From e7120c86c73d48658b87a42c9b288480dbc8ca1d Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Fri, 8 Mar 2024 09:31:36 +0000 Subject: [PATCH] build based on aac1c5b --- dev/.documenter-siteinfo.json | 2 +- dev/guide/index.html | 2 +- dev/index.html | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 30d50e4..ca96bd1 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-03-08T09:30:59","documenter_version":"1.3.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-03-08T09:31:30","documenter_version":"1.3.0"}} \ No newline at end of file diff --git a/dev/guide/index.html b/dev/guide/index.html index 266cfee..70e40a4 100644 --- a/dev/guide/index.html +++ b/dev/guide/index.html @@ -10,4 +10,4 @@ @assert isapprox(f2, f3, rtol=1e-2) println("NI:", f1) println("MC:", f2) -println("TH:", f3)

Shuttling of entangled spin pairs.

+println("TH:", f3)

Shuttling of entangled spin pairs.

diff --git a/dev/index.html b/dev/index.html index 5cd92b1..0b72910 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,3 +1,3 @@ Home · SpinShuttling.jl
GitHub

SpinShuttling.jl

Simulate the multiple-spin shuttling problem under correlated stochastic noise.

Installation

SpinShuttling can be installed using the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run

pkg> add SpinShuttling

APIs

SpinShuttling.OneSpinModel — Function

General one spin shuttling model initialized at initial state |Ψ₀⟩, with arbitrary shuttling path x(t).

Arguments

  • Ψ::Vector{<:Number}: Initial state of the spin system, the length of the vector must be `2^n
  • T::Real: Maximum time
  • N::Int: Time discretization
  • B::GaussianRandomField: Noise field
  • x::Function: Shuttling path
source

One spin shuttling model initialzied at |Ψ₀⟩=|+⟩. The qubit is shuttled at constant velocity along the path x(t)=L/T*t, with total time T in μs and length L in μm.

source
SpinShuttling.OneSpinForthBackModel — Function

One spin shuttling model initialzied at |Ψ₀⟩=|+⟩. The qubit is shuttled at constant velocity along a forth-back path x(t, T, L) = t<T/2 ? 2L/T*t : 2L/T*(T-t), with total time T in μs and length L in μm.

source
SpinShuttling.TwoSpinModel — Function

General two spin shuttling model initialized at initial state |Ψ₀⟩, with arbitrary shuttling paths x₁(t), x₂(t).

Arguments

  • Ψ::Vector{<:Number}: Initial state of the spin system, the length of the vector must be `2^n
  • T::Real: Maximum time
  • N::Int: Time discretization
  • B::GaussianRandomField: Noise field
  • x₁::Function: Shuttling path for the first spin
  • x₂::Function: Shuttling path for the second spin
source

Two spin shuttling model initialized at the singlet state |Ψ₀⟩=1/√2(|↑↓⟩-|↓↑⟩). The qubits are shuttled at constant velocity along the path x₁(t)=L/T₁*t and x₂(t)=L/T₁*(t-T₀). The delay between the them is T₀ and the total shuttling time is T₁+T₀. It should be noticed that due to the exclusion of fermions, x₁(t) and x₂(t) cannot overlap.

source
SpinShuttling.TwoSpinParallelModel — Function

Two spin shuttling model initialized at the singlet state |Ψ₀⟩=1/√2(|↑↓⟩-|↓↑⟩). The qubits are shuttled at constant velocity along the 2D path x₁(t)=L/T*t, y₁(t)=0 and x₂(t)=L/T*t, y₂(t)=D. The total shuttling time is T and the length of the path is L in μm.

source
SpinShuttling.fidelity — Function

Sample a phase integral of the process. The integrate of a random function should be obtained from directly summation without using high-order interpolation (Simpson or trapezoid).

source
SpinShuttling.sampling — Function

Monte-Carlo sampling of any objective function. The function must return Tuple{Real,Real} or Tuple{Vector{<:Real},Vector{<:Real}}

Arguments

  • samplingfunction::Function: The function to be sampled
  • M::Int: Monte-Carlo sampling size

Returns

  • Tuple{Real,Real}: The mean and variance of the sampled function
  • Tuple{Vector{<:Real},Vector{<:Real}}: The mean and variance of the sampled function

Example

f(x) = x^2
-sampling(f, 1000)

Reference

https://en.wikipedia.org/wiki/Standarddeviation#Rapidcalculation_methods

source

Sampling an observable that defines on a specific spin shuttling model

Arguments

  • model::ShuttlingModel: The spin shuttling model
  • objective::Function: The objective function objective(mode::ShuttlingModel; randseq)`
  • M::Int: Monte-Carlo sampling size
source
SpinShuttling.PinkBrownianField — Type

Pink-Brownian Field, the correlation function of which is σ^2 * (expinti(-γ[2]abs(t₁ - t₂)) - expinti(-γ[1]abs(t₁ - t₂)))/log(γ[2]/γ[1]) * exp(-|x₁-x₂|/θ) where expinti is the exponential integral function.

source
SpinShuttling.RandomFunction — Type

Similar type of RandomFunction in Mathematica. Generate a time series on a given time array subject to a Gaussian random process traced from a Gaussian random field.

source
SpinShuttling.φ — Function

Analytical average fidelity of a one-spin shuttling model.

source

Analytical average fidelity of a sequenced two-spin EPR pair shuttling model.

source

Theoretical fidelity of a one-spin shuttling model for a pink-brownian noise.

source
+sampling(f, 1000)

Reference

https://en.wikipedia.org/wiki/Standarddeviation#Rapidcalculation_methods

source

Sampling an observable that defines on a specific spin shuttling model

Arguments

  • model::ShuttlingModel: The spin shuttling model
  • objective::Function: The objective function objective(mode::ShuttlingModel; randseq)`
  • M::Int: Monte-Carlo sampling size
source
SpinShuttling.averagefidelity — Function

Calculate the average fidelity of a spin shuttling model using numerical integration of the covariance matrix.

source
SpinShuttling.OrnsteinUhlenbeckField — Type

Ornstein-Uhlenbeck field, the correlation function of which is σ^2 * exp(-|t₁ - t₂|/θ_t) * exp(-|x₁-x₂|/θ_x) where t is time and x is position.

source
SpinShuttling.PinkBrownianField — Type

Pink-Brownian Field, the correlation function of which is σ^2 * (expinti(-γ[2]abs(t₁ - t₂)) - expinti(-γ[1]abs(t₁ - t₂)))/log(γ[2]/γ[1]) * exp(-|x₁-x₂|/θ) where expinti is the exponential integral function.

source
SpinShuttling.RandomFunction — Type

Similar type of RandomFunction in Mathematica. Generate a time series on a given time array subject to a Gaussian random process traced from a Gaussian random field.

source
SpinShuttling.φ — Function

Analytical average fidelity of a one-spin shuttling model.

source

Analytical average fidelity of a sequenced two-spin EPR pair shuttling model.

source

Theoretical fidelity of a one-spin shuttling model for a pink-brownian noise.

source