Algebraic canonical quantization of lumped superconducting networks

  1. I. L. Egusquiza,
  2. and A. Parra-Rodriguez
We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is based
on an original, explicit, and constructive implementation of the symplectic diagonalization of positive semidefinite Hamiltonian matrices, a particular instance of Williamson’s theorem. With it, we derive canonically quantized discrete-variable descriptions of passive causal systems. We exemplify the algorithm with representative {\it singular} electrical networks, a nonreciprocal extension for the black-box quantization method, as well as an archetypal Landau quantization problem.

Charge qubits in the ultrastrong coupling regime

  1. J. Yu,
  2. F. A. Cárdenas-López,
  3. C. K. Andersen,
  4. E. Solano,
  5. and A. Parra-Rodriguez
We study the feasibility of reaching the ultrastrong (USC) and deep-strong coupling (DSC) regimes of light-matter interaction, in particular at resonance condition, with a superconducting
charge qubit, also known as Cooper-Pair box (CPB). We show that by shunting the charge qubit with a high-impedance LC-circuit, one can maximally reach both USC and DSC regimes exceeding the classical upper bound |g|≤ωqωr−−−−√/2 between two harmonic systems with frequencies ωq and ωr. In our case, the fundamental model corresponds to an enhanced quantum Rabi model, which contains a displacement field operator that breaks its internal parity symmetry. Furthermore, we consider a multipartite device consisting of two CPBs ultrastrongly coupled to an oscillator as a mediator and study a quantum state transfer protocol between a pair of transmon qubits, all of them subjected to local incoherent noise channels with realistic parameters. This work opens the door for studying light-matter interactions beyond the quantum Rabi model at extreme coupling strengths, providing a new building block for applications within quantum computation and quantum information processing.

Canonical quantization of telegrapher’s equations coupled by ideal circulators

  1. A. Parra-Rodriguez,
  2. and I. L. Egusquiza
We develop a systematic procedure to quantize canonically Hamiltonians of light-matter models of transmission lines point-wise coupled through linear lossless ideal circulators in a
circuit QED set-up. This is achieved through a description in terms of both flux and charge fields. This apparent redundancy allows the derivation of the relevant Hamiltonian. By making use of the electromagnetic duality symmetry proper to the case at hand we provide unambiguous identification of the physical degrees of freedom, separating out the nondynamical parts. Furthermore, this doubled description is amenable to a treatment of other pointwise contacts that is regular and presents no spurious divergences, as we show explicitly in the example of a circulator connected to a Josephson junction through a transmission line. This theory enhances the quantum engineering toolbox to design complex networks with nonreciprocal elements.

Chiral states and nonreciprocal phases in a Josephson junction ring

  1. R. Asensio-Perea,
  2. A. Parra-Rodriguez,
  3. G. Kirchmair,
  4. E. Solano,
  5. and E. Rico
In this work, we propose how to load and manipulate chiral states in a Josephson junction ring in the so called transmon regimen. We characterise these states by their symmetry properties
under time reversal and parity transformations. We describe an explicit protocol to load and detect the states within a realistic set of circuit parameters and show simulations that reveal the chiral nature. Finally, we explore the utility of these states in quantum technological nonreciprocal devices.

Secure quantum remote state preparation of squeezed microwave states

  1. S. Pogorzalek,
  2. K. G. Fedorov,
  3. M. Xu,
  4. A. Parra-Rodriguez,
  5. M. Sanz,
  6. M. Fischer,
  7. E. Xie,
  8. K. Inomata,
  9. Y. Nakamura,
  10. E. Solano,
  11. A. Marx,
  12. F. Deppe,
  13. and R. Gross
Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular,
remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. We quantify security in our implementation using the concept of the one-time pad. Our results represent a significant step towards microwave quantum networks between superconducting circuits.

Canonical Circuit Quantization with Non-Reciprocal Devices

  1. A. Parra-Rodriguez,
  2. I. L. Egusquiza,
  3. D. P. DiVincenzo,
  4. and E. Solano
Non-reciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that it couples, and they can be used to create chiral information
processing networks. We study how to systematically include ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general non-reciprocal networks on the quantum regime. We apply it to useful and pedagogical examples of circuits containing Josephson junctions and non-reciprocal ideal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on non-reciprocal devices characterized by impedance and/or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and non-reciprocal devices.

Quantum Networks in Divergence-free Circuit QED

  1. A. Parra-Rodriguez,
  2. E. Rico,
  3. E. Solano,
  4. and I. L. Egusquiza
Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models
that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analog quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.