Publications from 2022

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the annealing dynamics in real-time.We introduce the spin-vector Langevin (SVL) model as an alternative benchmark in which the time evolution is described by Langevin dynamics. The SVL model is shown to provide a more stringent test than the SVMC model for the identification of quantum signatures in the performance of quantum annealing devices, as we illustrate by describing the Kibble-Zurek scaling associated with the dynamics of symmetry breaking in the transverse field Ising model, recently probed using D-Wave machines. Specifically, we show that D-Wave data are reproduced by the SVL model.

The heavy fluxonium at zero external flux has a long-lived state when coupled capacitively to any other system. We analyze it by projecting all the fluxonium relevant operators into the qutrit subspace, as this long-lived configuration corresponds to the second excited fluxonium level. This state becomes a bound-state in the continuum (BIC) when the coupling occurs to an extended system supporting a continuum of modes. In the case without noise, we find BIC lifetimes that can be much larger than seconds $T_1\gg {\rm s}$ when the fluxonium is coupled to a superconducting waveguide, while typical device frequencies are in the order of ${\rm GHz}$. We have performed a detailed study of the different sources of decoherence in a realistic experiment, obtaining that upward transitions caused by a finite temperature in the waveguide and decay induced by $1/f$-flux noise are the most dangerous ones. Even in their presence, BICs decay times could reach the range of ${T_1\sim \rm 10^{-1} ms},$ while preparation times are of the order of $10^{2}$ns.

We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green’s functions in terms of effective non-Hermitian Hamiltonians that contain all the relevant topological information. We arrive at a frequency dependent topological index that is linked to the response of the system to perturbations at a given frequency. We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases

We introduce a self-consistent tomography for arbitrary quantum non-demolition (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 back-action 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. We illustrate this on a realistic Jaynes-Cummings simulation of superconducting qubit readout. We characterize non-dispersive errors, quantify the back-action introduced by the readout cavity, and calibrate the optimal measurement point.

We present a complex field formulation of the quantum estimation theory that works natively with complex statistics on the dependence of complex parameters. This formulation states new complex versions of the main quantities and results of the estimation theory depending on complex parameters, such as Fisher information matrices and Cram\’er-Rao bounds. This can be useful in contexts where the quantum states are described through complex parameters, such as coherent states or squeezed states. We show an example of an application of our theory in quantum communication with coherent states.

Recent experimental advances enable the fabrication of photonic lattices in which the light propagates with non-trivial energy dispersions. When interfaced with quantum emitters, such systems yield strong collective spontaneous emission phenomena, such as perfect sub-radiance, in which the decay into the bath is completely suppressed, forming bound-states-in-the-continuum. Since such photonic lattices are generally lossy, an alternative way of probing them consists in coherently driving them to an steady-state from which photoluminescence can be extracted. Here, we formalize connections between these two seemingly different situations and use that intuition to predict the formation of non-trivial photonic steady-states in one and two dimensions. In particular, we show that subradiant emitter configurations are linked to the emergence of steady-state light-localization in the driven-dissipative setting, in which the light features the same form than the spontaneously formed bound-states-in-the-continuum. Besides, we also find configurations which leads to the opposite behaviour, an anti-localization of light, that is, it distributes over all the system except for the region defined between the driving lasers. These results shed light on the recently reported optically-defined cavities in polaritonic lattices, and can guide further experimental studies.

The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green’s function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification.

We study the physics of a magnetic molecule described by a “giant” spin with multiple ($d > 2$) spin states interacting with the quantized cavity field produced by a superconducting resonator. By means of the input-output formalism, we derive an expression for the output modes in the dispersive regime of operation. It includes the effect of magnetic anisotropy, which makes different spin transitions addressable. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits. We discuss, from an effective Hamiltonian perspective, the conditions under which the qudit read-out is a non-demolition measurement and consider possible experimental protocols to perform it. Finally, we illustrate our results with simulations performed for realistic models of existing magnetic molecules.

Single photons constitute a main platform in quantum science and technology: they carry quantum information over extended distances in the future quantum internet and can be manipulated in advanced photonic circuits enabling scalable photonic quantum computing. The main challenge in quantum photonics is how to generate advanced entangled resource states and efficient light-matter interfaces. Here we utilize the efficient and coherent coupling of a single quantum emitter to a nanophotonic waveguide for realizing quantum nonlinear interaction between single-photon wavepackets. This inherently multimode quantum system constitutes a new research frontier in quantum optics. We demonstrate control of a photon with another photon and experimentally unravel the dynamical response of two-photon interactions mediated by a quantum emitter, and show that the induced quantum correlations are controlled by the pulse duration. The work will open new avenues for tailoring complex photonic quantum resource states.

