Microscopics of Quantum Annealing in the Disordered Dipolar Ising Ferromagnet LiHo $_{x}$ Y $_{1-x}$ F $_4$ Microscopics of Quantum Annealing in the Disordered Dipolar Ising Ferromagnet LiHo$_{x}$Y$_{1-x}$F$_4$

S. Säubert, Colin L. Sarkis, F. Ye +2 more

Quantum annealing (QA) refers to an optimization process that uses quantum fluctuations to find the global minimum of a rugged energy landscape with many local minima. Conceptually, QA is often framed in the context of the disordered transverse field Ising model, in which a magnetic field applied perpendicular to the Ising axis tunes the quantum fluctuations and enables the system to tunnel through energy barriers, and hence reach the ground state more quickly. A solid state material closely related to this model, LiHo $_{0.45}$ Y $_{0.55}$ F $_4$ , was shown to exhibit faster dynamics after a QA protocol, compared to thermal annealing (TA), but little is known about the actual process of optimization involved or the nature of the spin correlations in the state that is reached. Here, we report on the microscopics of QA in this material using diffuse magnetic neutron scattering. Comparing a QA to a TA protocol that reach the same end-point, we find very similar final diffuse scattering which consists of pinch-point scattering, largely consistent with critical scattering near a phase boundary in the dipolar Ising ferromagnetic model. However, comparing the time evolution at the end of the protocols, we find that the spin correlations evolve more significantly after TA, suggesting that QA produces a state closer to equilibrium. We also observe experimental evidence that the transverse field produces random fields, which had been previously predicted for this material and studied in other contexts. Thus, while the material does exhibit a quantum speedup under quantum annealing conditions, it is not a simple annealing problem; the energy landscape being optimized is changing as the optimization proceeds.Quantum annealing (QA) refers to an optimization process that uses quantum fluctuations to find the global minimum of a rugged energy landscape with many local minima. Conceptually, QA is often framed in the context of the disordered transverse field Ising model, in which a magnetic field applied perpendicular to the Ising axis tunes the quantum fluctuations and enables the system to tunnel through energy barriers, and hence reach the ground state more quickly. A solid state material closely related to this model, LiHo$_{0.45}$Y$_{0.55}$F$_4$, was shown to exhibit faster dynamics after a QA protocol, compared to thermal annealing (TA), but little is known about the actual process of optimization involved or the nature of the spin correlations in the state that is reached. Here, we report on the microscopics of QA in this material using diffuse magnetic neutron scattering. Comparing a QA to a TA protocol that reach the same end-point, we find very similar final diffuse scattering which consists of pinch-point scattering, largely consistent with critical scattering near a phase boundary in the dipolar Ising ferromagnetic model. However, comparing the time evolution at the end of the protocols, we find that the spin correlations evolve more significantly after TA, suggesting that QA produces a state closer to equilibrium. We also observe experimental evidence that the transverse field produces random fields, which had been previously predicted for this material and studied in other contexts. Thus, while the material does exhibit a quantum speedup under quantum annealing conditions, it is not a simple annealing problem; the energy landscape being optimized is changing as the optimization proceeds.

arXiv:2105.03408May 7, 20211 citation

Optimization algorithms for Quantum Annealing

E. Arvidsson

Jan 1, 20200 citations

Pulsed Quantum Annealing

Vasilios D. Karanikolas, Shiro Kawabata

We propose a modified quantum annealing protocol, i. e., pulsed quantum annealing} (PQA), in order to increase the success probability by a pulse application during the quantum annealing process. It is well known that the success probability of the conventional quantum annealing is reduced due to the Landau-Zener transitions. By applying a pulse to the system, we modulate the success probability and increase it, compared to the conventional quantum annealing, by optimizing the pulse parameters. We demonstrate our findings for a single qubit both numerically and analytically. The analytical model is based on the tranfer matrix approach and it is in good agreement with the full numerical results. We also investigate the PQA protocol for multi-qubit cases $i. e.,$ random spin-glass instances, and we present an overall increase of the success probability over the conventional quantum annealing, by optimizing the pulse parameters. Our results indicate that PQA can be used to design future high-performance quantum annealing machines, especially for hard instances that the conventional QA protocol behaves poorly.We propose a modified quantum annealing protocol, i. e., pulsed quantum annealing} (PQA), in order to increase the success probability by a pulse application during the quantum annealing process. It is well known that the success probability of the conventional quantum annealing is reduced due to the Landau-Zener transitions. By applying a pulse to the system, we modulate the success probability and increase it, compared to the conventional quantum annealing, by optimizing the pulse parameters. We demonstrate our findings for a single qubit both numerically and analytically. The analytical model is based on the tranfer matrix approach and it is in good agreement with the full numerical results. We also investigate the PQA protocol for multi-qubit cases $i. e.,$ random spin-glass instances, and we present an overall increase of the success probability over the conventional quantum annealing, by optimizing the pulse parameters. Our results indicate that PQA can be used to design future high-performance quantum annealing machines, especially for hard instances that the conventional QA protocol behaves poorly.

