Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States.

In this Letter, we provide analytical and numerical evidence that the single-layer quantum approximate optimization algorithm on universal Ising spin models produces thermal-like states. We find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to the general state-of-the-art condition that ensures rapid mixing for Ising models. Moreover, we observe that the temperature depends on a hidden universal correlation between the energy of a state and the covariance of other energy levels and the Hamming distances of the state to those energies.

Universal Time-Dependent Control Scheme for Realizing Arbitrary Linear Bosonic Transformations.

We study the implementation of arbitrary excitation-conserving linear transformations between two sets of N stationary bosonic modes, which are connected through a photonic quantum channel. By controlling the individual couplings between the modes and the channel, an initial N-partite quantum state in register A can be released as a multiphoton wave packet and, successively, be reabsorbed in register B. Here we prove that there exists a set of control pulses that implement this transfer with arbitrarily high fidelity and, simultaneously, realize a prespecified N×N unitary transformation between the two sets of modes.

Complete Physical Characterization of Quantum Nondemolition Measurements via Tomography.

We introduce a self-consistent tomography for arbitrary quantum nondemolition (QND) detectors. Based on this, we build a complete physical characterization of the detector, including the measurement processes and a quantification of the fidelity, ideality, and backaction of the measurement. This framework is a diagnostic tool for the dynamics of QND detectors, allowing us to identify errors, and to improve their calibration and design.

Remote Individual Addressing of Quantum Emitters with Chirped Pulses.

We propose to use chirped pulses propagating near a band gap to remotely address quantum emitters. We introduce a particular family of chirped pulses that dynamically self-compress to subwavelength spot sizes during their evolution in a medium with a quadratic dispersion relation. We analytically describe how the compression distance and width of the pulse can be tuned through its initial parameters.

Experimental Reconstruction of the Few-Photon Nonlinear Scattering Matrix from a Single Quantum Dot in a Nanophotonic Waveguide.

Coherent photon-emitter interfaces offer a way to mediate efficient nonlinear photon-photon interactions, much needed for quantum information processing. Here we experimentally study the case of a two-level emitter, a quantum dot, coupled to a single optical mode in a nanophotonic waveguide. We carry out few-photon transport experiments and record the statistics of the light to reconstruct the scattering matrix elements of one- and two-photon components.

Projected Entangled Pair States: Fundamental Analytical and Numerical Limitations.

Matrix product states and projected entangled pair states (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While matrix product states are comprehensively understood, in PEPS fundamental questions, relevant analytically as well as numerically, remain open, such as how to encode symmetries in full generality, or how to stabilize numerical methods using canonical forms. Here, we show that these key problems, as well as a number of related questions, are algorithmically undecidable, that is, they cannot be fully resolved in a systematic way.

Single Photons by Quenching the Vacuum.

Heisenberg's uncertainty principle implies that the quantum vacuum is not empty but fluctuates. These fluctuations can be converted into radiation through nonadiabatic changes in the Hamiltonian. Here, we discuss how to control this vacuum radiation, engineering a single-photon emitter out of a two-level system (2LS) ultrastrongly coupled to a finite-band waveguide in a vacuum state.

Modulated Continuous Wave Control for Energy-Efficient Electron-Nuclear Spin Coupling.

We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts.

Ultrastrong Coupling Few-Photon Scattering Theory.

We study the scattering of individual photons by a two-level system ultrastrongly coupled to a waveguide. The scattering is elastic for a broad range of couplings and can be described with an effective U(1)-symmetric Hamiltonian. This simple model allows the prediction of scattering resonance line shapes, validated up to α=0.

Multiphoton Scattering Tomography with Coherent States.

In 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.

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.

Light-matter decoupling and A(2) term detection in superconducting circuits.

The spontaneous and stimulated emission of a superconducting qubit in the presence of propagating microwaves originates from an effective light-matter interaction that, similarly to the case of the atomic case, can contain a diamagnetic term proportional to the square vector potential A(2). In the present work we prove that an increase in the strength of the diamagnetic term leads to an effective decoupling of the qubit from the electromagnetic field, and that this effect is observable at any range of qubit-photon coupling. To measure this effect we propose to use a transmon suspended over a transmission line, where the relative strength of the A(2) term is controlled by the qubit-line separation.