The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system’s critical exponents at equilibrium and the quenching rate. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution, on an open access IBM quantum computer (IBM-Q). We find that for this simple one-qubit model, experimental data validates the central KZM assumption of the adiabatic-impulse approximation for a well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies, separately elucidating the role of crosstalk between qubits and the increasing decoherence effects associated with the quantum circuit depth on the KZM predictions. Our results strongly suggest that increasing circuit depth acts as a decoherence source, producing a rapid deviation of experimental data from theoretical unitary predictions.

This document is meant to be a practical introduction to the analytical and numerical manipulation of Fermionic Gaussian systems. Starting from the basics, we move to relevant modern results and techniques, presenting numerical examples and studying relevant Hamiltonians, such as the transverse field Ising Hamiltonian, in detail. We finish introducing novel algorithms connecting Fermionic Guassian states with matrix product states techniques. All the numerical examples make use of the free Julia package F_utilities.

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $\phi^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly-coupled superconductor indicating the suppression of defect-defect spatial correlations.

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.

In this work we propose and theoretically characterize optical isolators consisting of an all-dielectric and non-magnetic resonator featuring an intensity-dependent refractive index and a strong coherent field propagating in a single direction. Such devices can be straightforwardly realized in state-of-the-art integrated photonics platforms. The mechanism underlying optical isolation is based on the breaking of optical reciprocity induced by the asymmetric action of four-wave mixing processes coupling a strong propagating pump field with co-propagating signal/idler modes but not with reverse-propagating ones. Taking advantage of a close analogy with fluids of light, our proposed isolation mechanism is physically understood in terms of the Bogoliubov dispersion of collective excitations on top of the strong pump beam. A few most relevant set-ups realizing our proposal are specifically investigated, such as a coherently illuminated passive ring resonator and unidirectionally lasing ring or Taiji resonators.

We determine the phase diagram of the Abelian-Higgs model in one spatial dimension and time (1+1D) on a lattice. We identify a line of first order phase transitions separating the Higgs region from the confined one. This line terminates in a quantum critical point above which the two regions are connected by a smooth crossover. We analyze the critical point and find compelling evidences for its description as the product of two non-interacting systems, a massless free fermion and a massless free boson. However, we find also some surprizing results that cannot be explained by our simple picture, suggesting this newly discovered critical point to be an unusual one.

Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial optimization problem that can be addressed by quantum and quantum-inspired algorithms. In this work we present an integer simulated annealing method to find optimal portfolios in the presence of discretized convex and non-convex cost functions. Our algorithm can deal with large size portfolios with hundreds of assets. We introduce a performance metric, the time to target, based on a lower bound to the cost function obtained with the continuous relaxation of the combinatorial optimization problem. This metric allows us to quantify the time required to achieve a solution with a given quality. We carry out numerical experiments and we benchmark the algorithm in two situations: (i) Monte Carlo instances are started at random, and (ii) the algorithm is warm-started with an initial instance close to the continuous relaxation of the problem. We find that in the case of warm-starting with convex cost functions, the time to target does not grow with the size of the optimization problem, so discretized versions of convex portfolio optimization problems are not hard to solve using classical resources. We have applied our method to the problem of re-balancing in the presence of non-convex transaction costs, and we have found that our algorithm can efficiently minimize those terms.

In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\”odinger-type, Hamiltonian partial differential equations (PDEs), using space-efficient variational circuits, including the symmetries of the problem, and global and gradient-based optimizers. We use this algorithm to benchmark the performance of the representation techniques by means of the computation of the ground state in three PDEs, i.e., the one-dimensional quantum harmonic oscillator, and the transmon and flux qubits, studying how they would perform in ideal and near-term quantum computers. With the Fourier methods developed here, we obtain low infidelities of order $10^{-4}-10^{-5}$ using only three to four qubits, demonstrating the high compression of information in a quantum computer. Practical fidelities are limited by the noise and the errors of the evaluation of the cost function in real computers, but they can also be improved through error mitigation techniques.

We analyse the implementation of a fast nonadiabatic CZ gate between two transmon qubits with tuneable coupling. The gate control method is based on a theory of dynamical invariants which leads to reduced leakage and robustness against decoherence. The gate is based on a description of the resonance between the $|11\rangle$ and $|20\rangle$ using an effective Hamiltonian with the 6 lowest energy states. A modification of the invariants method allows us to take into account the higher-order perturbative corrections of this effective model. This enables a gate fidelity several orders of magnitude higher than other quasiadiabatic protocols, with gate times that approach the theoretical limit.

