Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

This tutorial introduces the theoretical and experimental basics of electromagnetically induced transparency (EIT) in thermal alkali vapors. We first give a brief phenomenological description of EIT in simple three-level systems of stationary atoms and derive analytical expressions for optical absorption and dispersion under EIT conditions. Then we focus on how the thermal motion of atoms affects various parameters of the EIT system. Specifically, we analyze the Doppler broadening of optical transitions, ballistic versus diffusive atomic motion in a limited-volume interaction region, and collisional depopulation and decoherence. Finally, we discuss the common trade-offs important for optimizing an EIT experiment and give a brief 'walk-through' of a typical EIT experimental setup. We conclude with a brief overview of current and potential EIT applications.

A visualization scheme for quantum many-body wavefunctions is described that we have termed qubism. Its main property is its recursivity: increasing the number of qubits results in an increase in the image resolution. Thus, the plots are typically fractal. As examples, we provide images for the ground states of commonly used Hamiltonians in condensed matter and cold atom physics, such as Heisenberg or ITF. Many features of the wavefunction, such as magnetization, correlations and criticality, can be visualized as properties of the images. In particular, factorizability can be easily spotted, and a way to estimate the entanglement entropy from the image is provided.

In this work we present theoretical calculations and analysis of the vibronic structure of the spin-triplet optical transition in diamond nitrogen-vacancy (NV) centres. The electronic structure of the defect is described using accurate first-principles methods based on hybrid functionals. We devise a computational methodology to determine the coupling between electrons and phonons during an optical transition in the dilute limit. As a result, our approach yields a smooth spectral function of electron–phonon coupling and includes both quasi-localized and bulk phonons on equal footings. The luminescence lineshape is determined via the generating function approach. We obtain a highly accurate description of the luminescence band, including all key parameters such as the Huang–Rhys factor, the Debye–Waller factor, and the frequency of the dominant phonon mode. More importantly, our work provides insight into the vibrational structure of NV centres, in particular the role of local modes and vibrational resonances. In particular, we find that the pronounced mode at 65 meV is a vibrational resonance, and we quantify localization properties of this mode. These excellent results for the benchmark diamond (NV) centre provide confidence that the procedure can be applied to other defects, including alternative systems that are being considered for applications in quantum information processing.

Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.

Quantum mechanics is an incredibly successful theory and yet the statistical nature of its predictions is hard to accept and has been the subject of numerous debates. The notion of inherent randomness, something that happens without any cause, goes against our rational understanding of reality. To add to the puzzle, randomness that appears in non-relativistic quantum theory tacitly respects relativity, for example, it makes instantaneous signaling impossible. Here, we argue that this is because the special theory of relativity can itself account for such a random behavior. We show that the full mathematical structure of the Lorentz transformation, the one which includes the superluminal part, implies the emergence of non-deterministic dynamics, together with complex probability amplitudes and multiple trajectories. This indicates that the connections between the two seemingly different theories are deeper and more subtle than previously thought.

There has been rapid development of systems that yield strong interactions between freely propagating photons in one-dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing with photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized 'input–output' formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.

We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global 'micro-canonical' constraint, i.e. conserving the total magnetization. We will show that this system has an additional discrete symmetry that is specific to the Liouvillean description of the problem. Such symmetry reduces the dynamics even more than would be expected in the standard Hilbert space formalism and establishes existence of multiple steady states. Interestingly, numerical simulations of the XXZ model suggest that a pair of distinct non-equilibrium steady states becomes indistinguishable in the thermodynamic limit, and exhibit sub-diffusive spin transport in the easy-axis regime of anisotropy Δ > 1.

The metascreen-based acoustic passive phased array provides a new degree of freedom for manipulating acoustic waves due to their fascinating properties, such as a fully shifting phase, keeping impedance matching, and holding subwavelength spatial resolution. We develop acoustic theories to analyze the transmission/reflection spectra and the refracted pressure fields of a metascreen composed of elements with four Helmholtz resonators (HRs) in series and a straight pipe. We find that these properties are also valid under oblique incidence with large angles, with the underlying physics stemming from the hybrid resonances between the HRs and the straight pipe. By imposing the desired phase profiles, the refracted fields can be tailored in an anomalous yet controllable manner. In particular, two types of negative refraction are exhibited, based on two distinct mechanisms: one is formed from classical diffraction theory and the other is dominated by the periodicity of the metascreen. Positive (normal) and negative refractions can be converted by simply changing the incident angle, with the coexistence of two types of refraction in a certain range of incident angles.

