Following a consistent geometrical description previously introduced [Quantum 8, 1466 (2024)], we present an exact method for obtaining canonically quantizable Hamiltonian descriptions of nonlinear, nonreciprocal quasilumped electrical networks. We identify and classify singularities arising in the quest for Hamiltonian descriptions of general quasilumped element networks via the Faddeev-Jackiw technique. We offer systematic solutions to cases previously considered singular-a major challenge in the context of canonical circuit quantization. The solution relies on the correct identification of the reduced classical circuit-state manifold, i.e., a mix of flux and charge fields and functions. Starting from the geometrical description of the transmission line, we provide a complete program including lines coupled to one-port lumped-element networks, as well as multiple lines connected to multiport nonreciprocal lumped-element networks, with intrinsic ultraviolet cutoff. On the way, we naturally extend the canonical quantization of transmission lines coupled through frequency-dependent, nonreciprocal linear systems, such as practical circulators. Additionally, we demonstrate how our method seamlessly facilitates the characterization of general nonreciprocal, dissipative linear environments. This is achieved by extending the Caldeira-Leggett formalism, using continuous limits of series of immittance matrices. We provide a tool in the analysis and design of electrical circuits and of special interest in the context of canonical quantization of superconducting networks. For instance, this work provides a solid ground for a precise nondivergent inputoutput theory in the presence of nonreciprocal devices, e.g., within (chiral) waveguide QED platforms.

The analysis conducted by Rymarz and DiVincenzo (Phys. Rev. X 13, 021017 (2023)) regarding quantization of superconducting circuits is insufficient to justify their general conclusions, most importantly the need to discard Kirchhoff's laws to effect variable reductions. Amongst a variety of reasons, one source of several disagreements with experimental and theoretical results is the long-standing dispute between extended vs compact variables in the presence of Josephson junctions.

In lumped-element electrical circuit theory, the problem of solving Maxwell's equations in the presence of media is reduced to two sets of equations, the constitutive equations encapsulating local geometry and dynamics of a confined energy density, and the Kirchhoff equations enforcing conservation of charge and energy in a larger, topological, scale. We develop a new geometric and systematic description of the dynamics of general lumped-element electrical circuits as first order differential equations, derivable from a Lagrangian and a Rayleigh dissipation function. Through the Faddeev-Jackiw method we identify and classify the singularities that arise in the search for Hamiltonian descriptions of general networks. The core of our solution relies on the correct identification of the reduced manifold in which the circuit state is expressible, e.g., a mix of flux and charge degrees of freedom, including the presence of compact ones. We apply our fully programmable method to obtain (canonically quantizable) Hamiltonian descriptions of nonlinear and nonreciprocal circuits which would be cumbersome/singular if pure node-flux or loop-charge variables were used as a starting configuration space. We also propose a specific assignment of topology for the branch variables of energetic elements, that when used as input to the procedure gives results consistent with classical descriptions as well as with spectra of more involved quantum circuits. This work unifies diverse existent geometrical pictures of electrical network theory, and will prove useful, for instance, to automatize the computation of exact Hamiltonian descriptions of superconducting quantum chips.

We characterize the role of the roton instability in the formation of a supersolid state of an elongated dipolar condensate, following a quench of the contact interactions across the superfluid-supersolid transition, as observed in recent experiments. We perform dynamical simulations by means of the extended Gross-Pitaevskii equation including quantum corrections, for different final values of the $s-$wave scattering length. The corresponding excitation spectrum is computed using an effective one-dimensional description, revealing that the calculated growth rates of the unstable roton mode accurately reproduce the observed behavior. Our results provide valuable insights regarding the formation time of the supersolid and its scaling behavior with respect to the $s$-wave scattering length.

We present a systematic canonical quantization procedure for lumped-element superconducting networks by using 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 descrip-tions of passive causal systems. We exemplify the algorithm with representative singular electrical networks, a nonreciprocal extension for the black-box quantization method, as well as an archetypal Landau quantization problem.