Conformal Field Theories (CFTs) have been used extensively to understand the physics of critical lattice models at equilibrium. However, the applicability of CFT calculations to the behavior of the lattice systems in the out-of-equilibrium setting is not entirely understood. In this work, we compare the CFT results of the evolution of the entanglement spectrum after a quantum quench with numerical calculations of the entanglement spectrum of the three-state Potts model using matrix product state simulations. Our results lead us to conjecture that CFT does not describe the entanglement spectrum of the three-state Potts model at long times, contrary to what happens in the Ising model. We thus numerically simulate the out-of-equilibrium behaviour of the Potts model according to the CFT protocol – i.e. by taking a particular product state and “cooling” it, then quenching to the critical point and find that, in this case, the entanglement spectrum is indeed described by the CFT at long times.

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.

We introduce an inductive $n$-qubit pure-state estimation method. This is based on projective measurements on states of $2n+1$ separable bases or $2$ entangled bases plus the computational basis. Thus, the total number of measurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the proposed method exhibits a very favorable scaling in the number of qubits when compared to other estimation methods. Monte Carlo numerical experiments show that the method can achieve a high estimation fidelity. For instance, an average fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with $21$ separable bases. The use of separable bases makes our estimation method particularly well suited for applications in noisy intermediate-scale quantum computers, where entangling gates are much less accurate than local gates. We experimentally demonstrate the proposed method in one of IBM’s quantum processors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a fidelity close to $0.875$ via separable bases. Other $10$-qubit separable and entangled states achieve an estimation fidelity in the order of $0.85$ and $0.7$, respectively.

Quantum spin models find applications in many different areas, such as spintronics, high-Tc superconductivity, and even complex optimization problems. However, studying their many-body behaviour, especially in the presence of frustration, represents an outstanding computational challenge. To overcome it, quantum simulators based on cold, trapped atoms and ions have been built, shedding light already on many non-trivial phenomena. Unfortunately, the models covered by these simulators are limited by the type of interactions that appear naturally in these systems. Waveguide QED setups have recently been pointed out as a powerful alternative due to the possibility of mediating more versatile spin-spin interactions with tunable sign, range, and even chirality. Yet, despite their potential, the many-body phases emerging from these systems have only been scarcely explored. In this manuscript, we fill this gap analyzing the ground states of a general class of spin models that can be obtained in such waveguide QED setups. Importantly, we find novel many-body phases different from the ones obtained in other platforms, e.g., symmetry-protected topological phases with large-period magnetic orderings, and explain the measurements needed to probe them.

Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with values of the objective function obtained in a quantum processor. A proper choice of optimization algorithm is essential to achieve good performance. Here, we review the use of first-order, second-order, and quantum natural gradient stochastic optimization methods, which are defined in the field of real numbers, and propose new stochastic algorithms defined in the field of complex numbers. The performance of all methods is evaluated by means of their application to variational quantum eigensolver, quantum control of quantum states, and quantum state estimation. In general, complex number optimization algorithms perform best, with first-order complex algorithms consistently achieving the best performance, closely followed by complex quantum natural algorithms, which do not require expensive hyperparameters calibration. In particular, the scalar formulation of the complex quantum natural algorithm allows to achieve good performance with low classical computational cost.

Low-noise microwave amplifiers are crucial for detecting weak signals in fields such as quantum technology and radio astronomy. However, designing an ideal amplifier is challenging, as it must cover a wide frequency range, add minimal noise, and operate directionally – amplifying signals only in the observer’s direction while protecting the source from environmental interference. In this work, we demonstrate that an array of non-linearly coupled Josephson parametric amplifiers (JPAs) can collectively function as a directional, broadband quantum amplifier by harnessing topological effects. By applying a collective four-wave-mixing pump with inhomogeneous amplitudes and linearly increasing phase, we break time-reversal symmetry in the JPA array and stabilize a topological amplification regime where signals are exponentially amplified in one direction and exponentially suppressed in the opposite. We show that compact devices with few sites $N\sim 11-17$ can achieve exceptional performance, with gains exceeding 20 dB over a bandwidth ranging from hundreds of MHz to GHz, and reverse isolation suppressing backward noise by more than 30 dB across all frequencies. The device also operates near the quantum noise limit and provides topological protection against up to 15% fabrication disorder, effectively suppressing gain ripples. The amplifier’s intrinsic directionality eliminates the need for external isolators, paving the way for fully on-chip, near-ideal superconducting pre-amplifiers.

