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Quantum Hamiltonian simulation, which simulates the evolution of quantum systems and probes quantum phenomena, is one of the most promising applications of quantum computing. Recent experimental results suggest that Hamiltonian-oriented analog quantum simulation would be advantageous over circuit-oriented digital quantum simulation in the Noisy Intermediate-Scale Quantum (NISQ) machine era. However, programming analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software. In this paper, we design and implement SimuQ, the first framework for quantum Hamiltonian simulation that supports Hamiltonian programming and pulse-level compilation to heterogeneous analog quantum simulators. Specifically, in SimuQ, front-end users specify the target quantum system with Hamiltonian Modeling Language, and the Hamiltonian-level programmability of analog quantum simulators is specified through a new abstraction called the abstract analog instruction set (AAIS) and programmed in AAIS Specification Language by hardware providers. Through a solver-based compilation, SimuQ generates executable pulse schedules for real devices to simulate the evolution of desired quantum systems, which is demonstrated on superconducting (IBM), neutral-atom (QuEra), and trapped-ion (IonQ) quantum devices. Moreover, we demonstrate the advantages of exposing the Hamiltonian-level programmability of devices with native operations or interaction-based gates and establish a small benchmark of quantum simulation to evaluate SimuQ's compiler with the above analog quantum simulators.

Meditation is an umbrella term for a number of mental training practices designed to improve the monitoring and regulation of attention and emotion. Some forms of meditation are now being used for clinical intervention. To accompany the increased clinical interest in meditation, research investigating the neural basis of these practices is needed. A central hypothesis of contemplative neuroscience is that meditative states, which are unique on a phenomenological level, differ on a neurophysiological level. To identify the electrophysiological correlates of meditation practice, the electrical brain activity of highly skilled meditators engaging in one of six meditation styles (shamatha, vipassana, zazen, dzogchen, tonglen, and visualization) was recorded. A mind-wandering task served as a control. Lempel–Ziv complexity showed differences in nonlinear brain dynamics (entropy) during meditation compared with mind wandering, suggesting that meditation, regardless of practice, affects neural complexity. In contrast, there were no differences in power spectra at six different frequency bands, likely due to the fact that participants engaged in different meditation practices. Finally, exploratory analyses suggest neurological differences among meditation practices. These findings highlight the importance of studying the electroencephalography (EEG) correlates of different meditative practices.