Julia
This part contains the methods and structs in Julia that are called by the Python-Julia packagea and the full Julia package.
QuanEstimation.AD — Method.¶
AD(;max_episode=300, epsilon=0.01, beta1=0.90, beta2=0.99, Adam::Bool=true)
Optimization algorithm: AD.
max_episode: The number of episodes.epsilon: Learning rate.beta1: The exponential decay rate for the first moment estimates.beta2: The exponential decay rate for the second moment estimates.Adam: Whether or not to use Adam for updating control coefficients.
QuanEstimation.CFIM_obj — Method.¶
CFIM_obj(;M=missing, W=missing, eps=GLOBAL_EPS)
Choose CFI [\(\mathrm{Tr}(WI^{-1})\)] as the objective function with \(W\) the weight matrix and \(I\) the CFIM.
M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).W: Weight matrix.eps: Machine epsilon.
QuanEstimation.CMopt — Type.¶
CMopt(ctrl=missing, M=missing, ctrl_bound=[-Inf, Inf], seed=1234)
Control and measurement optimization.
ctrl: Guessed control coefficients.M: Guessed projective measurement (a set of basis)ctrl_bound: Lower and upper bounds of the control coefficients.seed: Random seed.
QuanEstimation.ControlOpt — Method.¶
ControlOpt(ctrl=missing, ctrl_bound=[-Inf, Inf], seed=1234)
Control optimization.
ctrl: Guessed control coefficients.ctrl_bound: Lower and upper bounds of the control coefficients.seed: Random seed.
<!-- ## QuanEstimation.DDPG — Method.
DDPG(;max_episode::Int=500, layer_num::Int=3, layer_dim::Int=200, seed::Number=1234)
``` -->
Optimization algorithm: DE.
* `max_episode`: The number of populations.
* `layer_num`: The number of layers (include the input and output layer).
* `layer_dim`: The number of neurons in the hidden layer.
* `seed`: Random seed.
<a target='_blank' href='https://github.com/QuanEstimation/QuanEstimation.jl/blob/5f47a686c13b059023de2abe67017d7c9564bc9d/src/Algorithm/Algorithm.jl#L146-L155' class='documenter-source'>source</a><br>
## **`QuanEstimation.DE`** — *Method*.
```julia
DE(;max_episode::Number=1000, p_num::Number=10, ini_population=missing, c::Number=1.0, cr::Number=0.5, seed::Number=1234)
Optimization algorithm: DE.
max_episode: The number of populations.p_num: The number of particles.ini_population: Initial guesses of the optimization variables.c: Mutation constant.cr: Crossover constant.
QuanEstimation.GRAPE — Method.¶
GRAPE(;max_episode=300, epsilon=0.01, beta1=0.90, beta2=0.99, Adam::Bool=true)
Control optimization algorithm: GRAPE.
max_episode: The number of episodes.epsilon: Learning rate.beta1: The exponential decay rate for the first moment estimates.beta2: The exponential decay rate for the second moment estimates.Adam: Whether or not to use Adam for updating control coefficients.
QuanEstimation.HCRB_obj — Method.¶
HCRB_obj(;W=missing, eps=GLOBAL_EPS)
Choose HCRB as the objective function.
W: Weight matrix.eps: Machine epsilon.
sourceLD operator. Options can be: "original" (default) and "eigen".
* eps: Machine epsilon.
QuanEstimation.Kraus — Method.¶
Kraus(ρ0::AbstractMatrix, K::AbstractVector, dK::AbstractVector)
The parameterization of a state is \(\rho=\sum_i K_i\rho_0K_i^{\dagger}\) with \(\rho\) the evolved density matrix and \(K_i\) the Kraus operator.
ρ0: Initial state (density matrix).K: Kraus operators.dK: Derivatives of the Kraus operators with respect to the unknown parameters to be estimated. For example, dK[0] is the derivative vector on the first parameter.
