diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index dfe64e7..0f62642 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-04-15T21:53:48","documenter_version":"1.3.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-04-15T21:54:15","documenter_version":"1.3.0"}} \ No newline at end of file diff --git a/dev/guide/index.html b/dev/guide/index.html index 3ea1b26..62ac87c 100644 --- a/dev/guide/index.html +++ b/dev/guide/index.html @@ -12,4 +12,4 @@ @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 4042219..0121c91 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

Spin Shuttling Models

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.

Arguments

  • T::Real: Maximum time
  • L::Real: Length of the path
  • N::Int: Time discretization
  • B::GaussianRandomField: Noise field
  • v::Real: Velocity of the shuttling
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

Fidelity Metric

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.W — 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

Stochastics

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. Can be used to generate a time series on a given time array subject to a Gaussian random process traced from a Gaussian random field.

Arguments

  • μ::Vector{<:Real}: mean of the process
  • P::Array{<:Real}: time-position array
  • Σ::Symmetric{<:Real}: covariance matrices
  • C::Cholesky: cholesky decomposition of the covariance matrices
source
SpinShuttling.CompositeRandomFunction — Function

Create a new random function composed by a linear combination of random processes. The input random function represents the direct sum of these processes. The output random function is a tensor contraction from the input.

source
SpinShuttling.characteristicvalue — Function

Compute the final phase of the characteristic functional of the process from the numerical quadrature of the covariance matrix. Using Simpson's rule by default.

source
SpinShuttling.covariancematrix — Function

Covariance matrix of a Gaussian random field. When P₁=P₂, it is the auto-covariance matrix of a Gaussian random process. When P₁!=P₂, it is the cross-covariance matrix between two Gaussian random processes.

Arguments

  • P₁::Matrix{<:Real}: time-position array
  • P₂::Matrix{<:Real}: time-position array
  • process::GaussianRandomField: a Gaussian random field
source

Auto-Covariance matrix of a Gaussian random process.

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

source
SpinShuttling.averagefidelity — Function

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

source
SpinShuttling.W — 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

Stochastics

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. Can be used to generate a time series on a given time array subject to a Gaussian random process traced from a Gaussian random field.

Arguments

  • μ::Vector{<:Real}: mean of the process
  • P::Array{<:Real}: time-position array
  • Σ::Symmetric{<:Real}: covariance matrices
  • C::Cholesky: cholesky decomposition of the covariance matrices
source
SpinShuttling.CompositeRandomFunction — Function

Create a new random function composed by a linear combination of random processes. The input random function represents the direct sum of these processes. The output random function is a tensor contraction from the input.

source
SpinShuttling.characteristicfunction — Function

Compute the characteristic functional of the process from the numerical quadrature of the covariance matrix. Using Simpson's rule by default.

source
SpinShuttling.characteristicvalue — Function

Compute the final phase of the characteristic functional of the process from the numerical quadrature of the covariance matrix. Using Simpson's rule by default.

source
SpinShuttling.covariancematrix — Function

Covariance matrix of a Gaussian random field. When P₁=P₂, it is the auto-covariance matrix of a Gaussian random process. When P₁!=P₂, it is the cross-covariance matrix between two Gaussian random processes.

Arguments

  • P₁::Matrix{<:Real}: time-position array
  • P₂::Matrix{<:Real}: time-position array
  • process::GaussianRandomField: a Gaussian random field
source

Auto-Covariance matrix of a Gaussian random process.

source
SpinShuttling.covariance — Function

Covariance function of Ornstein-Uhlenbeck process.

source

Covariance function of Pink-Brownian process.

source