We study the system where a superconducting flux qubit is capacitively coupled to an LC resonator. In three devices with different coupling capacitance, the magnitude of the dispersive shift is enhanced by the third level of the qubit and quantitatively agrees with the theory. We show by numerical calculation that the capacitive coupling plays an essential role for the enhancement in the dispersive shift. We investigate the coherence properties in two of these devices, which are in the strong-dispersive regime, and show that the qubit energy relaxation is currently not limited by the coupling. We also observe the discrete ac-Stark effect, a hallmark of the strong-dispersive regime, in accordance with the theory.

Recent experiments, combing ultrafast strong-field irradiation of surfaces with time- and angle-resolved photoemission spectroscopy, allow for monitoring the time-dependent charge carrier dynamics and the build-up of transient sidebands due to the radiation pulses. While these structures are reminiscent of Floquet–Bloch bands, standard Floquet theory is not applicable since it requires a strictly time-periodic driving field. To study the emergence and formation of such sidebands, i.e. to provide a link between common Floquet physics and dynamical mechanisms underlying short driving pulses, we consider a generalization of Floquet theory, the so-called $t-t^{^{\prime}}$ formalism. This approach naturally extents Floquet theory to driving field amplitudes with a superimposed envelope shape. Motivated by experiments we study 2D Dirac Hamiltonians subject to linearly and circularly polarised light waves with a Gaussian field envelope of a few cycles. For these Floquet–Bloch Hamiltonians we study the evolution of their Floquet–Bloch spectra, accompanied by a systematic analysis of the time-dependent (sideband) transitions. We show that sideband occupation requires circularly polarized light for linear Dirac systems such as graphene, while for Dirac models with trigonal warping, describing surface states of topological insulators such as $\mathrm{Bi_2 Se_3}$, both linearly and circularly polarised pulses induce sideband excitations.

Current research in statistical mechanics mostly concerns the investigation of out-of-equilibrium, irreversible processes, which are ubiquitous in nature and still far from being theoretically understood. Even the precise characterization of irreversibility is the object of an open debate: while in the context of Hamiltonian systems the one-century-old proposal by M. Smoluchowski looks still valid (a process appears irreversible when the initial state has a recurrence time that is long compared to the time of observation (Smoluchowski 1916 Z. Phys.17 557–85)), in dissipative systems, particularly in the case of stochastic processes, the problem is more involved, and quantifying the 'degree of irreversibility' is a pragmatic need. The most employed strategies rely on the estimation of entropy production: this quantity, although mathematically well-defined, is often difficult to compute, especially when analyzing experimental data. Moreover, being a global observable, entropy production fails to capture specific aspects of irreversibility in extended systems, such as the role of different currents and their spatial development. This review aims to address various conceptual and technical challenges encountered in the analysis of irreversibility, including the role of the coarse-graining procedure and the treatment of data in the absence of complete information. The discussion will be mostly based on simple models, analytically treatable, and supplemented by examples of complex, more realistic non-equilibrium systems.

The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQAs) are a promising family of hybrid quantum–classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search, a powerful artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits.

The Thouless theory of quantum pumps establishes the conditions for quantized particle transport per cycle, and determines its value. When describing the pump from a moving reference frame, transported and existing charges transform, though not independently. This transformation is inherent to Galilean space and time, but it is underpinned by a transformation of vector bundles. Different formalisms can be used to describe this transformation, including one based on Bloch theory. Depending on the chosen formalism, the two types of charges will be realized as indices of either the same or different kinds. Finally, we apply the bulk-edge correspondence principle, so as to implement the transformation law within Büttiker's scattering theory of quantum pumps.

Newly calculated bounds on the strength of the coupling of an electron to a proton or a neutron by a fifth force are presented. These results are derived from the high precision spectroscopic data currently available for hydrogen, deuterium, helium-3 and helium-4. They do not depend on specific assumptions on how the interaction would couple to a deuteron compared to a proton or would couple to an α particle compared to a helion. They depend on its coupling to a muon, but not in a significant way for carrier masses below 100 keV if one assumes that the strength of the interaction with a muon would be of a similar order of magnitude as the strength of the interaction with an electron in that mass region.

Current research in statistical mechanics mostly concerns the investigation of out-of-equilibrium, irreversible processes, which are ubiquitous in nature and still far from being theoretically understood. Even the precise characterization of irreversibility is the object of an open debate: while in the context of Hamiltonian systems the one-century-old proposal by M. Smoluchowski looks still valid (a process appears irreversible when the initial state has a recurrence time that is long compared to the time of observation (Smoluchowski 1916 Z. Phys.17 557–85)), in dissipative systems, particularly in the case of stochastic processes, the problem is more involved, and quantifying the 'degree of irreversibility' is a pragmatic need. The most employed strategies rely on the estimation of entropy production: this quantity, although mathematically well-defined, is often difficult to compute, especially when analyzing experimental data. Moreover, being a global observable, entropy production fails to capture specific aspects of irreversibility in extended systems, such as the role of different currents and their spatial development. This review aims to address various conceptual and technical challenges encountered in the analysis of irreversibility, including the role of the coarse-graining procedure and the treatment of data in the absence of complete information. The discussion will be mostly based on simple models, analytically treatable, and supplemented by examples of complex, more realistic non-equilibrium systems.

