## Action-noise-assisted quantum control

We study the effect of action noise on state-to-state control protocols. Action noise creates dephasing in the instantaneous eigenbasis of the Hamiltonian and hampers the fidelity of the final state with respect to the target state. We find that for shorter protocols the noise more strongly influences the dynamics and degrades fidelity. We suggest improving the fidelity by inducing stronger dephasing rates along the process. The effects of action noise on the dynamics and its manipulation is described for a general Hamiltonian and is then studied by examples.

## Coherent manipulation of three-qubit states in a molecular single-ion magnet

We study the quantum spin dynamics of nearly isotropic Gd3+ ions entrapped in polyoxometalate molecules and diluted in crystals of a diamagnetic Y3+ derivative. The full energy-level spectrum and the orientations of the magnetic anisotropy axes have been determined by means of continuous-wave electron paramagnetic resonance experiments, using X-band (9–10 GHz) cavities and on-chip superconducting waveguides and 1.5-GHz resonators. The results show that seven allowed transitions between the 2S+1 spin states can be separately addressed. Spin coherence T2 and spin-lattice relaxation T1 rates have been measured for each of these transitions in properly oriented single crystals. The results suggest that quantum spin coherence is limited by residual dipolar interactions with neighbor electronic spins. Coherent Rabi oscillations have been observed for all transitions. The Rabi frequencies increase with microwave power and agree quantitatively with predictions based on the spin Hamiltonian of the molecular spin. We argue that the spin states of each Gd3+ ion can be mapped onto the states of three addressable qubits (or, alternatively, of a d=8 -level “qudit”), for which the seven allowed transitions form a universal set of operations. Within this scheme, one of the coherent oscillations observed experimentally provides an implementation of a controlled-controlled-NOT (or Toffoli) three-qubit gate.

## Dynamical signatures of bound states in waveguide QED

We study the spontaneous decay of an impurity coupled to a linear array of bosonic cavities forming a single-band photonic waveguide. The average frequency of the emitted photon is different from the frequency for single-photon resonant scattering, which perfectly matches the bare frequency of the excited state of the impurity. We study how the energy of the excited state of the impurity influences the spatial profile of the emitted photon. The farther the energy is from the middle of the photonic band, the farther the wave packet is from the causal limit. In particular, if the energy lies in the middle of the band, the wave packet is localized around the causal limit. Besides, the occupation of the excited state of the impurity presents a rich dynamics: it shows an exponential decay up to intermediate times, this is followed by a power-law tail in the long-time regime, and it finally reaches an oscillatory stationary regime. Finally, we show that this phenomenology is robust under the presence of losses, both in the impurity and in the cavities.

## Energy consumption for shortcuts to adiabaticity

Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the “energy cost” of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.

## Entanglement of superconducting qubits via acceleration radiation

We show that simulated relativistic motion can generate entanglement between artificial atoms and protect them from spontaneous emission. We consider a pair of superconducting qubits coupled to a resonator mode, where the modulation of the coupling strength can mimic the harmonic motion of the qubits at relativistic speeds, generating acceleration radiation. We find the optimal feasible conditions for generating a stationary entangled state between the qubits when they are initially prepared in their ground state. Furthermore, we analyse the effects of motion on the probability of spontaneous emission in the standard scenarios of single-atom and two-atom superradiance, where one or two excitations are initially present. Finally, we show that relativistic motion induces sub-radiance and can generate a Zeno-like effect, preserving the excitations from radiative decay.

## Entanglement, coherence, and redistribution of quantum resources in double spontaneous down-conversion processes

We study the properties of bisqueezed tripartite Gaussian states created by two spontaneous parametric down-conversion processes that share a common idler. We give a complete description of the quantum correlations across all partitions, as well as of the genuine multipartite entanglement, obtaining analytical expressions for most of the quantities of interest. We find that the state contains genuine tripartite entanglement, in addition to the bipartite entanglement among the modes that are directly squeezed. We also investigate the effect of homodyne detection of the photons in the common idler mode, and analyze the final reduced state of the remaining two signal modes. We find that this measurement leads to a conversion of the coherence of the two signal modes into entanglement, a phenomenon that can be regarded as a redistribution of quantum resources between the modes. The applications of these results to quantum optics and circuit quantum electrodynamics platforms are also discussed.