Nonlinear quantum optics in the (ultra)strong light-matter coupling.

The propagation of N photons in one dimensional waveguides coupled to M qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of N, M, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the matrix product states technique.

Scattering in the ultrastrong regime: nonlinear optics with one photon.

The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using matrix product states. It is found that the scattering is strongly influenced by the single- and multiphoton dressed bound states present in the system.

Inducing nonclassical lasing via periodic drivings in circuit quantum electrodynamics.

We show how a pair of superconducting qubits coupled to a microwave cavity mode can be used to engineer a single-atom laser that emits light into a nonclassical state. Our scheme relies on the dressing of the qubit-field coupling by periodic modulations of the qubit energy. In the dressed basis, the radiative decay of the first qubit becomes an effective incoherent pumping mechanism that injects energy into the system, hence turning dissipation to our advantage.

Hybrid quantum magnetism in circuit QED: from spin-photon waves to many-body spectroscopy.

We introduce a model of quantum magnetism induced by the nonperturbative exchange of microwave photons between distant superconducting qubits. By interconnecting qubits and cavities, we obtain a spin-boson lattice model that exhibits a quantum phase transition where both qubits and cavities spontaneously polarize. We present a many-body ansatz that captures this phenomenon all the way, from a the perturbative dispersive regime where photons can be traced out, to the nonperturbative ultrastrong coupling regime where photons must be treated on the same footing as qubits.

Quantum chaos in an ultrastrongly coupled bosonic junction.

The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters.

Phase stabilization of a frequency comb using multipulse quantum interferometry.

From the interaction between a frequency comb and an atomic qubit, we derive quantum protocols for the determination of the carrier-envelope offset phase, using the qubit coherence as a reference, and without the need of frequency doubling or an octave spanning comb. Compared with a trivial interference protocol, the multipulse protocol results in a polynomial enhancement of the sensitivity O(N-2) with the number N of laser pulses involved. We specialize the protocols using optical or hyperfine qubits, Λ schemes, and Raman transitions, and introduce methods where the reference is another phase-stable cw laser or frequency comb.

Nonequilibrium and nonperturbative dynamics of ultrastrong coupling in open lines.

The time and space resolved dynamics of a qubit with an Ohmic coupling to propagating 1D photons is studied, from weak coupling to the ultrastrong coupling regime. A nonperturbative study based on matrix product states shows the following results, (i) The ground state of the combined systems contains excitations of both the qubit and the surrounding bosonic field. (ii) An initially excited qubit equilibrates through spontaneous emission to a state, which under certain conditions is locally close to that ground state, both in the qubit and the field.

Lieb-Robinson bounds for spin-boson lattice models and trapped ions.

We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a system of trapped ions and find that the propagation of spin correlations, as mediated by the phonons of the ion crystal, can be faster than the regimes currently explored in experiments. We propose a scheme to test the bounds by measuring retarded correlation functions via the crystal fluorescence.

Circuit QED bright source for chiral entangled light based on dissipation.

We present a scalable and tunable framework for the quantum simulation of critical dissipative models based on a circuit QED cavity array interacting with driven superconducting qubits. We will show that the strongly correlated many-body state of the cavities can be mapped into the state of propagating photons in a transmission line. This allows not only for an efficient way of accessing the correlations in the many-body system, but also provides a bright source of chiral entangled light where directionality and entanglement are assisted by collective phenomena and breaking of reflection symmetry.

Shaping an itinerant quantum field into a multimode squeezed vacuum by dissipation.

We show that inducing sidebands in the emission of a single emitter into a one-dimensional waveguide, together with a dissipative repumping process, a photon field is cooled down to a multimode squeezed vacuum. Our method does not require being in the strong coupling regime, works with a continuum of propagating field modes, and leads to sources of tunable multimode squeezed light in circuit-QED systems.

Quantum simulation of quantum field theories in trapped ions.

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.

Seeing topological order in time-of-flight measurements.

In this Letter, we provide a general methodology to directly measure topological order in cold atom systems. As an application, we propose the realization of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentum-space Skyrmions.