Consistent Quantization of Nearly Singular Superconducting Circuits
- URL: http://arxiv.org/abs/2208.11767v1
- Date: Wed, 24 Aug 2022 20:40:46 GMT
- Title: Consistent Quantization of Nearly Singular Superconducting Circuits
- Authors: Martin Rymarz, David P. DiVincenzo
- Abstract summary: We demonstrate the failure of the Dirac-Bergmann theory for the quantization of realistic, nearly singular superconducting circuits.
The correct treatment of nearly singular systems involves a perturbative Born-Oppenheimer analysis.
We find that the singular limit of this regularized analysis is, in many cases, completely unlike the singular theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The theory of circuit quantum electrodynamics has successfully analyzed
superconducting circuits on the basis of the classical Lagrangian, and the
corresponding quantized Hamiltonian, describing these circuits. In many
simplified versions of these networks, the modeling involves a Lagrangian that
is singular, describing an inherently constrained system. In this work, we
demonstrate the failure of the Dirac-Bergmann theory for the quantization of
realistic, nearly singular superconducting circuits, both reciprocal and
nonreciprocal. The correct treatment of nearly singular systems involves a
perturbative Born-Oppenheimer analysis. We rigorously prove the validity of the
corresponding perturbation theory using Kato-Rellich theory. We find that the
singular limit of this regularized analysis is, in many cases, completely
unlike the singular theory. Dirac-Bergmann, which uses the Kirchhoff's (and
Tellegen's) laws to deal with constraints, predicts dynamics that depend on the
detailed parameters of nonlinear circuit elements, e.g., Josephson inductances.
By contrast, the limiting behavior of the low-energy dynamics obtained from the
regularized Born-Oppenheimer approach exhibits a fixed point structure, flowing
to one of a few universal fixed points as parasitic capacitance values go to
zero.
Related papers
- Structural Stability Hypothesis of Dual Unitary Quantum Chaos [0.0]
spectral correlations over small enough energy scales are described by random matrix theory.
We consider fate of this property when moving from dual-unitary to generic quantum circuits.
arXiv Detail & Related papers (2024-02-29T12:25:29Z) - Flux-charge symmetric theory of superconducting circuits [0.0]
We present a theory of circuit quantization that treats charges and flux on a manifestly symmetric footing.
For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space.
We discuss the extent to which such circuit dualities generalize to non-planar circuits.
arXiv Detail & Related papers (2024-01-16T18:18:52Z) - Lecture Notes on Quantum Electrical Circuits [49.86749884231445]
Theory of quantum electrical circuits goes under the name of circuit quantum electrodynamics or circuit-QED.
The goal of the theory is to provide a quantum description of the most relevant degrees of freedom.
These lecture notes aim at giving a pedagogical overview of this subject for theoretically-oriented Master or PhD students in physics and electrical engineering.
arXiv Detail & Related papers (2023-12-08T19:26:34Z) - Functional Renormalization Group Approach to Circuit Quantum
Electrodynamics [0.0]
A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electromagnetic continuum.
Our results indicate that a nonperturbative analysis is essential for a comprehensive understanding of cQED platforms.
arXiv Detail & Related papers (2022-08-30T09:43:39Z) - Gaussian initializations help deep variational quantum circuits escape
from the barren plateau [87.04438831673063]
Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years.
However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number.
This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
arXiv Detail & Related papers (2022-03-17T15:06:40Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Intrinsic mechanisms for drive-dependent Purcell decay in
superconducting quantum circuits [68.8204255655161]
We find that in a wide range of settings, the cavity-qubit detuning controls whether a non-zero photonic population increases or decreases qubit decay Purcell.
Our method combines insights from a Keldysh treatment of the system, and Lindblad theory.
arXiv Detail & Related papers (2021-06-09T16:21:31Z) - Canonical Quantization of Superconducting Circuits [0.0]
We develop mathematically consistent and precise Hamiltonian models to describe ideal superconducting networks.
We pave the way on how to quantize general frequency-dependent gyrators and circulators coupled to both transmission lines and other lumped-element networks.
arXiv Detail & Related papers (2021-04-19T15:58:16Z) - Engineering dissipation with resistive elements in circuit quantum
electrodynamics [0.0]
This article discusses how to simulate thermal baths by inserting resistive elements in networks of superconducting qubits.
The aim of the manuscript is to be both an instructive tutorial about how to derive and characterize the Hamiltonian of general dissipative superconducting circuits with capacitive coupling.
arXiv Detail & Related papers (2021-03-31T09:59:45Z) - Hardware-Encoding Grid States in a Non-Reciprocal Superconducting
Circuit [62.997667081978825]
We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code.
We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.
arXiv Detail & Related papers (2020-02-18T16:45:09Z) - Theoretical methods for ultrastrong light-matter interactions [91.3755431537592]
This article reviews theoretical methods developed to understand cavity quantum electrodynamics in the ultrastrong-coupling regime.
The article gives a broad overview of the recent progress, ranging from analytical estimate of ground-state properties to proper computation of master equations.
Most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached.
arXiv Detail & Related papers (2020-01-23T18:09:10Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.