Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2409.11020

Quantum simulation of wave optics in weakly inhomogeneous media using block-encoding

Siavash Davani, Gärttner, Martin, Falk X. Eilenberger

Published Sep 17, 2024• 0 citations
arXivHTMLPDF

Abstract

We propose a quantum algorithm that simulates the propagation of a light field through a weakly inhomogeneous medium. In the paraxial approximation, the wave equation in an inhomogeneous material takes the form of the Schrödinger equation with a time-dependent Hamiltonian. This reduction is used to simulate wave optical dynamics on a quantum computer. Beam propagator operators for a short propagation distance are constructed using an efficient and flexible block-encoding that enables the simulation of various optical setups. The algorithm is showcased by simulating the propagation of a one-dimensional Gaussian beam through a lens of finite thickness, and the resulting spherical aberration is demonstrated.

DOI
10.48550/arxiv.2409.11020

Related papers

Quantum signal processing for simulating cold plasma waves

I. Novikau, Edward A. Startsev, I. Y. Dodin

Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future. Here, we propose how to do such modeling for cold plasma waves, in particular, for an X wave propagating in an inhomogeneous one-dimensional plasma. The wave system is represented in the form of a vector Schr\"odinger equation with a Hermitian Hamiltonian. Block encoding is used to represent the Hamiltonian through unitary operations that can be implemented on a quantum computer. To perform the modeling, we apply the so-called quantum signal processing algorithm and construct the corresponding circuit. Quantum simulations with this circuit are emulated on a classical computer, and the results show agreement with traditional classical calculations. We also discuss how our quantum circuit scales with the resolution.

arXiv:2112.06086•Physical Review A•Jun 24, 2022•18 citations

Numerical simulations of an atomic beam focused by an optical potential

T. Kidan, Joan Adler, A. Ron

We present a model to describe the behavior of an atomic beam in a focusing experiment and discuss its implementation. Such modeling is relevant to the development of atom lithography. For simplicity, the light-atom interaction may be treated as a conserving potential (neglecting spontaneous emission) so that the Schrödinger equation is sufficient for a description of the problem. We start from a two-dimensional time-dependent Schrödinger equation that is reduced to a one-dimensional equation by a paraxial approximation, and then solved iteratively via Padé approximation. The solution is implemented in an interactive routine with Matlab(5.x) to compute and visualize the atomic wave packet development as it propagates through the laser light optical potential. We present examples of our implementation, starting with cases that have known analytic solutions such as propagation of the atomic wave packet through free space and through a parabolic potential. We also present a case that does not have a simple analytic solution, namely the propagation of the atomic wave packet through a focusing optical potential, which has a Gaussian profile in the propagation direction and a parabolic profile in the perpendicular direction. © 1998 American Institute of Physics.

Computers in Physics•Sep 1, 1998•4 citations

Beam propagation in a thick lens using the quantum mechanics formulism

G Héctor Lorduy, L. Castellanos, Ángel Salazar +2 more

This paper has to do with the introduction of an algebraic operator method suitable for applications in a wide area of optics. The algebraic structure of this method allows us to derive results usually obtained by using the method of rays in classical optics. Here, we treat the propagation of electromagnetic waves in the framework of paraxial approach, where the paraxial wave equation is viewed as the Schrödinger's wave equation of quantum theory. The time variable of the Schrödinger's equation plays the role of a coordinate along the propagation axis. From this point of view, a formal analogy among the wave optics and quantum mechanics is constructed. In this work, the impulse response function (IRF) for a thick lens is obtained, and from this, the well known corresponding matrix transformation in classical optics is deduced.

AIP conference proceedings•Jan 1, 2008•0 citations

Efficient light propagation algorithm using quantum computers

Chanaprom Cholsuk, Siavash Davani, Lorcán O. Conlon +2 more

Abstract Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires O ( NlogN ) computation steps, where N is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with O logN 2 single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.

arXiv:2303.07032•Physica Scripta•Feb 26, 2024•3 citations

Optical realization of quantum Kerr medium dynamics

Francisco Soto, Victor M. Arrizon, Arturo Zúñiga-Segundo +1 more

We use the propagation of a conveniently shaped Gaussian beam in a GRIN media to mimic a quantum cavity filled with a Kerr medium. This is attained by introducing a second-order correction to the paraxial propagation of the beam. An additional result is that a Gaussian beam propagating in GRIN media may split into two Gaussian beams, corresponding to the generation of superposition of coherent states (Schrödinger cat states) in the cavity filled with the Kerr medium.

