Among the different implementations, atomic and molecular optical (AMO) systems are some the most prominent examples of such simulators with many experimental realizations which have already benchmarked the validity of the quantum simulation approach.

In our group, we work intensively in these systems either by finding novel functionalities of these systems (e.g., simulating other problems), discovering new ways of detecting their properties, as well as developing new platforms that overcome the limitations of existing systems.

Ultra-cold atom simulators

Cold atoms in optical lattices are one of the most versatile analog simulators, which can simulate models in one, two, and three-dimensions. In these systems, the atoms are trapped by an optical potential made by sending counter-propagating lasers in free-space, such that both the atomic tunneling and interactions can be controlled to a large extent through these lasers. Originally, these systems were conceived as a way of simulating condensed-matter problems, such as electron transport in solids. However, in the recent years there is an interest in using them for different areas of physics such as high-energy physics or quantum chemistry.

In our group, we study the possibility of using these systems to emulate quantum chemistry dynamics [1] or non-trivial quantum optical phenomena with matter-waves [2]. Besides, we also develop new techniques to probe their emergent dynamics in, e.g., topological models [3].

Trapped ions simulators

Trapped ions are charged atoms that can be held in vacuum with electromagnetic fields. They form beautiful Coulomb crystals and they can be manipulated and addressed one-by-one with laser light or magnetic fields. That is the reason why trapped ions are the building blocks of one of the most promising technological platforms for quantum computing. But it turns out that this degree of controllability can also be used for quantum simulation. By shining a trapped ion crystal with laser light we can induce interactions between ions and make them emulate condensed matter systems such as quantum magnets, ultracold boson fluids, quantum Hall systems or tiny thermal machines.

In our group, we have made pioneering proposals in these systems to use them for simulating quantum magnets [4] or out-of-equilibrium dynamics [5]. In one of our collaborations with a Tobias Schaetz’ experimental group at U. Freiburg, we were able to investigate how thermal states emerge in a few ion crystal. More recently, in collaboration with the same group, we where able to manipulate the phonons in a trapped ion system, so that they would behave as electrons in a magnetic field [6].

New platforms for quantum simulation

Despite the excellent features of the two previously mentioned simulators, they also suffer from some limitations. For example, the atoms in optical lattices have limited kinetic energy as they hop through the lattice, setting stringent temperature requirements of the experiment. Besides, atomic interactions are generally local or short range.

For this reason, in our group we also develop alternative implementations that can overcome some of these limitations, like hybrid atom-nanophotonics platforms [7].

Selected Group Publications

1. J. Argüello-Luengo, A González-Tudela, T Shi, P Zoller, JI Cirac. Analogue Quantum Chemistry Simulation. Nature 574 (7777), 215-218 (2019)
2. I. de Vega, D Porras, JI Cirac. Matter-wave emission in optical lattices: Single particle and collective effects. Physical Review Letters 101 (26), 26040 (2008).
3. A. Rubio-García, C. N. Self, J.J. García-Ripoll, and J. K. Pachos. Seeing topological edge and bulk currents in time-of-flight images. Phys. Rev. B 102, 041123 (R) (2020)
4. D. Porras, J. I. Cirac. Effective quantum spin systems with trapped ions. Physical Review Letters 92 (20), 207901 (2004)
5. G Clos, D Porras, U Warring, T Schaetz. Time-resolved observation of thermalization in an isolated quantum system. Physical Review Letters 117 (17), 170401 (2016)
6. Floquet-Engineered Vibrational Dynamics in a Two-Dimensional Array of Trapped Ions. P. Kiefer, F. Hakelberg, M. Wittemer, A. Bermúdez, D. Porras, U. Warring, T. Schaetz. Physical Review Letters 113, 213605 (2019).
7. DE Chang, JS Douglas, A. González-Tudela, C-L Hung, HJ Kimble. Colloquium: Quantum matter built from nanoscopic lattices of atoms and photons. Reviews of Modern Physics 90 (3), 031002 (2018)

Group members working in this field

• Juan José García Ripoll
• Diego Porras Torre
• Alejandro González-Tudela
• Tomás Ramos
• Álvaro Gómez-León
• Carlos Vega García

Quantum optimization

A wide range of optimization problems can be mapped into a QUBO problem or an Ising Hamiltonian, from finance and the more academic MaxCut problem to finding the ground state of spin glass Hamiltonians. Quantum variational optimization has emerged as a promising framework to solve these problems faster and at a larger scale than what classical methods allow. In this regard, we study the performance of state-of-art algorithms such as the Variational Quantum Eigensolver [1]. Furthermore, we explore practical applications in finance, where we have developed a hybrid quantum-classical algorithm to choose a series of assets that track a particular financial index [2].

