Quantum logic gates are fundamental building blocks of quantum computers. Their integration into quantum networks requires strong qubit coupling to network channels, as can be realized with neutral atoms and optical photons in cavity quantum electrodynamics. Here we demonstrate that the long-range interaction mediated by a flying photon performs a gate between two stationary atoms inside an optical cavity from which the photon is reflected. This single step executes the gate in $2\,\mathrm{\mu s}$. We show an entangling operation between the two atoms by generating a Bell state with 76(2)% fidelity. The gate also operates as a CNOT. We demonstrate 74.1(1.6)% overlap between the observed and the ideal gate output, limited by the state preparation fidelity of 80.2(0.8)%. As the atoms are efficiently connected to a photonic channel, our gate paves the way towards quantum networking with multiqubit nodes and the distribution of entanglement in repeater-based long-distance quantum networks.

The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum computers. A possibility of simulating Loop Quantum Gravity is discussed and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.

One of the important features of quantum mechanics is that non-orthogonal quantum states cannot be perfectly discriminated. Therefore, a fundamental problem in quantum mechanics is to design a optimal measurements to discriminate a collection of non-orthogonal quantum states. We prove that the geometric coherence of a quantum state is the minimal error probability to discrimination a set of linear independent pure states, which provides an operational interpretation for geometric coherence. Moreover, the closest incoherent states are given in terms of the corresponding optimal von Neumann measurements. Based on this idea, the explicitly expression of geometric coherence are given for a class of states. On the converse, we show that, any discrimination task for a collection of linear independent pure states can be also regarded as the problem of calculating the geometric coherence for a quantum state, and the optimal measurement can be obtain through the corresponding closest incoherent state.

In this work I argue for the existence of an ontological state in which no entity in it can be more basic than the others in such a state. This is used to provide conceptual justification for a method that is applied to obtain the Schr\"{o}dinger equation, the Klein-Gordon equation, and the Klein-Gordon equation for a particle in an electromagnetic field. Additionally, it is argued that the existence of such state is incompatible with indirect realism; and the discussion suggests that a panexeperientialist view is a straightforward means to embrace it.

We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel---we here consider the so-called Werner channel. To characterize our results, we introduce a two-dimensional space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.

Randomized benchmarking provides a tool for obtaining precise quantitative estimates of the average error rate of a physical quantum channel. Here we define real randomized benchmarking, which enables a separate determination of the average error rate in the real and complex parts of the channel. This provides more fine-grained information about average error rates with approximately the same cost as the standard protocol. The protocol requires only averaging over the real Clifford group, a subgroup of the full Clifford group, and makes use of the fact that it forms an orthogonal 2-design. Our results are therefore especially useful when considering quantum computations on rebits (or real encodings of complex computations), in which case the real Clifford group now plays the role of the complex Clifford group when studying stabilizer circuits.

For the fermion transformation in the space all books of quantum mechanics propose to use the unitary operator $\widehat{U}_{\vec n}(\varphi)=\exp{(-i\frac\varphi2(\widehat\sigma\cdot\vec n))}$, where $\varphi$ is angle of rotation around the axis $\vec{n}$. But this operator turns the spin in inverse direction presenting the rotation to the left. The error of defining of $\widehat{U}_{\vec n}(\varphi)$ action is caused because the spin supposed as simple vector which is independent from $\widehat\sigma$-operator a priori. In this work it is shown that each fermion marked by number $i$ has own Pauli-vector $\widehat\sigma_i$ and both of them change together. If we suppose the global $\widehat\sigma$-operator and using the Bloch Sphere approach define for all fermions the common quantization axis $z$ the spin transformation will be the same: the right hand rotation around the axis $\vec{n}$ is performed by the operator $\widehat{U}^+_{\vec n}(\varphi)=\exp{(+i\frac\varphi2(\widehat\sigma\cdot\vec n))}$.

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an $n$-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the $m$ output modes. We examine two models of losses. In the first model a fixed number of particles is lost. We prove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than $\sqrt{n}$. In the second loss model, every time a photon passes through a beamsplitter in the network, it has some probability of being lost. For this model the relevant parameter is $s$, the smallest number of beamsplitters that any photon traverses as it propagates through the network. We prove that it is possible to approximately simulate the output statistics already if $s$ grows logarithmically with $m$, regardless of the geometry of the network. The latter result is obtained by proving that it is always possible to commute $s$ layers of uniform losses to the input of the network regardless of its geometry, which could be a result of independent interest. We believe that our findings put strong limitations on future experimental realizations of quantum computational supremacy proposals based on boson sampling.

We present analytical formulas for the vacuum-polarization Uehling potential in the case where the finite size of the nucleus is modeled by a Fermi charge distribution. Using a Sommerfeld-type development, the potential is expressed in terms of multiple derivatives of a particular integral. The latter and its derivatives can be evaluated exactly in terms of Bickley-Naylor functions, which connection to the Uehling potential was already pointed out in the pure Coulomb case, and of usual Bessel functions of the second kind. The cusp and asymptotic expressions for the Uehling potential with a Fermi charge distribution are also provided. Analytical results for the higher-order-contribution K\"all\`en-Sabry potential are given.

We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<\infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.

We present a detailed study on the properties of single photons generated by spontaneous parametric down conversion (SPDC) when both the spectral and spatial degrees of freedom are controlled by means of filters. Our results show that it is possible to obtain pure heralded single photons with high heralding efficiency despite the use of filters. Moreover, we report an asymmetry on the single photon properties exhibited in type-II SPDC sources that depends on choosing the signal or the idler photon as the heralding one.

