Enhancing quantum utility: Simulating large-scale quantum spin chains on superconducting quantum computers

Abstract

We present the quantum simulation of the frustrated quantum spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mfrac><a:mn>1</a:mn><a:mn>2</a:mn></a:mfrac></a:math> antiferromagnetic Heisenberg spin chain with competing nearest-neighbor <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>(</b:mo><b:msub><b:mi>J</b:mi><b:mn>1</b:mn></b:msub><b:mo>)</b:mo></b:mrow></b:math> and next-nearest-neighbor <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>(</c:mo><c:msub><c:mi>J</c:mi><c:mn>2</c:mn></c:msub><c:mo>)</c:mo></c:mrow></c:math> exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest-neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing the first-order Trotterization. Furthermore, our implementation of the second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era. Published by the American Physical Society 2024

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