Quantum PDE solvers

The solution of partial differential equations is a ubiquitous problem, with a broad impact in many areas of science and technology, from physics and chemistry to finance and engineering. Existing numerical methods are limited in the size and complexity of the problems they can solve. It is therefore of great interest to find alternative techniques that can provide size or time speedups in the manipulation of PDE and their solutions.

In our group we are exploring the use of a variational hybrid quantum-classical algorithm to tackle this problem. The idea is to encode a complex multidimensional function as the superposition state of a quantum computer, manipulating this state to find the best approximation to the solution of a PDE.

In our first work in this topic [3], we have studied the performance of existing and new variational ansätze and optimization techniques, gauging their application in current and near-term NISQ hardware. This work illustrates the power of quantum Fourier interpolation as an acceleration technique to reduce the dimensionality of the quantum states, obtaining accurate representations with exponentially reduced numbers of qubits. It also confirms the limitations of existing hardware and qubit quality in the application of these ideas.

Tensor networks

Tensor networks are a mathematical description to represent quantum-many body states based on the entanglement structure. This formalism allows to reduce the number of parameters that represent a state, and hence is efficient for the simulation of many body systems. This can be applied to quantum computing, by using tensor networks to represent qubits, allowing for the use of a greater number of qubits than current quantum computers, both real and simulators. By using tensor networks we aim at developing quantum-inspired algorithms for a variety of problems, such as multivariate analysis [4].

Group members working on this field

• Juan José García Ripoll
• Diego Porras Torre
• Álvaro Rubio García
• Pablo Díez Valle
• Paula García Molina

Publications

[1] Quantum variational optimization: the role of entanglement and problem hardness, Pablo Díez-Valle, Diego Porras, Juan José García-Ripoll, Phys. Rev. A 104, 062426 (2021).

[2] Hybrid quantum-classical optimization for financial index tracking, Samuel Fernández-Lorenzo, Diego Porras, Juan José García-Ripoll, Quantum Sci. Technol. 6 034010 (2021).

[3] Quantum Fourier analysis for multivariate functions and applications to a class of Schrödinger-type partial differential equations, Paula García-Molina, Javier Rodríguez-Mediavilla, Juan José García-Ripoll, Phys. Rev. A 105, 012433 (2022).

[4] Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations, Juan José García-Ripoll, Quantum 5, 431 (2021).

In free-space this interaction is generally weak, which is why in the last years there has been a lot of research of developing new platforms that surpass this limitation, e.g., integrating quantum emitters with nanophotonic platforms (quantum nanophotonics), exploiting collective effects in subwavelength atomic arrays, or mimicking this interaction with superconducting circuits (circuit QED).

In our group, we work at the frontier of this field by both developing novel light-matter interfaces that provide enhanced functionalities over state-of-the-art systems and exploiting them for generating novel states of light and matter that can be used for applications. Some of the research lines we are currently exploring:

Topological Quantum Photonics and Amplifiers

Topological phases of matter are characterized by exotic boundary physics, namely by the existence of protected modes at the edge of the system that are immune to local perturbations such as disorder or defects. Such robustness triggered the interest of the photonics community to export these ideas into their platforms to obtain robust and unidirectional photon flows. These efforts have recently culminated in the experimental realization of these ideas in several platforms, but mostly focusing in the linear (classical) regime since the interactions between photons are generally very weak.

In our group, we aim to study the quantum optical consequences of such topological photonic systems beyond the regimes usually considered in the literature. For example, by considering the interaction of quantum emitters, a strongly interacting system, with such topological photonic environments, which results in unconventional quantum emitter dynamics and interactions [1]. Besides, we also consider driven dissipative situations that lead to topological quantum amplification [2] that can be potentially harnessed to amplify weak quantum signals.

Generation of non-classical states of light & matter

Engineering and control of quantum states of light and matter are central in photonic quantum technologies, ranging from quantum communication and computation (single photon states) or quantum metrology (single and multi-mode Fock states).

In our group, we develop protocols aiming to surpass the limitations of current ones based on novel light-matter interfaces, such as waveguide QED [3] or circuit QED platforms [4].

Quantum spectroscopy: multi-photon scattering and detection

Complex quantum optical systems can have an intrinsic complicated dynamics which is sometimes difficult to know a priori. One alternative to characterize them is to use their interaction with light to unravel their behaviour. When the light has a non-classical character, this is tipically labelled as quantum spectroscopy.

In our group, we explore several of these scenarios. For example, by sending multi-photon wave-packets and analyzing the associated reflection and transmission properties, we have shown how one can gain a lot of information of the system [5]. Besides, we also explore how to use a frequency-resolved version of Hanbury-Brown-Twiss interferometer to obtain also such information “passively”.

