Quantum optimization of maximum independent set using Rydberg atom arrays

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.

Probing topological spin liquids on a programmable quantum simulator

[Figure: see text].

Controlling quantum many-body dynamics in driven Rydberg atom arrays

The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.

Generation and manipulation of Schrödinger cat states in Rydberg atom arrays

Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of "Schrödinger cat" states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.

A randomized, single blind placebo controlled clinical trial on the effect of continuous ultrasound on low back pain

Low back pain (LBP) is a very common problem in primary care and a major cause of disability. There is no evidence for the efficacy of therapeutic modalities such as ultrasound in LBP In a randomized, single blind placebo controlled clinical trial, we aimed to evaluate the effect of continuous ultrasound (US) in patients with non specific LBP Of the fifty eight patients recruited, 10 patients (8 women and 2 men) randomly allocated to ultrasound (n=5) or placebo controlled (n=5) groups. The patients were treated by either US or sham-US for ten sessions, three days per week, every other day. The outcome measures were Functional Rating Index (FRI), Hmax/Mmax ratio and range of motion (ROM), which were measured at baseline, after 5 treatment sessions and at the end of treatment. To analyze the data, The Mann Whitney U test and Wilcoxon Signed Rank test were used. After treatment, both US and placebo groups showed statistically significant decrease in FRI scores indicating improvement in functional ability (p = 0.042 and p = 0.043, respectively). The mean changes of FRI during the second five treatment sessions and after the end of treatment was significantly better in the US group than in the placebo group (p = 0.016 and p = 0.032, respectively). Before and after treatment, the mean H reflex latency and Hmax/Mmax ratio, right and left side were similar in the groups (p > 0.05), and no significant changes were observed in the treatment groups (p > 0.05). After treatment, the extension and lateral flexion range of motion significantly increased in the US group (p = 0.04), but the back movements in the placebo group did not show significant changes (p > 0.05). The present study supports the significant effect of US on LBP, and suggests that US may improve the functional ability of patients with non specific low back pain.