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.

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.

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.

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.

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.

We implement a Szilard engine using a 2-bit logical unit consisting of inductively coupled quantum flux parametrons—Josephson-junction superconducting circuits with applications in both the classical and quantum information processing regimes. Detailed simulations show that it is highly thermodynamically efficient while functioning as a Maxwell demon—converting heat to work. The physically-calibrated design is targeted to direct experimental exploration. However, in realizing experiments variations in Josephson junction fabrication introduce asymmetries that result in energy inefficiency and low operational fidelity. We provide a design solution that mitigates these practical challenges. The resulting platform is ideally suited to probe the thermodynamic foundations of information processing devices far from equilibrium.

We show theoretically that it is possible to coherently transfer vibrational excitation between trapped neutral atoms over a micrometer apart. To this end we consider three atoms, where two are in the electronic ground state and one is excited to a Rydberg state whose electronic orbital overlaps with the positional wave functions of the two ground-state atoms. The resulting scattering of the Rydberg electron with the ground-state atoms provides the interaction required to transfer vibrational excitation from one trapped atom to the other. By numerically investigating the dependence of the transfer dynamics on the distance between traps and their relative frequencies we find that there is a 'sweet spot' where the transfer of a vibrational excitation is nearly perfect and fast compared to the Rydberg lifetime. We investigate the robustness of this scenario with respect to changes of the parameters. In addition, we derive a intuitive effective Hamiltonian which explains the observed dynamics.

Radiofrequency ion traps are essential for many experiments, ranging from quantum computing to physical chemistry and fundamental science. However, in some circumstances the trapping fields may cause undesired effects and need to be switched off briefly during operation without compromising the trap stability. By employing interference in the trap resonator circuit to enable switching faster than the resonator's natural decay, the electric field in the trap can be extinguished by $\gt$50 dB. We have demonstrated that it is possible to switch a linear Paul trap off for several microseconds without the loss of ⁴⁰Ca⁺ ions, even for large three-dimensional ion crystals, and have examined the effect of the switching parameters on the ion dynamics by monitoring the fluorescence rate. We have loaded N${\,}_2^+$ ions into a crystal of trapped calcium ions via photoionisation using this technique, demonstrating that it is also possible to capture ions despite the absence of a trapping field during the ionisation.

The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact, a useful way to distinguish between classical and nonclassical states of light is to ask whether their Wigner function has a Gaussian profile or not, respectively. In this paper, we use the basis of Fock states to provide the closed-form expression for the Wigner function of an arbitrary quantum state. Thus, we provide the general expression for the Wigner function of a squeezed Fock, coherent and thermal states, with an arbitrary squeezing parameter. Then, we consider the most fundamental quantum system, Resonance Fluorescence, and obtain closed-form expressions for its Wigner function under various excitation regimes. With them, we discuss the conditions for obtaining a negative-valued Wigner function and the relation it has with population inversion. Finally, we address the problem of the observation of the radiation field, introducing physical detectors into the description of the emission. Notably, we show how to expose the quantumness of a radiation field that has been observed with a detector with finite spectral resolution, even if the observed Wigner function is completely positive.

We demonstrate how to prepare magnon-polariton (MP) multistable entangled states in a single crystal with a nonlinear cavity magnonic system. The switching and control between classical and quantum regimes are achieved solely through external amplitude modulation of a magnetic sample. Our work represents the first study of multistable quantum correlations between MPs and can be applied to quantum multistable switches and protection of entangled states in quantum communication.

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.

Hybrid quantum systems based on magnons in magnetic materials have made significant progress in the past decade. They are built based on the couplings of magnons with microwave photons, optical photons, vibration phonons, and superconducting qubits. In particular, the interactions among magnons, microwave cavity photons, and vibration phonons form the system of cavity magnomechanics (CMM), which lies in the interdisciplinary field of cavity QED, magnonics, quantum optics, and quantum information. Here, we review the experimental and theoretical progress of this emerging field. We first introduce the underlying theories of the magnomechanical coupling, and then some representative classical phenomena that have been experimentally observed, including magnomechanically induced transparency, magnomechanical dynamical backaction, magnon-phonon cross-Kerr nonlinearity, etc. We also discuss a number of theoretical proposals, which show the potential of the CMM system for preparing different kinds of quantum states of magnons, phonons, and photons, and hybrid systems combining magnomechanics and optomechanics and relevant quantum protocols based on them. Finally, we summarize this review and provide an outlook for the future research directions in this field.

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.

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.

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 (VQA) 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 decisionmaking
problem and tackle it with an adaptation of Monte Carlo Tree Search (MCTS), a common 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.

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 [1]), 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.

Higher-order interactions are widely existed in complex systems, which induce diverse phenomena beyond pairwise interactions. Here, we explore the nonlinear dynamics of higher-order Kuramoto model on sparse simplicial complexes. We observe anti-phase cluster synchronization, where individuals within a system spontaneously divide into two opposing groups, when both pairwise and three-body interactions are repulsive. We investigate the microscopic mechanisms behind this phenomenon and reveal that multiple edges shared by multiple 2-simplices facilitate its emergence. Furthermore, we explore the suppressing impact of pairwise-only interactions on this synchronization and explain the trade-off between multiple and pairwise-only edges underlying the system's structure. Our findings are further validated on the heterogeneous simplicial complex and real dataset. Finally, we discuss the splitting of non-antiphase clusters under the traveling wave states when pairwise interactions become attractive. These results highlight the unique mechanism of repulsive coupling, offering valuable insights into the relationship between higher-order structures and dynamics, and contributing to a deeper understanding of synchronization in real-world systems, such as social networks and the brain.