations with small numbers of qubits. This study provides a paradigm for applying NISQ hardware to study nontrivial topological quantum states.

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[2] John P. T. Stenger, Nicholas T. Bronn, Daniel J. Egger, and David Pekker, "Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer", Physical Review Research 3 3, 033171 (2021).

[3] Philippe Suchsland, Panagiotis Kl. Barkoutsos, Ivano Tavernelli, Mark H. Fischer, and Titus Neupert, "Simulating a ring-like Hubbard system with a quantum computer", arXiv:2104.06428.

[4] Junmo Jeon and SungBin Lee, "Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals", arXiv:2108.02212.

[5] Tatiana A. Bespalova and Oleksandr Kyriienko, "Quantum simulation and ground state preparation for the honeycomb Kitaev model", arXiv:2109.13883.

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