High fidelity microwave photon counting is an important tool for various areas from background radiation analysis in astronomy to the implementation of circuit QED architectures for the realization of a scalable quantum information processor. In this work we describe a microwave photon counter coupled to a semi-infinite transmission line. We employ input-output theory to examine a continuously driven transmission line as well as traveling photon wave packets. Using analytic and numerical methods, we calculate the conditions on the system parameters necessary to optimize measurement and achieve high detection efficiency.

Understanding computational speed-up is fundamental for the development of efficient quantum algorithms. In this paper, we study such problem under the framework of the Quantum Query Model, which represents the probability of output $x \in \{0,1\}^n$ as a function $\pi(x)$, and denotes by $L(\pi)$ the spectral norm for $\pi$ defined over the Fourier basis of the linear space of functions $f: \left\{0,1\right\}^{n} \rightarrow \mathbb{R}$. We then present a classical simulation for output probabilities $\pi$, whose error depends on $L(\pi)$. Such dependence implies upper-bounds for the quotient between the number of queries of an optimal classical algorithm and our quantum algorithm, respectively. These upper-bounds show a strong relation between spectral norm and quantum parallelism. This result also implies that there is no asymptotic quantum speed-up for a sequence of boolean functions of constant degree.

Recent experimental progress have revealed Meissner and Vortex phases in low-dimensional ultracold atoms systems. Atomtronic setups can realize ring ladders, while explicitly taking the finite size of the system into account. This enables the engineering of quantized chiral currents and phase slips in-between them. We find that the mesoscopic scale modifies the current. Full control of the lattice configuration reveals a reentrant behavior of Vortex and Meissner phases. Our approach allows a feasible diagnostic of the currents' configuration through time of flight measurements.

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals -- the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek's idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

We prove that as conjectured by Ac\'{\i}n et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant Bell inequality. This suggests a surprising connection between maximal entanglement, complete sets of mutually unbiased bases, and elements of symmetric informationally complete positive operator-valued measures, on one side, and the optimal way of certifying maximal randomness, on the other.

We discuss the quantum mechanics of a particle restricted to the half-line $x > 0$ with potential energy $V = \alpha/x^2$ for $-1/4 < \alpha < 0$. It is known that two scale-invariant theories may be defined. By regularizing the near-origin behavior of the potential by a finite square well with variable width $b$ and depth $g$, it is shown how these two scale-invariant theories occupy fixed points in the resulting $(b,g)$-space of Hamiltonians. A renormalization group flow exists in this space and scaling variables are shown to exist in a neighborhood of the fixed points. Consequently, the propagator of the regulated theory enjoys homogeneous scaling laws close to the fixed points. Using renormalization group arguments it is possible to discern the functional form of the propagator for long distances and long imaginary times, thus demonstrating the extent to which fixed points control the behavior of the cut-off theory.

By keeping the width fixed and varying only the well depth, we show how the mean position of a bound state diverges as $g$ approaches a critical value. It is proven that the exponent characterizing the divergence is universal in the sense that its value is independent of the choice of regulator.

Two classical interpretations of the results are discussed: standard Brownian motion on the real line, and the free energy of a certain one-dimensional chain of particles with prescribed boundary conditions. In the former example, $V$ appears as part of an expectation value in the Feynman-Kac formula. In the latter example, $V$ appears as the background potential for the chain, and the loss of extensivity is dictated by a universal power law.

A Bose-Einstein condensate confined in ring shaped lattices interrupted by a weak link and pierced by an effective magnetic flux defines the atomic counterpart of the SQUID: The Atomtronic Quantum Interference Device (AQUID). In this paper, we report on the detection of current states in the system through a self-heterodyne protocol. Following the original proposal of the NIST and Paris groups, the ring-condensate many-body wave function interferes with a reference condensate expanding from the center of the ring. We focus on the rf-AQUID which realizes effective qubit dynamics. Both the Bose-Hubbard and Gross-Pitaevskii dynamics are studied. For the Bose-Hubbard dynamics, we demonstrate that the self-heterodyne protocol can be applied, but higher order correlations in the evolution of the interfering condensates are measured to read-out of the current states of the system. We study how states with macroscopic quantum coherence can be told apart analysing the noise in the time-of-flight of the ring condensate.

We study the effects of the quantum geometric tensor, i.e., the Berry curvature and the Fubini-Study metric, on the steady state of driven-dissipative bosonic lattices. We show that the quantum-Hall-type response of the steady-state wave function in the presence of an external potential gradient depends on all the components of the quantum geometric tensor. Looking at this steady-state Hall response, one can map out the full quantum geometric tensor of a sufficiently flat band in momentum space using a driving field localized in momentum space. We use the two-dimensional Lieb lattice as an example and numerically demonstrate how to measure the quantum geometric tensor.

We observe collective quantum spin states of an ensemble of atoms in a one-dimensional light-atom interface. Strings of hundreds of cesium atoms trapped in the evanescent fiel of a tapered nanofiber are prepared in a coherent spin state, a superposition of the two clock states. A weak quantum nondemolition measurement of one projection of the collective spin is performed using a detuned probe dispersively coupled to the collective atomic observable, followed by a strong destructive measurement of the same spin projection. For the coherent spin state we achieve the value of the quantum projection noise 40 dB above the detection noise, well above the 3 dB required for reconstruction of the negative Wigner function of nonclassical states. We analyze the effects of strong spatial inhomogeneity inherent to atoms trapped and probed by the evanescent waves. We furthermore study temporal dynamics of quantum fluctuations relevant for measurement-induced spin squeezing and assess the impact of thermal atomic motion. This work paves the road towards observation of spin squeezed and entangled states and many-body interactions in 1D spin ensembles.