Related papers: Symplectic geometry and circuit quantization
The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to…
Here we show that to quantize any lumped element circuit, the circuit geometry must be included in a mathematical model of either the circuit fluxes or the circuit charges. By geometry of the circuit, we refer to the so-called parasitic…
Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static. Time dependence naturally arises, however, when flux is…
The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
During the last 30 years, stimulated by the quest to build superconducting quantum processors, a theory of quantum electrical circuits has emerged and this theory goes under the name of circuit quantum electrodynamics or circuit-QED. The…
Superconducting circuit quantisation conventionally starts from classical Euler-Lagrange circuit equations-of-motion. Invoking the correspondence principle yields a canonically quantised circuit description of circuit dynamics over a…
We present a formulation of quantum circuits where the focus is set on whether a given circuit (made of unitary operators and projective measurements with definite outcomes) does reflect an actually realizable physical experiment. In order…
Quantum circuit theory has emerged as an essential tool for the study of the dynamics of superconducting circuits. Recently, the problem of accounting for time-dependent driving via external magnetic fields was addressed by Riwar-DiVincenzo…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
In this work, we introduce new methods for the quantization, decomposition, and extraction (from electromagnetic simulations) of lumped-element circuit models for superconducting quantum devices. Our flux-charge symmetric procedures center…
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…
The conventional approach to circuit quantization is based on node fluxes and traces the motion of node charges on the islands of the circuit. However, for some devices, the relevant physics can be best described by the motion of…
The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
In the quest to produce quantum technology, superconducting networks, working at temperatures just above absolute zero, have arisen as one of the most promising physical implementations. The precise analysis and synthesis of such circuits…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
In this work we exploit Dirac's Constraint Analysis (DCA) in Hamiltonian formalism to study different types of Superconducting Quantum Circuits (SQC) in a {\it{unified}} way. The Lagrangian of a SQC reveals the constraints, that are…