There are several mathematical formulations of quantum mechanics. The Schrödinger picture expresses quantum states in terms of wavefunctions over, e.g. position or momentum. Alternatively, phase-space formulations represent states with quasi-probability distributions over, e.g. position and momentum. A quasi-probability distribution resembles a probability distribution but may have negative and non-real entries. The most famous quasi-probability distribution, the Wigner function, has played a pivotal role in the development of a continuous-variable quantum theory that has clear analogues of position and momentum. However, the Wigner function is ill-suited for much modern quantum-information research, which is focused on finite-dimensional systems and general observables. Instead, recent years have seen the Kirkwood–Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summarise the KD distribution's extensive usage in the study or development of measurement disturbance; quantum metrology; weak values; direct measurements of quantum states; quantum thermodynamics; quantum scrambling and out-of-time-ordered correlators; and the foundations of quantum mechanics, including Leggett–Garg inequalities, the consistent-histories interpretation and contextuality. We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities. Third, we delve into the KD distribution's mathematical structure. We summarise the current knowledge regarding the geometry of KD-positive states (the states for which the KD distribution is a classical probability distribution), describe how to witness and quantify KD non-positivity, and outline relationships between KD non-positivity, coherence and observables' incompatibility.

We investigate known mechanisms for enhancing nuclear fusion rates at ambient temperatures and pressures in solid-state environments. In deuterium fusion, on which the paper is focused, an enhancement of >40 orders of magnitude would be needed to achieve observable fusion. We find that different mechanisms for fusion rate enhancement are known across the domains of atomic physics, nuclear physics, and quantum dynamics. Cascading multiple such mechanisms could lead to an overall enhancement of 40 orders of magnitude or more. We present a roadmap with examples of how hypothesis-driven research could be conducted in—and across—each domain to probe the plausibility of technologically-relevant fusion in the solid state.

Alkali atomic vapor lasers have gained significant attention in recent decades as a promising option for high-powered and efficient laser systems. Utilizing hot alkali atomic vapor as the optical gain medium, these lasers, in principle, offer several advantages, such as high quantum efficiency, reduced thermal issues, and high beam quality. This paper reviews critical techniques developed in recent years to enhance the power and efficiency of these lasers. We discuss continuous wave laser optimization strategies, optical amplifier schemes, and pulsed laser generation based on hot alkali atomic vapor cells. Additionally, select findings from the authors' research group are presented.

Turbulence closure modeling using machine learning (ML) is at an early crossroads. The extraordinary success of ML in a variety of challenging fields had given rise to an expectation of similar transformative advances in the area of turbulence closure modeling. However, by most accounts, the current rate of progress toward accurate and predictive ML-RANS (Reynolds Averaged Navier–Stokes) closure models has been very slow. Upon retrospection, the absence of rapid transformative progress can be attributed to two factors: the underestimation of the intricacies of turbulence modeling and the overestimation of ML's ability to capture all features without employing targeted strategies. To pave the way for more meaningful ML closures tailored to address the nuances of turbulence, this article seeks to review the foundational flow physics to assess the challenges in the context of data-driven approaches. Revisiting analogies with statistical mechanics and stochastic systems, the key physical complexities and mathematical limitations are explicated. It is noted that the current ML approaches do not systematically address the inherent limitations of a statistical approach or the inadequacies of the mathematical forms of closure expressions. The study underscores the drawbacks of supervised learning-based closures and stresses the importance of a more discerning ML modeling framework. As ML methods evolve (which is happening at a rapid pace) and our understanding of the turbulence phenomenon improves, the inferences expressed here should be suitably modified.

Superfluid helium, the inviscid low-temperature phase of liquid 4He, enables investigation of flows with reduced dimensionality since, due to the vanishing viscosity, sub-micron flow channels can be constructed. In such strongly confined volumes filled with superfluid, the longitudinal acoustic wave is a coupled fluctuation of pressure and entropy density called fourth sound. In this work, we use multiple 4th sound acoustic modes inside a nano-superfluidic acoustic resonator in a pump-probe arrangement to observe localized clusters of quantized vortices leading to two-dimensional turbulence. The localised turbulence enables controllable and asymmetric dissipative coupling between acoustic modes. Furthermore, we derive a general procedure for analytically estimating the superfluid acoustic resonance frequencies inside a volume with mechanically compliant walls. Our work confirms earlier assumptions that turbulence in similar nanofluidic systems initially develops in localized areas of high shear. The multimode pump-probe methods presented here will allow future experiments to study the dynamics of two-dimensional quantum turbulence, e.g., the free decay.

