Semantics for variational Quantum programming

We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The classical subsystem of the language is the Probabilistic FixPoint Calculus (PFPC), which is a lambda calculus with mixed-variance recursive types, term recursion and probabilistic choice. The quantum subsystem is a first-order linear type system that can manipulate quantum information. The two subsystems are related by mixed classical/quantum terms that specify how classical probabilistic effects are induced by quantum measurements, and conversely, how classical (probabilistic) programs can influence the quantum dynamics. We also describe a sound and computationally adequate denotational semantics for the language. Classical probabilistic effects are interpreted using a recently-described commutative probabilistic monad on DCPO. Quantum effects and resources are interpreted in a category of von Neumann algebras that we show is enriched over (continuous) domains. This strong sense of enrichment allows us to develop novel semantic methods that we use to interpret the relationship between the quantum and classical probabilistic effects. By doing so we provide a very detailed denotational analysis that relates domain-theoretic models of classical probabilistic programming to models of quantum programming.

An Open Dynamical System Approach to Dissipative Quantum Dot Array Antennas

A new computational approach to quantum antennas based on first principle open stochastic quantum dynamics.<div><br></div><div>We develop a general computational approach for the analysis and design of quantum antenna systems comprised of coupled quantum dot arrays interacting with external fields and producing quantum radiation. The method is based on using the GKSL master equation to model quantum dissipation and decoherence. The density operator of a coupled two-level quantum dot (qbit) array, excited by classical external signals with variable amplitude and phase, is evolved in time using a quantum Liouville-like equation (the master equation). We illustrate the method in a numerical example where it is shown that manipulating the phase excitations of individual quantum dots may significantly enhance the directive radiation properties of the quantum dot antenna system<br></div>

An Open Dynamical System Approach to Dissipative Quantum Dot Array Antennas

A new computational approach to quantum antennas based on first principle open stochastic quantum dynamics.<div><br></div><div>We develop a general computational approach for the analysis and design of quantum antenna systems comprised of coupled quantum dot arrays interacting with external fields and producing quantum radiation. The method is based on using the GKSL master equation to model quantum dissipation and decoherence. The density operator of a coupled two-level quantum dot (qbit) array, excited by classical external signals with variable amplitude and phase, is evolved in time using a quantum Liouville-like equation (the master equation). We illustrate the method in a numerical example where it is shown that manipulating the phase excitations of individual quantum dots may significantly enhance the directive radiation properties of the quantum dot antenna system<br></div>

Observing the loss and revival of long-range phase coherence through disorder quenches

Relaxation of quantum systems is a central problem in nonequilibrium physics. In contrast to classical systems, the underlying quantum dynamics results not only from atomic interactions but also from the long-range coherence of the many-body wave function. Experimentally, nonequilibrium states of quantum fluids are usually created using moving objects or laser potentials, directly perturbing and detecting the system’s density. However, the fate of long-range phase coherence for hydrodynamic motion of disordered quantum systems is less explored, especially in three dimensions. Here, we unravel how the density and phase coherence of a Bose–Einstein condensate of 6Li2 molecules respond upon quenching on or off an optical speckle potential. We find that, as the disorder is switched on, long-range phase coherence breaks down one order of magnitude faster than the density of the quantum gas responds. After removing it, the system needs two orders of magnitude longer times to reestablish quantum coherence, compared to the density response. We compare our results with numerical simulations of the Gross–Pitaevskii equation on large three-dimensional grids, finding an overall good agreement. Our results shed light on the importance of long-range coherence and possibly long-lived phase excitations for the relaxation of nonequilibrium quantum many-body systems.

Quantum Dynamics of Water from Møller-Plesset Perturbation Theory via a Neural Network Potential

We report the static and dynamical properties of liquid water at the level of second-order Møller-Plesset per- perturbation theory (MP2) with classical and quantum nuclear dynamics using a neural network potential. We examined the temperature-dependent radial distribution functions, diffusion, and vibrational dynamics. MP2 theory predicts over-structured liquid water as well as a lower diffusion coefficient at ambient conditions compared to experiments, which may be attributed to the incomplete basis set. A better agreement with experimental structural properties and the diffusion constant are observed at an elevated temperature of 340 K from our simulations. Although the high-level electronic structure calculations are expensive, training a neural network potential requires only a few thousand frames. The approach is promising as it involves modest human effort and is straightforwardly extensible to other simple liquids.