Subwavelength atomic arrays, recently labeled as quantum metamaterials, have emerged as an exciting platform for obtaining novel quantum optical phenomena. The strong interference effects in these systems generate subradiant excitations that propagate through the atomic array with very long lifetimes. Here, we demonstrate that one can harness these excitations to obtain tunable directional emission patterns and collective dissipative couplings when placing judiciously additional atoms nearby the atomic array. For doing that, we first characterize the optimal array geometry to obtain directional emission patterns. Then, we characterize the best atomic positions to couple efficiently to the subradiant metasurface excitations, and provide several improvement strategies based on entangled atomic clusters or bilayers. Afterwards, we also show how the directionality of the emission pattern can be controlled through the relative dipole orientation between the auxiliary atoms and the one of the array. Finally, we benchmark how these directional emission patterns translate into to collective, anisotropic dissipative couplings between the auxiliary atoms by studying the lifetime modification of atomic entangled states.

The exchange of virtual photons between quantum optical emitters in cavity QED or quantum nanophotonic setups induces interactions between them which can be harnessed for quantum information and simulation purposes. So far, these interactions have been mostly characterized for two-level emitters, which restrict their application to engineering quantum gates among qubits or simulating spin-1/2 quantum many-body models. Here, we show how to harness multi-level emitters with several optical transitions to engineer a wide class of photon-mediated interactions between effective spin-1 systems. We characterize their performance through analytical and numerical techniques, and provide specific implementations based on the atomic level structure of Alkali atoms. Our results expand the quantum simulation toolbox available in such cavity QED and quantum nanophotonic setups, and open up new ways of engineering entangling gates among qutrits.

Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Fermionic atoms in ultracold atomic mixtures can act as mediators, giving rise to long-range RKKY-type interactions characterized by the dimensionality and density of the fermionic gas. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow to further control the range and shape of the mediated interactions, extending the existing quantum simulation toolbox. In particular, we include an additional optical lattice for the fermionic mediator, as well as anisotropic traps to change its dimensionality in a continuous manner. This allows us to interpolate between power-law and exponential decays, introducing an effective cutoff for the interaction range, as well as to tune the relative interaction strengths at different distances. Finally, we show how our approach allows to investigate frustrated regimes that were not previously accessible, where symmetry-protected topological phases as well as chiral spin liquids emerge.

A flux qubit can interact strongly when it is capacitively coupled to other circuit elements. This interaction can be separated in two parts, one acting on the qubit subspaces and one in which excited states mediate the interaction. The first term dominates the interaction between the flux qubit and an LC-resonator, leading to ultrastrong couplings of the form $\sigma^y(a+a^\dagger),$ which complement the inductive $\sigma^xi(a^\dagger-a)$ coupling. However, when coupling two flux qubits capacitively, all terms need to be taken into account, leading to complex non-stoquastic ultrastrong interaction of the $\sigma^y\sigma^y$, $\sigma^z\sigma^z$ and $\sigma^x\sigma^x$ type. Our theory explains all these interactions, describing them in terms of general circuit properties—coupling capacitances, qubit gaps, inductive, Josephson and capactive energies—, that apply to a wide variety of circuits and flux qubit designs.

Virtual states are a central concept in quantum mechanics. By definition, the probability of finding a quantum system in a virtual state should be vanishingly small at all times. In contrast to this notion, we report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit, even if they are not directly coupled to any dissipative channel. This means that the situation where the virtual state remains unpopulated can be metastable. We describe this effect by introducing a two-step adiabiatic elimination method, that we termed hierarchical adiabatic elimination, which allows one to obtain analytical expressions of the timescale of metastability in general open quantum systems. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.

We propose a realistic setup, inspired by already existing experiments, within which we develop a general formalism for the implementation of distributed quantum gates. Mediated by a quantum link that establishes a bidirectional quantum channel between distant nodes, our proposal works both for inter- and intra node communication and handles scenarios ranging from the few to the many modes limit of the quantum link. We are able to design fast and reliable state transfer protocols in every regime of operation, which, together with a detailed description of the scattering process, allows us to engineer two sets of deterministic universal distributed quantum gates. Gates whose implementation in quantum networks does not need entanglement distribution nor measurements. By employing a realistic description of the physical setup we identify the most relevant imperfections in the quantum links as well as optimal points of operation with resulting infidelities of $1-F \approx 10^{-2}-10^{-3}$.

Current noise levels in physical realizations of qubits and quantum operations limit the applicability of conventional methods to characterize entanglement. In this adverse scenario, we follow a quantum variational approach to estimate the geometric measure of entanglement of multiqubit pure states. The algorithm requires only single-qubit gates and measurements, so it is well suited for NISQ devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of $3$, $4$, and $5$ qubits. Numerical simulations with random states show the robustness and accuracy of the method. The scalability of the protocol is numerically demonstrated via matrix product states techniques up to $25$ qubits.