arXiv:1406.2959•Optics Letters•Oct 17, 2014•12 citations

Paraxial light and atom optics: The optical Schrödinger equation and beyond

Monika A. M. Marte, Stig Stenholm

Paraxial light and atom optics are compared. To lowest order the slowly varying amplitude of a light field in a dielectric medium with a spatially dependent refractive index satisfies an equation which has the form of a Schr\"odinger equation: the ``optical Schr\"odinger equation.'' The unsystematic procedure of neglecting certain second-order derivatives is replaced by a systematic expansion which allows the calculation of consecutive corrections. The general theory is applied to harmonic motion in a graded index fiber and to tunneling between coupled fibers. The physical relations between wave evolution of massive particles and paraxially propagating waves are elucidated.

Physical Review A•Oct 1, 1997•74 citations
We propose a quantum algorithm that simulates the propagation of a light field through a weakly inhomogeneous medium. In the paraxial approximation, the wave equation in an inhomogeneous material takes the form of the Schrödinger equation with a time-dependent Hamiltonian. This reduction is used to simulate wave optical dynamics on a quantum computer. Beam propagator operators for a short propagation distance are constructed using an efficient and flexible block-encoding that enables the simulation of various optical setups. The algorithm is showcased by simulating the propagation of a one-dimensional Gaussian beam through a lens of finite thickness, and the resulting spherical aberration is demonstrated.
Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future. Here, we propose how to do such modeling for cold plasma waves, in particular, for an X wave propagating in an inhomogeneous one-dimensional plasma. The wave system is represented in the form of a vector Schr\"odinger equation with a Hermitian Hamiltonian. Block encoding is used to represent the Hamiltonian through unitary operations that can be implemented on a quantum computer. To perform the modeling, we apply the so-called quantum signal processing algorithm and construct the corresponding circuit. Quantum simulations with this circuit are emulated on a classical computer, and the results show agreement with traditional classical calculations. We also discuss how our quantum circuit scales with the resolution.
We present a model to describe the behavior of an atomic beam in a focusing experiment and discuss its implementation. Such modeling is relevant to the development of atom lithography. For simplicity, the light-atom interaction may be treated as a conserving potential (neglecting spontaneous emission) so that the Schrödinger equation is sufficient for a description of the problem. We start from a two-dimensional time-dependent Schrödinger equation that is reduced to a one-dimensional equation by a paraxial approximation, and then solved iteratively via Padé approximation. The solution is implemented in an interactive routine with Matlab(5.x) to compute and visualize the atomic wave packet development as it propagates through the laser light optical potential. We present examples of our implementation, starting with cases that have known analytic solutions such as propagation of the atomic wave packet through free space and through a parabolic potential. We also present a case that does not have a simple analytic solution, namely the propagation of the atomic wave packet through a focusing optical potential, which has a Gaussian profile in the propagation direction and a parabolic profile in the perpendicular direction. © 1998 American Institute of Physics.
This paper has to do with the introduction of an algebraic operator method suitable for applications in a wide area of optics. The algebraic structure of this method allows us to derive results usually obtained by using the method of rays in classical optics. Here, we treat the propagation of electromagnetic waves in the framework of paraxial approach, where the paraxial wave equation is viewed as the Schrödinger's wave equation of quantum theory. The time variable of the Schrödinger's equation plays the role of a coordinate along the propagation axis. From this point of view, a formal analogy among the wave optics and quantum mechanics is constructed. In this work, the impulse response function (IRF) for a thick lens is obtained, and from this, the well known corresponding matrix transformation in classical optics is deduced.
Abstract Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires O ( NlogN ) computation steps, where N is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with O logN 2 single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.
Paraxial light and atom optics are compared. To lowest order the slowly varying amplitude of a light field in a dielectric medium with a spatially dependent refractive index satisfies an equation which has the form of a Schr\"odinger equation: the ``optical Schr\"odinger equation.'' The unsystematic procedure of neglecting certain second-order derivatives is replaced by a systematic expansion which allows the calculation of consecutive corrections. The general theory is applied to harmonic motion in a graded index fiber and to tunneling between coupled fibers. The physical relations between wave evolution of massive particles and paraxially propagating waves are elucidated.