Symplectic geometry and circuit quantization

• URL: http://arxiv.org/abs/2304.08531v1
• Date: Mon, 17 Apr 2023 18:02:35 GMT
• Title: Symplectic geometry and circuit quantization
• Authors: Andrew Osborne, Trevyn Larson, Sarah Jones, Ray W. Simmonds, Andr\'as Gyenis, Andrew Lucas
• Abstract summary: We present a Hamiltonian formulation of non-dissipative electrodynamic circuits. We show how to re-derive known results from our formalism, and provide an efficient algorithm for quantizing circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose degrees of freedom are either magnetic fluxes or electric charges in the circuit. By combining nonlinear circuit elements (such as Josephson junctions or quantum phase slips), it is possible to build circuits where a standard Lagrangian description (and thus the standard quantization method) does not exist. Inspired by the mathematics of symplectic geometry and graph theory, we address this challenge, and present a Hamiltonian formulation of non-dissipative electrodynamic circuits. The resulting procedure for circuit quantization is independent of whether circuit elements are linear or nonlinear, or if the circuit is driven by external biases. We explain how to re-derive known results from our formalism, and provide an efficient algorithm for quantizing circuits, including those that cannot be quantized using existing methods.

Related papers

• 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)
• A Complete Equational Theory for Quantum Circuits [58.720142291102135]
  We introduce the first complete equational theory for quantum circuits. Two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations.
  arXiv  Detail & Related papers  (2022-06-21T17:56:31Z)
• LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits [58.720142291102135]
  We introduce the LOv-calculus, a graphical language for reasoning about linear optical quantum circuits. Two LOv-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LOv-calculus.
  arXiv  Detail & Related papers  (2022-04-25T16:59:26Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• 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)
• Quantum Circuits in Additive Hilbert Space [0.0]
  We show how conventional circuits can be expressed in the additive space and how they can be recovered. In particular in our formalism we are able to synthesize high-level multi-controlled primitives from low-level circuit decompositions. Our formulation also accepts a circuit-like diagrammatic representation and proposes a novel and simple interpretation of quantum computation.
  arXiv  Detail & Related papers  (2021-11-01T19:05:41Z)
• The principle of majorization: application to random quantum circuits [68.8204255655161]
  Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. We verified that all the families of circuits satisfy on average the principle of majorization. Clear differences appear in the fluctuations of the Lorenz curves associated to states.
  arXiv  Detail & Related papers  (2021-02-19T16:07:09Z)
• Capacity and quantum geometry of parametrized quantum circuits [0.0]
  Parametrized quantum circuits can be effectively implemented on current devices. We evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space. Our results enhance the understanding of parametrized quantum circuits for improving variational quantum algorithms.
  arXiv  Detail & Related papers  (2021-02-02T18:16:57Z)
• Free Mode Removal and Mode Decoupling for Simulating General Superconducting Quantum Circuits [4.568911586155097]
  We consider and solve two issues involved in simulating general superconducting circuits. One is the handling of free modes in the circuit, that is, circuit modes with no potential term in the Hamiltonian. The other is the challenge of simulating strongly coupled multimode circuits.
  arXiv  Detail & Related papers  (2020-11-20T18:59:29Z)
• The Energy of an Arbitrary Electrical Circuit, Classical and Quantum [0.0]
  I introduce an algorithmic method to find the conservative energy and non-conservative power of a large class of electric circuits. I consider only two-port linear circuits with holonomic constraints provided by either Kirchhoff's current laws or Kirchhoff's voltage laws.
  arXiv  Detail & Related papers  (2020-07-15T23:44:47Z)

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.