Selected Group Publications

1. Bello, M., Platero, G., Cirac, J. I., & González-Tudela, A. (2019). Unconventional quantum optics in topological waveguide QED. Science advances, 5(7), eaaw0297.
2. Ramos, T., García-Ripoll, J. J., & Porras, D. (2021). Topological input-output theory for directional amplification. Physical Review A, 103(3), 033513.
3. González-Tudela, A, Paulisch, V., Kimble, H. J., Cirac, J. I. Efficient multiphoton generation in waveguide quantum electrodynamics. Physical Review Letters 118 (21), 213601 (2017).
4. Li, M., García-Ripoll, J. J., Ramos. T, Scalable multiphoton generation from cavity-synchronized single-photon sources. arXiv: 2009.02382.
5. Ramos, T., & García-Ripoll, J. J. (2017). Multiphoton scattering tomography with coherent states. Physical Review Letters, 119(15), 153601.
6. Schmidt, M. K., Esteban, R., Giedke, G., Aizpurua, J. González-Tudela, A. Frequency-resolved photon correlations in cavity optomechanics. Quantum Science and Technology 6 (3), 034005 (2021).

Group members working in this field

• Juan José García Ripoll
• Diego Porras Torre
• Alejandro González-Tudela
• Tomás Ramos
• Álvaro Gómez-León
• Carlos Vega García

Superconducting Qubits

Superconducting qubits consist of a micro scale electrical circuit with some nonlinear element, typically a Josephson junction. This element, essentially a capacitor that allows the tunneling of Cooper pairs, offers incredible possibilities. However, there are multiple ways in which several Josephson Junctions, as well as coils and capacitors can be combined to form a qubit. Some examples are: charge qubits, three Josephson junction flux qubits, fluxonion qubits… This flexibility in the design, together with the possibility of using circuit elements to mediate interactions between them, makes superconducting circuits one of the most promising platforms for the realization of quantum computing devices. In fact, it is nowadays the supporting platform of most of the state-of-the-art implementations of quantum devices such as IBM’s gate-based quantum computer, Google’s gate-based quantum computer, or D-wave’s quantum annealer.

In this context, our group takes part in the project AVaQus (Annealing-based Variational Quantum Processors) which aims at a radical upgrade of present quantum annealing technology by engineering novel superconducting quantum circuits. AVaQus is a European project funded in the FET-Open 2019 call and brings together research groups and companies to develop a quantum processor that demonstrates coherent quantum annealing and its potential to solve real-life optimization problems.  Our work here consists of theoretically designing and analyzing novel circuit architectures for quantum computing and optimization. In particular, we study the possibility of finding strong tunable interactions between three Josephson junction flux qubits and with other circuit elements for its later implementation on the construction of a real quantum annealer.

Quantum Links

We believe that superconducting circuits are a promising platform for quantum information processing, however, they have a very specific drawback: the temperatures at which they operate. Whereas with current technologies, the needed temperatures of a few miliKelvin are easily and cheaply reached, the size of the refrigerators becomes a problem when we aim to scale up the setup. 

The solution that we propose for this is to implement a local area network in which we connect several refrigerators via quantum links [1]. This ambitious idea is tackled within the context of the european collaboration SuperQulan (Superconducting Quantum Local Area Network). Quinfog is in the theory division of this interdisciplinary project designing protocols for distributed quantum information processing. Among these are:

• Shaping of individual photons for state transfer and high fidelity data writing and retrieval by means of time dependent couplings. 
• Implementation of a controlled phase gate and eventually of a universal set of gates between distant nodes of the network.
• Entanglement distribution.

For all of this we use quantum optical techniques such as Input-Output formalism and master equation modelization. Our mid term goal is to find a theory that takes full account of the phenomenology for both short and long links and develop a python library that can be used as a toolbox to solve problems related with any distributed setup.

Selected Group Publications

• Hita-Pérez, M., Orellana, P., García-Ripoll, J.J., Pino M. (2022). Bound states in the continuum in a heavy fluxonium qutrit. Phys. Rev. A 106, 062602.
• Peñas, G.F., Puebla, R., Ramos, T., Rabl, P., García-Ripoll, J.J. (2022). Universal Deterministic Quantum Operations in Microwave Quantum Links. Physical Review Applied 17, 054038.
• Hita-Pérez, M., Jaumà, G., Pino, M., & García-Ripoll, J.J. (2022). Ultrastrong capacitive coupling of flux qubits. Physical Review Applied 17, 014028.
• Hita-Pérez, M., Jaumà, G., Pino, M., & García-Ripoll, J.J. (2021). Three-Josephson junctions flux qubit couplings. Applied Physics Letters 119, 222601.
• Peropadre, B., Forn-Díaz, P., Solano, E., & García-Ripoll, J. J. (2010). Switchable Ultrastrong Coupling in Circuit QED. Physical Review Letters 105, 023601.

Group members working in this field

• Juan José García Ripoll
• Manuel Pino
• Tomás Ramos
• Ricardo Puebla
• Guillermo F. Peñas
• María Hita Pérez