Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The $q$-means algorithm has convergence and precision guarantees similar to $k$-means, and it outputs with high probability a good approximation of the $k$ cluster centroids like the classical algorithm. Given a dataset of $N$ $d$-dimensional vectors $v_i$ (seen as a matrix $V \in \mathbb{R}^{N \times d})$ stored in QRAM, the running time of q-means is $\widetilde{O}\left( k d \frac{\eta}{\delta^2}\kappa(V)(\mu(V) + k \frac{\eta}{\delta}) + k^2 \frac{\eta^{1.5}}{\delta^2} \kappa(V)\mu(V) \right)$ per iteration, where $\kappa(V)$ is the condition number, $\mu(V)$ is a parameter that appears in quantum linear algebra procedures and $\eta = \max_{i} ||v_{i}||^{2}$. For a natural notion of well-clusterable datasets, the running time becomes $\widetilde{O}\left( k^2 d \frac{\eta^{2.5}}{\delta^3} + k^{2.5} \frac{\eta^2}{\delta^3} \right)$ per iteration, which is linear in the number of features $d$, and polynomial in the rank $k$, the maximum square norm $\eta$ and the error parameter $\delta$. Both running times are only polylogarithmic in the number of datapoints $N$. Our algorithm provides substantial savings compared to the classical $k$-means algorithm that runs in time $O(kdN)$ per iteration, particularly for the case of large datasets.

We address the nature of spin transport in the integrable XXZ spin chain, focusing on the isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based on generalized hydrodynamics combined with Gaussian fluctuations: we find that it diverges, and show that a self-consistent treatment of this divergence gives superdiffusion, with an effective time-dependent diffusion constant that scales as $D(t) \sim t^{1/3}$. This exponent had previously been observed in large-scale numerical simulations, but had not been theoretically explained. We briefly discuss XXZ models with easy-axis anisotropy $\Delta > 1$. Our method gives closed-form expressions for the diffusion constant $D$ in the infinite-temperature limit for all $\Delta > 1$. We find that $D$ saturates at large anisotropy, and diverges as the Heisenberg limit is approached, as $D \sim (\Delta - 1)^{-1/2}$.

This work reports the functioning of a single atom energy-conversion device, operating either as a quantum engine or a refrigerator, coupled to a quantum load. The "working fluid" is comprised of two optical levels of a single ion, and the load is one vibrational mode of the same ion cooled down to the quantum regime. The energy scales of these two modes differ by 9 orders of magnitude. We realize cyclic energy transfers between the working fluid and the quantum load, either increasing or decreasing the population of the vibrational mode. This is achieved albeit the interaction between the load and the working fluid leads to a significant population redistribution and quantum correlations between them. The performance of the engine cycles as a function of several parameters is examined, and found to be in agreement with theory. We specifically look at the ergotropy of the load, which indicates the amount of energy stored in the load that can be extracted with a unitary process. We show that ergotropy rises with the number of engine cycles despite an increase in the entropy of the load. Our experiment represents the first fully quantum 4-stroke energy-conversion device operating with a generic coupling to a quantum load.

Manipulating photons is an essential technique in quantum communication and computation. Combining the Raman electromagnetically induced transparency technology, we show that the photon blockade behavior can be actively controlled by using an external control field in a two atoms cavity-QED system. As a result, a versatile photon gateway can be achieved in this system, which changes the cavity photons from classical to quantum property and allows one photon, two photon and classical field leaking from the cavity. The proposal presented here has many potential applications for quantum information processing and can also be realized in many artificial atom system.

We examine the viability of quantum repeaters based on two-species trapped ion modules for long distance quantum key distribution. Repeater nodes comprised of ion-trap modules of co-trapped ions of distinct species are considered. The species used for communication qubits has excellent optical properties while the other longer lived species serves as a memory qubit in the modules. Each module interacts with the network only via single photons emitted by the communication ions. Coherent Coulomb interaction between ions is utilized to transfer quantum information between the communication and memory ions and to achieve entanglement swapping between two memory ions. We describe simple modular quantum repeater architectures realizable with the ion-trap modules and numerically study the dependence of the quantum key distribution rate on various experimental parameters, including coupling efficiency, gate infidelity, operation time and length of the elementary links. Our analysis suggests crucial improvements necessary in a physical implementation for co-trapped two-species ions to be a competitive platform in long-distance quantum communication.

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the "highlights for a physicist".

