Compressed Quantum Operators and Roots of Hermite Polynomials

• URL: http://arxiv.org/abs/2606.24792v1
• Date: Tue, 23 Jun 2026 16:46:39 GMT
• Title: Compressed Quantum Operators and Roots of Hermite Polynomials
• Abstract summary: We show that a finite rank compression of the position and momentum operator representation on Fock space has eigenvalues given by roots of the classical Hermites.<n>We discuss the corresponding compressed displacement operators and potential applications in approximate quantum error correction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The fundamental position and momentum operators of quantum mechanics are unbounded, but finite rank compressions of the operators can be considered to obtain partial information on the operators and their properties. Motivated by problems in photonic quantum computing, we bring together results from quantum theory and the theory of orthogonal polynomials to show that a natural finite rank compression of the position and momentum operator representation on Fock space Hilbert space has eigenvalues given by roots of the classical Hermite polynomials. We discuss the corresponding compressed displacement operators and potential applications in approximate quantum error correction.

Related papers

• Quantum Mechanical Studies of Photodissociation Dynamics on Quantum Computers [21.171497547707137]
  We present a quantum algorithm to study photodissociation dynamics on quantum computers.<n>The algorithm is robust to noise and statistical sampling errors, indicating the promising application of noisy devices to quantum dynamics studies.
  arXiv  Detail & Related papers  (2026-06-08T02:11:12Z)
• Hybrid quantum-classical simulations of semiclassical gravity [39.146761527401424]
  We propose a hybrid quantum-classical algorithm for the simulation of real-time dynamics in interacting quantum field theories coupled to classical fields.<n>By discretizing space and time, we construct an iterative protocol that simulates the Trotterized dynamics of the quantum fields subject to the classical fields.<n>Our work paves the way for future experiments exploring other non-tractable regimes, including non-perturbative interactions of the quantum fields.
  arXiv  Detail & Related papers  (2026-03-06T17:48:21Z)
• Spectral decomposition of field operators and causal measurement in quantum field theory [0.0]
  We construct the spectral decomposition of field operators in bosonic quantum field theory.<n>We use the decompositions to construct families of quantum operations implementing measurements of the field observables.<n>What is more, we show that these quantum operations do not lead to superluminal signaling and are possible measurements on quantum fields in the sense of Sorkin.
  arXiv  Detail & Related papers  (2024-09-13T11:59:28Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Relativistic Quantum Fields Are Universal Entanglement Embezzlers [41.94295877935867]
  Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system.<n>We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2024-01-14T13:58:32Z)
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• Complexified quantum field theory in operator form [0.0]
  This formalism is free of many dubious mathematical situations characteristic to the standard treatment of quantum fields. Proposed formalism offers adequate theoretical framework for proper description of the multicomponent fields, including quantum gravity.
  arXiv  Detail & Related papers  (2022-09-09T07:37:27Z)
• Unification of Mixed Hilbert-Space Representations in Condensed Matter Physics and Quantum Field Theory [0.0]
  We present a unification of mixed-space quantum representations in Condensed Matter Physics (CMP) and Quantum Field Theory (QFT) The unifying formalism is based on being able to expand any quantum operator, for bosons, fermions, and spin systems.
  arXiv  Detail & Related papers  (2022-04-16T00:59:34Z)
• From Quantum Field Theory to Quantum Mechanics [0.0]
  We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles. We provide the explicit relation between the position and momentum operators acting in the former spaces and the field operators acting on the latter. It may not be possible to extend the procedure to interacting field theories since it relies crucially on particle number conservation.
  arXiv  Detail & Related papers  (2021-07-25T04:49:54Z)
• Perturbation Theory for Quantum Information [1.2792576041526287]
  We develop theories for two classes of quantum state perturbations, perturbations that preserve the vector support of the original state and perturbations that extend the support beyond the original state. We apply our perturbation theories to find simple expressions for four of the most important quantities in quantum information theory.
  arXiv  Detail & Related papers  (2021-06-10T06:49:41Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)

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.