Holomorphic representation of quantum computations
- URL: http://arxiv.org/abs/2111.00117v3
- Date: Wed, 5 Oct 2022 12:00:44 GMT
- Title: Holomorphic representation of quantum computations
- Authors: Ulysse Chabaud and Saeed Mehraban
- Abstract summary: We study bosonic quantum computations using the Segal-Bargmann representation of quantum states.
We argue that this holomorphic representation is a natural one which gives a canonical description of bosonic quantum computing.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study bosonic quantum computations using the Segal-Bargmann representation
of quantum states. We argue that this holomorphic representation is a natural
one which not only gives a canonical description of bosonic quantum computing
using basic elements of complex analysis but also provides a unifying picture
which delineates the boundary between discrete- and continuous-variable quantum
information theory. Using this representation, we show that the evolution of a
single bosonic mode under a Gaussian Hamiltonian can be described as an
integrable dynamical system of classical Calogero-Moser particles corresponding
to the zeros of the holomorphic function, together with a conformal evolution
of Gaussian parameters. We explain that the Calogero-Moser dynamics is due to
unique features of bosonic Hilbert spaces such as squeezing. We then generalize
the properties of this holomorphic representation to the multimode case,
deriving a non-Gaussian hierarchy of quantum states and relating entanglement
to factorization properties of holomorphic functions. Finally, we apply this
formalism to discrete- and continuous- variable quantum measurements and obtain
a classification of subuniversal models that are generalizations of Boson
Sampling and Gaussian quantum computing.
Related papers
- 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) - Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices [44.99833362998488]
We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice.
This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation.
arXiv Detail & Related papers (2024-06-25T18:13:38Z) - On reconstruction of states from evolution induced by quantum dynamical
semigroups perturbed by covariant measures [50.24983453990065]
We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures.
Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
arXiv Detail & Related papers (2023-12-02T09:56:00Z) - Matter relative to quantum hypersurfaces [44.99833362998488]
We extend the Page-Wootters formalism to quantum field theory.
By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
arXiv Detail & Related papers (2023-08-24T16:39:00Z) - Classical stochastic representation of quantum mechanics [0.0]
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion.
The probabilistic character of quantum mechanics is devised by treating the wave function as a variable.
arXiv Detail & Related papers (2023-07-31T21:02:43Z) - Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann
Representation of Quantum States [0.0]
We propose a new approach to quantum states in Fock space in terms of classical hydrodynamics.
By conformal mapping of complex analytic function, representing the wave function of quantum states in Fock-Bargmann representation, we define the complex potential.
arXiv Detail & Related papers (2023-07-08T17:51:00Z) - The wave operator representation of quantum and classical dynamics [0.0]
We study the little-known wave operator representation of quantum dynamics.
We find it leads to novel semiclassical approximations of both real and imaginary time dynamics.
We argue that the wave operator provides a new perspective that links previously unrelated representations.
arXiv Detail & Related papers (2023-02-26T02:21:31Z) - 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) - Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders.
All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection.
This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z) - Particle on the sphere: group-theoretic quantization in the presence of
a magnetic monopole [0.0]
We consider the problem of quantizing a particle on a 2-sphere.
We construct the Hilbert space directly from the symmetry algebra.
We show how the Casimir invariants of the algebra determine the bundle topology.
arXiv Detail & Related papers (2020-11-10T04:42:08Z) - Coherent representation of fields and deformation quantization [0.0]
We explicitly consider the holomorphic representation for a scalar field within the deformation quantization program.
Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution.
arXiv Detail & Related papers (2020-05-28T22:41:26Z)
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.