arXiv:1806.08517Journal of the Physical Society of JapanAug 17, 20207 citations

Reverse annealing for the fully connected p-spin model

秀稔西森, Hidetoshi Nishimori, Daniel A. Lidar

Aug 1, 20180 citations

Greedy parameter optimization for diabatic quantum annealing

Tadashi Kadowaki, Hidetoshi Nishimori

A shorter processing time is desirable for quantum computation to minimize the effects of noise. We propose a simple procedure to variationally determine a set of parameters in the transverse-field Ising model for quantum annealing (QA) appended with a field along the [Formula: see text]-axis. The method consists of greedy optimization of the signs of coefficients of the [Formula: see text]-field term based on the outputs of short annealing processes. We test the idea in the ferromagnetic system with all-to-all couplings and spin-glass problems, and find that the method outperforms the traditional form of QA and simulated annealing in terms of the success probability and the time to solution, in particular, in the case of shorter annealing times, achieving the goal of improved performance while avoiding noise. The non-stoquastic [Formula: see text] term can be eliminated by a rotation in the spin space, resulting in a non-trivial diabatic control of the coefficients in the stoquastic transverse-field Ising model, which may be feasible for experimental realization. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.A shorter processing time is desirable for quantum computation to minimize the effects of noise. We propose a simple procedure to variationally determine a set of parameters in the transverse-field Ising model for quantum annealing (QA) appended with a field along the [Formula: see text]-axis. The method consists of greedy optimization of the signs of coefficients of the [Formula: see text]-field term based on the outputs of short annealing processes. We test the idea in the ferromagnetic system with all-to-all couplings and spin-glass problems, and find that the method outperforms the traditional form of QA and simulated annealing in terms of the success probability and the time to solution, in particular, in the case of shorter annealing times, achieving the goal of improved performance while avoiding noise. The non-stoquastic [Formula: see text] term can be eliminated by a rotation in the spin space, resulting in a non-trivial diabatic control of the coefficients in the stoquastic transverse-field Ising model, which may be feasible for experimental realization. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

arXiv:2111.13287Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesDec 4, 202215 citations

Microscopics of Quantum Annealing in the Disordered Dipolar Ising Ferromagnet LiHo

_{x}

_{1-x}

_4

_{0.45}

_{0.55}

_4

, was shown to exhibit faster dynamics after a QA protocol, compared to thermal annealing (TA), but little is known about the actual process of optimization involved or the nature of the spin correlations in the state that is reached. Here, we report on the microscopics of QA in this material using diffuse magnetic neutron scattering. Comparing a QA to a TA protocol that reach the same end-point, we find very similar final diffuse scattering which consists of pinch-point scattering, largely consistent with critical scattering near a phase boundary in the dipolar Ising ferromagnetic model. However, comparing the time evolution at the end of the protocols, we find that the spin correlations evolve more significantly after TA, suggesting that QA produces a state closer to equilibrium. We also observe experimental evidence that the transverse field produces random fields, which had been previously predicted for this material and studied in other contexts. Thus, while the material does exhibit a quantum speedup under quantum annealing conditions, it is not a simple annealing problem; the energy landscape being optimized is changing as the optimization proceeds.

i. e.,

random spin-glass instances, and we present an overall increase of the success probability over the conventional quantum annealing, by optimizing the pulse parameters. Our results indicate that PQA can be used to design future high-performance quantum annealing machines, especially for hard instances that the conventional QA protocol behaves poorly.