We develop a systematic procedure to quantise canonically Hamiltonians of light-matter models of transmission lines coupled through lumped linear lossless ideal nonreciprocal elements, that break time-reversal symmetry, in a circuit QED set-up. This is achieved through a description of the distributed subsystems in terms of both flux and charge fields. We prove that this apparent redundancy is required for the general derivation of the Hamiltonian for a wider class of networks. By making use of the electromagnetic duality symmetry in transmission lines (waveguides), we provide unambiguous identification of the physical degrees of freedom, separating out the nondynamical parts. This doubled description can also treat the case of other extended lumped interactions in a regular manner that 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.

We present an extension of the classical Nyquist-Thevenin theorem for multiport classical electrical networks by Twiss to the quantum case. Conversely, we extend the quantum fluctuation-dissipation result for one port electrical systems to the multiport case, both reciprocal and nonreciprocal. Our results are extended to lossy systems by depicting resistive components as continuous limits of purely lossless lumped-element networks. Simple circuit examples are analyzed, including a linear system lacking a direct impedance representation.

We present an exact full symmetry analysis of the 0-$\pi$ superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.

We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by G. Biagioni et al. [Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) 1D behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signalling the onset of a dimensional crossover.

The physics of high-energy colliders relies on the knowledge of different non-perturbative parton correlators, such as parton distribution functions, that encode the information on universal hadron structure and are thus the main building blocks of any factorization theorem of the underlying process in such collision. These functions are given in terms of gauge-invariant light-front operators, they are non-local in both space and real time, and are thus intractable by standard lattice techniques due to the well-known sign problem. In this paper, we propose a quantum algorithm to perform a quantum simulation of these type of correlators, and illustrate it by considering a space-time Wilson loop. We discuss the implementation of the quantum algorithm in terms of quantum gates that are accessible within actual quantum technologies such as cold atoms setups, trapped ions or superconducting circuits.

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.

Fast nonadiabatic control protocols known as shortcuts to adiabaticity have found a plethora of applications, but their use has been severely limited to speeding up the dynamics of isolated quantum systems. We introduce shortcuts for open quantum processes that make possible the fast control of Gaussian states in nonunitary processes. Specifically, we provide the time modulation of the trap frequency and dephasing strength that allow preparing an arbitrary thermal state in a finite time. Experimental implementation can be done via stochastic parametric driving or continuous measurements, readily accessible in a variety of platforms.

The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element; namely, capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. We consider a quantized Hodgkin-Huxley model based on a quantum-memristor formalism. We compare the behavior of the membrane voltage and the potassium-channel conductance when the circuit is subjected to ac sources, in both the classical realm and the quantum realm. Numerical simulations show an expected adaptation of the considered channel conductance depending on the signal history in all regimes. Remarkably, the computation of higher moments of the voltage shows purely quantum features related to the circuit zero-point energy. Finally, we study the implementation of the Hodgkin-Huxley quantum memristor as an asymmetric rf superconducting quantum-interference device in superconducting circuits. This study may allow the construction of quantum neuron networks inspired by the brain function, as well as the design of neuromorphic quantum architectures for quantum machine learning.

Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general nonreciprocal networks on the quantum regime. We apply it to pedagogical and pathological examples of circuits containing Josephson junctions and ideal nonreciprocal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on nonreciprocal devices characterized by impedance or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and nonreciprocal devices.

We study the Two Photon Quantum Rabi Model by way of its spectral functions and survival probabilities. This approach allows numerical precision with large truncation numbers, and thus exploration of the spectral collapse. We provide independent checks and calibration of the numerical results by studying an exactly solvable case and comparing the essential qualitative structure of the spectral functions. We stress that the large time limit of the survival probability provides us with an indicator of spectral collapse, and propose a technique for the detection of this signal in the current and upcoming quantum simulations of the model.

We prove, by means of a unified treatment, that the superradiant phase transitions of Dicke and classical oscillator limits of simple light-matter models are indeed of the same type. We show that the mean-field approximation is exact in both cases, and compute the structure and location of the transitions in parameter space. We extend this study to a fuller range of models, paying special attention to symmetry considerations. We uncover general features of the phase structure in the space of parameters of these models.

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.

A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dynamics of a two-mode squeezed state. When the initial density matrix is canonical, the Loschmidt echo of the purified double thermofield state provides a direct measure of information scrambling and can be related to the analytic continuation of the partition function. Information scrambling is then described by the quantum work statistics associated with the time-reversal operation on a single copy, associated with the sudden negation of the system Hamiltonian.