## Equivalence between spin Hamiltonians and boson sampling

Aaronson and Arkhipov showed that predicting or reproducing the measurement statistics of a general linear optics circuit with a single Fock-state input is a classically hard problem. Here we show that this problem, known as boson sampling, is as hard as simulating the short time evolution of a large but simple spin model with long-range XY interactions. The conditions for this equivalence are the same for efficient boson sampling, namely, having a small number of photons (excitations) as compared to the number of modes (spins). This mapping allows efficient implementations of boson sampling in small quantum computers and simulators and sheds light on the complexity of time evolution with critical spin models.

## Invariant-Based Inverse Engineering of Crane Control Parameters

By applying invariant-based inverse engineering in the small-oscillation regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length) to transport a load between two positions at different heights with minimal final-energy excitation for a microcanonical ensemble of initial conditions. The analogy between ion transport in multisegmented traps or neutral-atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.

## Mapping curved spacetimes into Dirac spinors

We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions.

## Multifractal metal in a disordered Josephson junctions array

We report the results of the numerical study of the nondissipative quantum Josephson junction chain with the focus on the statistics of many-body wave functions and local energy spectra. The disorder in this chain is due to the random offset charges. This chain is one of the simplest physical systems to study many-body localization. We show that the system may exhibit three distinct regimes: insulating, characterized by the full localization of many-body wave functions, a fully delocalized (metallic) one characterized by the wave functions that take all the available phase volume, and the intermediate regime in which the volume taken by the wave function scales as a nontrivial power of the full Hilbert-space volume. In the intermediate nonergodic regime the Thouless conductance (generalized to the many-body problem) does not change as a function of the chain length indicating a failure of the conventional single-parameter scaling theory of localization transition. The local spectra in this regime display the fractal structure in the energy space which is related with the fractal structure of wave functions in the Hilbert space. A simple theory of fractality of local spectra is proposed, and a scaling relationship between fractal dimensions in the Hilbert and energy spaces is suggested and numerically tested.

## Multiphoton Scattering Tomography with Coherent States

n this work we develop an experimental procedure to interrogate the single- and multiphoton scattering matrices of an unknown quantum system interacting with propagating photons. Our proposal requires coherent state laser or microwave inputs and homodyne detection at the scatterer’s output, and provides simultaneous information about multiple—elastic and inelastic—segments of the scattering matrix. The method is resilient to detector noise and its errors can be made arbitrarily small by combining experiments at various laser powers. Finally, we show that the tomography of scattering has to be performed using pulsed lasers to efficiently gather information about the nonlinear processes in the scatterer.

## Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture

In this work, we propose a flexible architecture of microwave resonators with tunable couplings to perform quantum simulations of problems from the field of molecular chemistry. The architecture builds on the experience of the D-Wave design, working with nearly harmonic circuits instead of qubits. This architecture, or modifications of it, can be used to emulate molecular processes such as vibronic transitions. Furthermore, we discuss several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity, and, finally, the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices.

## Quantum Rabi model in the Brillouin zone with ultracold atoms

The quantum Rabi model describes the interaction between a two-level quantum system and a single bosonic mode. We propose a method to perform a quantum simulation of the quantum Rabi model introducing a novel implementation of the two-level system, provided by the occupation of Bloch bands in the first Brillouin zone by ultracold atoms in tailored optical lattices. The effective qubit interacts with a quantum harmonic oscillator implemented in an optical dipole trap. Our realistic proposal allows to experimentally investigate the quantum Rabi model for extreme parameter regimes, which are not achievable with natural light-matter interactions. Furthermore, we also identify a generalized version of the quantum Rabi model in a periodic phase space.

