Numerical solution of stochastic quantum master equations using stochastic interacting wave functions

Mora, Carlos M.; Fernández, Jacqueline; Biscay, Rolando J.

doi:10.1016/j.jcp.2018.03.045

Cited by 4 publications

(1 citation statement)

References 52 publications

(121 reference statements)

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“…This paper deals with the computation of the mean value of X t j ( ), when j is smooth. We focus on the following Euler-Exponential scheme developed by [4,11] that solves accurately (1) with low computational cost (see, e.g., [2,7,11,12] for alternative schemes).…”

Section: Introductionmentioning

confidence: 99%

On the rate of convergence of an exponential scheme for the non-linear stochastic Schrödinger equation with finite-dimensional state space

Mora

Muñoz

2023

Phys. Scr.

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We address the numerical solution of the finite-dimensional non-linear stochastic Schrödinger equation, which is a locally Lipschitz stochastic differential equation modeling, for instance, quantum measurement processes. We study the rate of weak convergence of an exponential scheme that reproduces the norm of the desired solution by projecting onto the unit sphere. This justifies the use of the Talay-Tubaro extrapolation procedure in the numerical simulation of open quantum systems. In particular, we prove that an Euler-Exponential scheme converges with weak-order one, and we obtain the leading order term of its weak error expansion with respect to the step-size. Then, applying the Talay-Tubaro extrapolation procedure to the Euler-Exponential scheme under consideration we get a second-order method for computing the mean values of smooth functions of the solution of the non-linear stochastic Schrödinger equation. We also prove that the exponential scheme under study has order of strong convergence 1/2, which gives theoretical support to the use of the multilevel Monte Carlo method in simulating open quantum systems. We present a numerical experiment with a quantized electromagnetic field in interaction with a reservoir that illustrates the good performance of the weak second-order method, and the multilevel Monte Carlo method.

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Section: Introductionmentioning

confidence: 99%

On the rate of convergence of an exponential scheme for the non-linear stochastic Schrödinger equation with finite-dimensional state space

Mora

Muñoz

2023

Phys. Scr.

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Simulating Open Quantum Systems Using Hamiltonian Simulations

Ding,

Li,

Lin

2024

PRX Quantum

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We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order. Published by the American Physical Society 2024

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Basic Properties of a Mean Field Laser Equation

Fagnola

Mora

2019

Open Syst. Inf. Dyn.

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We study the non-linear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the non-linear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schröndiger equation. To this end, we find a regular solution for the non-autonomous linear quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form, and we prove the uniqueness of the solution to the non-autonomous linear adjoint quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form. Moreover, we obtain rigorously the Maxwell-Bloch equations from the mean field laser equation.Keywords: Open quantum system, nonlinear quantum master equation, Maxwell-Bloch equations, quantum master equation in the Gorini-Kossakowski-Sudarshan-Lindblad form, existence and uniqueness, regular solution, Ehrenfest-type theorem, stochastic Schrödinger equation.

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Numerical solution of stochastic quantum master equations using stochastic interacting wave functions

Cited by 4 publications

References 52 publications

On the rate of convergence of an exponential scheme for the non-linear stochastic Schrödinger equation with finite-dimensional state space

On the rate of convergence of an exponential scheme for the non-linear stochastic Schrödinger equation with finite-dimensional state space

Simulating Open Quantum Systems Using Hamiltonian Simulations

Basic Properties of a Mean Field Laser Equation

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