Digital-Analog Quantum Simulations with Superconducting Circuits

  1. Lucas Lamata,
  2. Adrian Parra-Rodriguez,
  3. Mikel Sanz,
  4. and Enrique Solano
Quantum simulations consist in the intentional reproduction of physical or unphysical models into another more controllable quantum system. Beyond establishing communication vessels
between unconnected fields, they promise to solve complex problems which may be considered as intractable for classical computers. From a historic perspective, two independent approaches have been pursued, namely, digital and analog quantum simulations. The former usually provide universality and flexibility, while the latter allows for scalability. Here, we review recent literature merging both paradigms in the context of superconducting circuits, yielding: digital-analog quantum simulations. In this manner, we aim at getting the best of both approaches in the most advanced quantum platform involving superconducting qubits and microwave transmission lines. The discussed merge of quantum simulation concepts, digital and analog, may open the possibility in the near future for outperforming classical computers in relevant problems, enabling the reach of quantum supremacy.

Divergence-free multi-mode circuit quantum electrodynamics

  1. Mario F. Gely,
  2. Adrian Parra-Rodriguez,
  3. Daniel Bothner,
  4. Ya. M. Blanter,
  5. Sal J. Bosman,
  6. Enrique Solano,
  7. and Gary A. Steele
Circuit quantum electrodynamics studies the interaction of artificial atoms and electromagnetic modes constructed from superconducting circuitry. While the theory of an atom coupled
to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a full quantum model of a multi-mode resonator coupled to a Josephson junction atom. Using circuit quantization, we find a Hamiltonian in which parameters of the atom are naturally renormalized as additional modes are considered. In our model, we circumvent the divergence problem, and its formulation reveals a physical understanding of the mechanisms of convergence in ubiquitous models in circuit quantum electrodynamics.

Superluminal Physics with Superconducting Circuit Technology

  1. Carlos Sabín,
  2. Borja Peropadre,
  3. Lucas Lamata,
  4. and Enrique Solano
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.

Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience

  1. Rui Li,
  2. Unai Alvarez-Rodriguez,
  3. Lucas Lamata,
  4. and Enrique Solano
It has been proven that quantum adders are forbidden by the laws of quantum mechanics. We analyze theoretical proposals for the implementation of approximate quantum adders and optimize
them by means of genetic algorithms, improving previous protocols in terms of efficiency and fidelity. Furthermore, we experimentally realize a suitable approximate quantum adder with the cloud quantum computing facilities provided by IBM Quantum Experience. The development of approximate quantum adders enhances the toolbox of quantum information protocols, paving the way for novel applications in quantum technologies.

Entanglement of superconducting qubits via acceleration radiation

  1. Laura García-Álvarez,
  2. Simone Felicetti,
  3. Enrique Rico,
  4. Enrique Solano,
  5. and Carlos Sabín
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 analyze 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.

Few-qubit quantum-classical simulation of strongly correlated lattice fermions

  1. Juha M Kreula,
  2. Laura García-Álvarez,
  3. Lucas Lamata,
  4. Stephen R Clark,
  5. Enrique Solano,
  6. and Dieter Jaksch
We study a proof-of-principle example of the recently proposed hybrid quantum-classical simulation of strongly correlated fermion models in the thermodynamic limit. In a „two-site“
dynamical mean-field theory (DMFT) approach we reduce the Hubbard model to an effective impurity model subject to self-consistency conditions. The resulting minimal two-site representation of the non-linear hybrid setup involves four qubits implementing the impurity problem, plus an ancilla qubit on which all measurements are performed. We outline a possible implementation with superconducting circuits feasible with near-future technology.

Spin-boson model with an engineered reservoir in circuit quantum electrodynamics

  1. Max Haeberlein,
  2. Frank Deppe,
  3. Andreas Kurcz,
  4. Jan Goetz,
  5. Alexander Baust,
  6. Peter Eder,
  7. Kirill Fedorov,
  8. Michael Fischer,
  9. Edwin P. Menzel,
  10. Manuel J. Schwarz,
  11. Friedrich Wulschner,
  12. Edwar Xie,
  13. Ling Zhong,
  14. Enrique Solano,
  15. Achim Marx,
  16. Juan José García-Ripoll,
  17. and Rudolf Gross
A superconducting qubit coupled to an open transmission line represents an implementation of the spin-boson model with a broadband environment. We show that this environment can be
engineered by introducing partial reflectors into the transmission line, allowing to shape the spectral function, J({\omega}), of the spin-boson model. The spectral function can be accessed by measuring the resonance fluorescence of the qubit, which provides information on both the engineered environment and the coupling between qubit and transmission line. The spectral function of a transmission line without partial reflectors is found to be Ohmic over a wide frequency range, whereas a peaked spectral density is found for the shaped environment. Our work lays the ground for future quantum simulations of other, more involved, impurity models with superconducting circuits.

Relativistic Quantum Teleportation with superconducting circuits

  1. Nicolai Friis,
  2. Antony R. Lee,
  3. Kevin Truong,
  4. Carlos Sabín,
  5. Enrique Solano,
  6. Göran Johansson,
  7. and Ivette Fuentes
We study the effects of relativistic motion on quantum teleportation and propose a realizable experiment where our results can be tested. We compute bounds on the optimal fidelity of
teleportation when one of the observers undergoes non-uniform motion for a finite time. The upper bound to the optimal fidelity is degraded due to the observer’s motion however, we discuss how this degradation can be corrected. These effects are observable for experimental parameters that are within reach of cutting-edge superconducting technology.