## Quantum coherence in the dynamical Casimir effect

We propose to use quantum coherence as the ultimate proof of the quantum nature of the radiation that appears by means of the dynamical Casimir effect in experiments with superconducting microwave waveguides. We show that, unlike previously considered measurements such as entanglement and discord, quantum coherence does not require a threshold value of the external pump amplitude and is highly robust to thermal noise.

## Quantum detection of wormholes

We show how to use quantum metrology to detect a wormhole. A coherent state of the electromagnetic field experiences a phase shift with a slight dependence on the throat radius of a possible distant wormhole. We show that this tiny correction is, in principle, detectable by homodyne measurements after long propagation lengths for a wide range of throat radii and distances to the wormhole, even if the detection takes place very far away from the throat, where the spacetime is very close to a flat geometry. We use realistic parameters from state-of-the-art long-baseline laser interferometry, both Earth-based and space-borne. The scheme is, in principle, robust to optical losses and initial mixedness.

## Quantum estimation methods for quantum illumination

Quantum illumination consists in shining quantum light on a target region immersed in a bright thermal bath with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we tackle this detection problem by using quantum estimation techniques to measure the reflectivity parameter of the object, showing an enhancement in the signal-to-noise ratio up to 3 dB with respect to the classical case when implementing only local measurements. Our approach employs the quantum Fisher information to provide an upper bound for the error probability, supplies the concrete estimator saturating the bound, and extends the quantum illumination protocol to non-Gaussian states. As an example, we show how Schrödinger’s cat states may be used for quantum illumination.

## Superluminal Physics with Superconducting Circuit Technology

We introduce a toolbox for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We consider as well possible setups for simulating the superluminal motion of a mirror, finding a link with the superradiant phase transition of the Dicke model.

## The Pauli objection

Schrödinger’s equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli con- cluded that constructing a general a time operator is impossible (although clearly it can be done in specific cases). Here we show how the Pauli argument fails when one uses an external system (a “clock”) to track time, so that time arises as correlations between the system and the clock (conditional probability amplitudes framework). In this case, the time operator is conjugate to the clock Hamiltonian and not to the sys- tem Hamiltonian, but its eigenvalues still satisfy the Schrödinger equation for arbitrary system Hamiltonians.

## The quantum Rabi model in a superfluid Bose-Einstein condensate

We propose a quantum simulation of the quantum Rabi model in an atomic quantum dot, which is a single atom in a tight optical trap coupled to the quasiparticle modes of a superfluid Bose-Einstein condensate. This widely tunable setup allows to simulate the ultrastrong coupling regime of light-matter interaction in a system which enjoys an amenable characteristic timescale, paving the way for an experimental analysis of the transition between the Jaynes-Cummings and the quantum Rabi dynamics using cold-atom systems. Our scheme can be naturally extended to simulate multi-qubit quantum Rabi models. In particular, we discuss the appearance of effective two-qubit interactions due to phononic exchange, among other features.

## Ultrastrong coupling of a single artificial atom to an electromagnetic continuum

The study of the interaction of light and matter has led to many fundamental discoveries as well as numerous important technologies. Over the last decades, great strides have been made in increasing the strength of this interaction at the single-photon level, leading to a continual exploration of new physics and applications. In recent years, a major achievement has been the demonstration of the so-called strong coupling regime, a key advancement enabling great progress in quantum information science. In this work, we demonstrate light-matter interaction over an order of magnitude stronger than previously reported, reaching a new regime of ultrastrong coupling (USC). We achieve this using a superconducting artificial atom tunably coupled to the electromagnetic continuum of a one-dimensional waveguide. For the largest values of the coupling, the spontaneous emission rate of the atom is comparable to its transition frequency. In this USC regime, the conventional quantum description of the atom and light as distinct entities breaks down, and a new description in terms of hybrid states is required. Our results open the door to a wealth of new physics and applications. Beyond light-matter interaction itself, the tunability of our system makes it promising as a tool to study a number of important physical systems such as the well-known spin-boson and Kondo models.