We explore the spin texture dynamics of a harmonically trapped spin-1 Bose-Einstein condensate with Rashba spin-orbit coupling and ferromagnetic spin-exchange interactions under a sinusoidally varying magnetic field along the $x$-direction. This interplay yields an intrinsic spin texture in the ground state, forming a linear chain of alternating skyrmions at the saddle points. Our study analyzes the spin-mixing dynamics for both a freely evolving and a controlled longitudinal magnetization. The spin-1 system exhibits the Einstein-de Haas effect for the first case, for which an exchange between the total orbital angular momentum and the spin angular momentum is observed, resulting in minimal oscillations about the initial position of the skyrmion chain. However, for the fixed magnetization dynamics, the skyrmion chain exhibits ample angular oscillations about the equilibrium position, with the temporary formation of new skyrmions to facilitate the oscillatory motion. For the case of fixed magnetization, this contrast now stems from the exchange between the canonical and spin-dependent contribution to the orbital angular momentum. The variation in canonical angular momentum is linked to the angular oscillations, while the spin-dependent angular momentum accounts for the creation or annihilation of skyrmions. We confirm the presence of scissors mode excitations in the spin texture due to the angular skyrmion oscillations.

Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin proved a powerful no-go theorem, according to which nonlinear quantum dynamics would lead to superluminal signalling, violating Einstein's causality. Here we analyse the theorem from the perspective of recent developments. First, we observe that it harmonises with the no-restriction hypothesis from General Probabilistic Theories. Second, we note that it requires a suitable synchronisation of Alice's and Bob's clocks and actions. Next, we argue that it does not automatically exclude the possibility of global nonlinear quantum dynamics on a tensor product Hilbert space. Consequently, we investigate a class of such dynamics inspired by discrete analogues of nonlinear Schrödinger equations. We show that, in general, they exhibit a chaotic character. In this context we inspect whether superluminal signalling can be avoided by relaxing the no-restriction hypothesis. We study three possible communication protocols involving either local measurements or modifications of a local Hamiltonian. We conclude that, in general, in all three cases, two spacelike separated parties can effectuate statistical superluminal information transfer. Nevertheless, we show an example of a nonlocal nonlinear quantum dynamics, which does not allow for it, provided that we relax the no-restriction hypothesis.

We study spin-dynamics and quantum magnetism with ultracold highly-magnetic atoms. In particular, we focus on the interactions among rare-earth atoms localized in a site of an optical-lattice potential, modeled as a cylindrically symmetric harmonic oscillator in the presence of a weak external magnetic field. The interactions between the atoms are modeled using multi-channel Hamiltonian containing multiple spin-spin and anisotropic spin-orbit interactions with strengths that depend on the separation between the atoms. We studied the eigenenergies of the atom pair in a site for different lattice-site geometries and magnetic field strengths. In parallel, we compared these energies to those found from a simplified approach, where the complex-collisional physics is replaced by a two-length-scale pseudo-potential containing a contact and the magnetic dipole-dipole interaction. The eigenenergies within this model can be computed analytically within the Born approximation as well as non-perturbatively for stronger contact interactions. We have shown that the pseudo-potential model can accurately represent the multi-channel Hamiltonian in certain parameter regimes of the shape or geometry of the site of an optical lattice. The pseudo-potential forms the starting point for many-body, condensed matter simulations involving many atom pairs in different sites of an optical lattice.

Alkali-noble-gas comagnetometers have become an essential tool for tests of fundamental physics and offer a compact platform for precision gyroscopy. They are, however, limited by technical noise at low frequencies, commonly due to their limited suppression of magnetic noise. Here we investigate a new method for co-magnetometry between a single noble gas and alkali species. While similar to well-known devices using self-compensation, our scheme introduces magnetic pulses that controllably perturb the noble gas and pulsed optical pumping to polarise the alkali atoms. These applied pulses allow our scheme to measure, rather than just suppress, the effect of magnetic noise thereby offering reduced cross-talk. We show numerically that our scheme retrieves four signals (rotations and magnetic fields on two transverse axes) with similar sensitivity to a single axis device. We also present a proof-of-principle experiment based on a 87Rb-129Xe cell. Our data shows a low magnetic-rotation cross-talk of 0.2 ±0.1µHz/pT, which is already on par with the most sensitive devices relying on self-compensation.