We demonstrate single-atom resolved imaging with a survival probability of $0.99932(8)$ and a fidelity of $0.99991(1)$, enabling us to perform repeated high-fidelity imaging of single atoms in tweezers for thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in $813.4~\text{nm}$ tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retro-reflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below $5~\mu$K, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of $0.996(1)$ and average state detection fidelity of $0.981(1)$. Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.

Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation, as well as reading and writing to memory locations. This perspective conforms to a macro-level view of physics and indeed these operations are realizable using macro-level devices involving thousands of electrons. This point of view is however incompatible with quantum mechanics, or even elementary thermodynamics, as both imply that information is a conserved quantity of physical processes, and hence of primitive computational operations.

Our aim is to re-develop foundational computational models that embraces the principle of conservation of information. We first define what conservation of information means in a computational setting. We emphasize that computations must be reversible transformations on data. One can think of data as modeled using topological spaces and programs as modeled by reversible deformations. We illustrate this idea using three notions of data. The first assumes unstructured finite data, i.e., discrete topological spaces. The corresponding notion of reversible computation is that of permutations. We then consider a structured notion of data based on the Curry-Howard correspondence; here reversible deformations, as a programming language for witnessing type isomorphisms, comes from proof terms for commutative semirings. We then "move up a level" to treat programs as data. The corresponding notion of reversible programs equivalences comes from the "higher dimensional" analog to commutative semirings: symmetric rig groupoids. The coherence laws for these are exactly the program equivalences we seek.

We conclude with some generalizations inspired by homotopy type theory and survey directions for further research.

Alternating current (ac) circuits can have electromagnetic edge modes protected by symmetries, analogous to topological band insulators or semimetals. How to make such a topological circuit? This paper illustrates a particular design idea by analyzing a series of topological circuits consisting purely of inductors (L) and capacitors (C) connected to each other by wires to form periodic lattices. All the examples are treated using a unifying approach based on Lagrangians and the dynamical $H$-matrix. First, the building blocks and permutation wiring are introduced using simple circuits in one dimension, the SSH transmission line and a braided ladder analogous to the ice-tray model also known as the $\pi$-flux ladder. Then, more general building blocks (loops and stars) and wiring schemes ($m$-shifts) are introduced. The key concepts of emergent pseudo-spin degrees of freedom and synthetic gauge fields are discussed, and the connection to quantum lattice Hamiltonians is clarified. A diagrammatic notation is introduced to simplify the design and presentation of more complicated circuits. These building blocks are then used to construct topological circuits in higher dimensions. The examples include the circuit analog of Haldane's Chern insulator in two dimensions and quantum Hall insulator in four dimensions featuring finite second Chern numbers. The topological invariants and symmetry protection of the edge modes are discussed based on the $H$-matrix.

The permutational invariance of identical two-level systems allows for an exponential reduction in the computational resources required to study the Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of both local and collective noise. Here we take advantage of this speedup to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir. Assessing the robustness of collective effects against local dissipation is paramount to predict their presence in different physical implementations. We have developed an open-source library in Python, the Permutational-Invariant Quantum Solver (PIQS), which we use to study a variety of phenomena in driven-dissipative open quantum systems. We consider both local and collective incoherent processes in the weak, strong, and ultrastrong-coupling regimes. Using PIQS, we reproduced a series of known physical results concerning collective quantum effects and extended their study to the local driven-dissipative scenario. Our work addresses the robustness of various collective phenomena, e.g., spin squeezing, superradiance, quantum phase transitions, against local dissipation processes.

No consensus regarding the universal validity of any particular interpretation of the measurement problem has been reached so far. The problem manifests strongly in various Wigner's-friend-type gedankenexperiments of which the extended Wigner's Friend gedankenexperiment devised by Daniela Frauchiger and Renato Renner is the most striking so far. All gedankenexperiments of this kind involve comparing quantum and classical information of which only the latter obeys the second law of thermodynamics. I conjecture that biological cell, as a dissipative structure, is the smallest agent capable of processing quantum information through its cytoplasmic membrane through which it performs measurements and reacts to the environment, while it must orient itself spatially similarly as Maxwell's demon attempting to decrease the entropy of a two compartment vessel under his control. If so, this mechanism must have been extended by natural evolution to endo- and exosemiosis in multicellular organisms, and further to language of Homo sapiens. I also discuss universal Turing machines, though in theory capable of performing measurements, yet unable to perform them infinitively, as well as viruses, though in theory capable of providing infinite time interval, yet unable to perform measurements.

