Simulations of Frustrated Ising Hamiltonians with Quantum Approximate Optimization

Abstract

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study Ising spin models on unit cells of square, Shastry-Sutherland, and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements ( < ∼ 100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.

Modelling noise in global Molmer-Sorensen interactions applied to quantum approximate optimization

“…One application is the quantum approximate optimization algorithm (QAOA) [14], which is often viewed as a leading candidate algorithm for near-term quantum computers [15]. QAOA has been a topic of contemporary research including experiments [16][17][18], theory [19][20][21][22][23], and simulations [24][25][26], with applications ranging from combinatorial optimization to quantum simulation [27][28][29]. In digital approaches to QAOA, it is expected that two-qubit gate error rates of 10 −5 − 10 −6 will be necessary for quantum advantage [30][31][32][33], while a recent proposal for QAOA with many-qubit MS interactions uses far shallower circuits in certain contexts [34], potentially avoiding the digital limitations.…”