Circuit Quantisation from First Principles

• URL: http://arxiv.org/abs/2411.12236v1
• Date: Tue, 19 Nov 2024 05:21:56 GMT
• Title: Circuit Quantisation from First Principles
• Authors: Yun-Chih Liao, Ben J. Powell, Thomas M. Stace,
• Abstract summary: We introduce the BCS ground-space as a subspace of the full fermionic Hilbert space. We show that projecting the electronic Hamiltonian onto this subspace yields the standard Hamiltonian terms for junctions, capacitors and inductors.
• Score: 0.0
• License:
• Abstract: 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 bosonic Hilbert space. This process has been very successful for describing experiments, but implicitly starts from the classical Ginsberg-Landau (GL) mean field theory for the circuit. Here we employ a different approach which starts from a microscopic fermionic Hamiltonian for interacting electrons, whose ground space is described by the Bardeen-Cooper-Schrieffer (BCS) many-body wavefuction that underpins conventional superconductivity. We introduce the BCS ground-space as a subspace of the full fermionic Hilbert space, and show that projecting the electronic Hamiltonian onto this subspace yields the standard Hamiltonian terms for Josephson junctions, capacitors and inductors, from which standard quantised circuit models follow. Importantly, this approach does not assume a spontaneously broken symmetry, which is important for quantised circuits that support superpositions of phases, and the phase-charge canonical commutation relations are derived from the underlying fermionic commutation properties, rather than imposed. By expanding the projective subspace, this approach can be extended to describe phenomena outside the BCS ground space, including quasiparticle excitations.

Related papers

• Generalized transmon Hamiltonian for Andreev spin qubits [0.0]
  We solve the problem of an interacting quantum dot embedded in a Josephson junction between two superconductors with finite charging energy. The approach is based on the flat-band approximation of the Richardson model, which reduces the Hilbert space to the point where exact diagonalisation is possible.
  arXiv  Detail & Related papers  (2024-02-03T10:58:08Z)
• 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)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Consistent Quantization of Nearly Singular Superconducting Circuits [0.0]
  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.
  arXiv  Detail & Related papers  (2022-08-24T20:40:46Z)
• Classical analog of qubit logic based on a magnon Bose-Einstein condensate [52.77024349608834]
  We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate. The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit.
  arXiv  Detail & Related papers  (2021-11-12T16:14:46Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• 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)
• A superconducting circuit realization of combinatorial gauge symmetry [0.0]
  We propose a superconducting quantum circuit based on a general principle -- gauge symmetry -- designed to emulate topologically-ordered quantum liquids. A key feature of the exact gauge symmetry is that amplitudes connecting different $mathbb Z$ loop states arise from paths having zero classical energy cost.
  arXiv  Detail & Related papers  (2020-06-17T18:00:02Z)
• Circuit Quantum Electrodynamics [62.997667081978825]
  Quantum mechanical effects at the macroscopic level were first explored in Josephson junction-based superconducting circuits in the 1980s. In the last twenty years, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The field of circuit quantum electrodynamics (QED) has now become an independent and thriving field of research in its own right.
  arXiv  Detail & Related papers  (2020-05-26T12:47:38Z)
• 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)

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.