Generative adversarial network (GAN) is an effective machine learning framework to train unsupervised generative models, and has drawn lots of attention in recent years. In the GAN framework, the generator is trained by an adversarial discriminator, in order to generate new samples that follows the probability distribution of a given training dataset. Classical GANs cannot generate discrete data due to the requirement of differentiability on the design of generators. In this paper, we propose a quantum version of GAN for generation of discrete data, which complements classical GANs. Our quantum GAN is composed of a parameterized quantum circuit as the generator and a classical feedforward neural network as the discriminator. Two families of quantum circuits, both composed of simple one-qubit rotation and two-qubit controlled-phase gates, are considered. The analytic gradient of the quantum generator can be estimated by sampling the same quantum generator, so gradient-based methods can be used in the training. The results of a small-scale proof-of-principle numerical simulation demonstrates the effectiveness of our scheme.

Author(s): Tobias Lipfert, Fabian Krumm, Mikhail I. Kolobov, and Werner Vogel

Recently [F. Krumm and W. Vogel, Phys. Rev. A **97**, 043806 (2018)], the detuned and nonlinear Jaynes-Cummings model describing the quantized motion of a trapped ion was introduced and its corresponding dynamics was solved via considering the driving laser in a quantized manner. For the dynamics with a...

[Phys. Rev. A 98, 063817] Published Wed Dec 12, 2018

Author(s): Sumei Huang and Aixi Chen

The ground-state cooling of a macroscopic mechanical oscillator is a crucial prerequisite for implementing the quantum manipulation of the mechanical oscillator. Here we show that a degenerate optical parametric amplifier (OPA) can significantly improve the cooling of the mechanical membrane in the ...

[Phys. Rev. A 98, 063818] Published Wed Dec 12, 2018

Author(s): Miguel A. Porras, Zoltán L. Horváth, and Balázs Major

We derive an analytical expression that describes the complete three-dimensional carrier-envelope-phase (CEP) distribution in the focal volume of ultrashort pulsed Gaussian beams focused by spherical mirrors or lenses. The focal CEP map depends on the so-called factor g specifying the frequency depe...

[Phys. Rev. A 98, 063819] Published Wed Dec 12, 2018

Author(s): Ania Bleszynski Jayich

Nitrogen-vacancy centers in diamond are found to be more affected by local charge than expected, which has implications for the use of the defects as quantum sensors.

[Physics 11, 126] Published Wed Dec 12, 2018

Categories: Physics

Celebrating its 50th anniversary, the internationally recognized journal *Leonardo* has been—and continues to be—a place for articles that bridge the gap between art and science.

[Physics 11, 128] Published Wed Dec 12, 2018

Categories: Physics

Author(s): E. V. Kovlakov, S. S. Straupe, and S. P. Kulik

High-dimensional entanglement is a valuable resource for quantum communication, and photon pairs entangled in orbital angular momentum (OAM) are commonly used for encoding high-dimensional quantum states. However, methods for the preparation of maximally entangled states of arbitrary dimensionality ...

[Phys. Rev. A 98, 060301(R)] Published Wed Dec 12, 2018

Author(s): Shilong Liu, Zhiyuan Zhou, Shikai Liu, Yinhai Li, Yan Li, Chen Yang, Zhaohuai Xu, Zhaodi Liu, Guangcan Guo, and Baosen Shi

Maximally entangled photon pairs with a spatial degree of freedom is a potential way for realizing high-capacity quantum computing and communication. However, methods to generate such entangled states with high quality, high brightness, and good controllability are needed. Here, a scheme is experime...

[Phys. Rev. A 98, 062316] Published Wed Dec 12, 2018

We introduce a hybrid machine-learning algorithm for designing quantum optics experiments that produce specific quantum states. Our algorithm successfully found experimental schemes to produce all 5 states we asked it to, including Schr\"odinger cat states and cubic phase states, all to a fidelity of over $96\%$. Here we specifically focus on designing realistic experiments, and hence all of the algorithm's designs only contain experimental elements that are available with current technology. The core of our algorithm is a genetic algorithm that searches for optimal arrangements of the experimental elements, but to speed up the initial search we incorporate a neural network that classifies quantum states. The latter is of independent interest, as it quickly learned to accurately classify quantum states given their photon-number distributions.