Quantum algorithm for solving the XXX-Heisenberg model describing spin dynamics in a trinuclear copper complex
ORAL
Abstract
Daria D. Nakritskaia1,2, Sergey A. Varganov1, Yuri Alexeev2
1 Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV 89557-0216, USA
2 Argonne National Laboratory, 9700 South Cass Avenue, Building 240, Argonne, IL, 60439, USA
Efficient dynamics simulation of spin systems on a classical computer is limited by the exponential growth of Hilbert space with the number of interacting spins. . The scalability of the problem reduces from exponential to linear when implemented on a quantum computer, which allows to expand the model size, with the limitation being only the number of qubits. The Heisenberg model is one of the simplest models that describes the behavior of spin systems and has been previously implemented on the quantum hardware for an XY model[SV1] . To make such quantum simulations more resilient to noise, the depth of quantum circuit can be reduced using the Yang-Baxter equation (YBE), which has been done before for the one-dimensional XY-Heisenberg model. We investigate spin dynamics in a Cu3(saltatris(2-hydroxybenzylidene)triaminoguanidine)(pyridine)6 complex, focusing on the three spin-1/2 Cu(II) ions. We obtain the antiferromagnetic exchange constant from the electronic structure calculations and map it on the XXX-Heisenberg model. We solve the XXX-Heisenberg Hamiltonian in time-dependent magnetic field using 1) traditional classical algorithm, 2) the YBE quantum algorithm on a quantum simulator and 3) the YBE algorithm on a multi-qubit quantum device.
1 Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV 89557-0216, USA
2 Argonne National Laboratory, 9700 South Cass Avenue, Building 240, Argonne, IL, 60439, USA
Efficient dynamics simulation of spin systems on a classical computer is limited by the exponential growth of Hilbert space with the number of interacting spins. . The scalability of the problem reduces from exponential to linear when implemented on a quantum computer, which allows to expand the model size, with the limitation being only the number of qubits. The Heisenberg model is one of the simplest models that describes the behavior of spin systems and has been previously implemented on the quantum hardware for an XY model[SV1] . To make such quantum simulations more resilient to noise, the depth of quantum circuit can be reduced using the Yang-Baxter equation (YBE), which has been done before for the one-dimensional XY-Heisenberg model. We investigate spin dynamics in a Cu3(saltatris(2-hydroxybenzylidene)triaminoguanidine)(pyridine)6 complex, focusing on the three spin-1/2 Cu(II) ions. We obtain the antiferromagnetic exchange constant from the electronic structure calculations and map it on the XXX-Heisenberg model. We solve the XXX-Heisenberg Hamiltonian in time-dependent magnetic field using 1) traditional classical algorithm, 2) the YBE quantum algorithm on a quantum simulator and 3) the YBE algorithm on a multi-qubit quantum device.
* Yuri Alexeev is supported by Argonne Leadership Computing Facility, a U.S. Department of Energy (DOE) Office of Science user facility at Argonne National Laboratory and is based on research supported by the U.S. DOE Office of Science-Advanced Scientific Computing Research Program, under Contract No. DE-AC02-06CH11357.
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Presenters
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Daria Nakritskaia
University of Nevada, Reno
Authors
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Daria Nakritskaia
University of Nevada, Reno
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Sergey A Varganov
University of Nevada, Reno
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Yuri Alexeev
Argonne National Laboratory