QuanEstimation.Kraus — Method.¶
Kraus(ψ0::AbstractMatrix, K::AbstractVector, dK::AbstractVector)
The parameterization of a state is \(\psi\rangle=\sum_i K_i|\psi_0\rangle\) with \(\psi\) the evolved state and \(K_i\) the Kraus operator.
ψ0: Initial state (ket).K: Kraus operators.dK: Derivatives of the Kraus operators with respect to the unknown parameters to be estimated. For example, dK[0] is the derivative vector on the first parameter.
QuanEstimation.Kraus — Method.¶
Kraus(opt::AbstractMopt, ρ₀::AbstractMatrix, K, dK; eps=GLOBAL_EPS)
Initialize the parameterization described by the Kraus operators for the measurement optimization.
QuanEstimation.Kraus — Method.¶
Kraus(opt::CompOpt, K, dK; eps=GLOBAL_EPS)
Initialize the parameterization described by the Kraus operators for the comprehensive optimization.
QuanEstimation.LLD — Method.¶
LLD(ρ::Matrix{T}, dρ::Vector{Matrix{T}}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
Calculate the left logarrithmic derivatives (LLDs). The LLD operator is defined as \(\partial_{a}\rho=\mathcal{R}_a^{\dagger}\rho\), where ρ is the parameterized density matrix.
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.rep: Representation of the LLD operator. Options can be: "original" (default) and "eigen".eps: Machine epsilon.
QuanEstimation.LLD — Method.¶
LLD(ρ::Matrix{T}, dρ::Matrix{T}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
When applied to the case of single parameter.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::AbstractMopt, tspan, ρ₀, H0, dH; Hc=missing, ctrl=missing, decay=missing, dyn_method=:Expm, eps=GLOBAL_EPS)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the measurement optimization.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::ControlMeasurementOpt, tspan, ρ₀, H0, dH, Hc; decay=missing, dyn_method=:Expm, eps=GLOBAL_EPS)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the comprehensive optimization on control and measurement.
sourcenstant.
* ae: Expansion constant.
* ac: Constraction constant.
* as0: Shrink constant.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::ControlOpt, tspan, ρ₀, H0, dH, Hc; decay=missing, dyn_method=:Expm, eps=GLOBAL_EPS)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the control optimization.
sourceuanEstimation.PSO` — Method.
PSO(;max_episode::Union{T,Vector{T}} where {T<:Int}=[1000, 100], p_num::Number=10, ini_particle=missing, c0::Number=1.0, c1::Number=2.0, c2::Number=2.0, seed::Number=1234)
Optimization algorithm: PSO.
max_episode: The number of episodes, it accepts both integer and array with two elements.p_num: The number of particles.ini_particle: Initial guesses of the optimization variables.c0: The damping factor that assists convergence, also known as inertia weight.c1: The exploitation weight that attracts the particle to its best previous position, also known as cognitive learning factor.c2: The exploitation weight that attracts the particle to the best position in the neighborhood, also known as social learning factor.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::StateControlMeasurementOpt, tspan, H0, dH, Hc; decay=missing, dyn_method=:Expm, eps=GLOBAL_EPS)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the comprehensive optimization on state, control and measurement.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::StateControlOpt, tspan, H0, dH, Hc; decay=missing, dyn_method=:Expm, eps=GLOBAL_EPS)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the comprehensive optimization on state and control.
sourcee set as the objective function. Options are :SLD (default), :RLD and :LLD.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::StateMeasurementOpt, tspan, H0, dH; Hc=missing, ctrl=missing, decay=missing, dyn_method=:Expm)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the comprehensive optimization on state and measurement.
QuanEstimation.Lindblad — Method.¶
Lindblad(opt::StateOpt, tspan, H0, dH; Hc=missing, ctrl=missing, decay=missing, dyn_method=:Expm, eps=GLOBAL_EPS)
Initialize the parameterization described by the Lindblad master equation governed dynamics for the state optimization.
sourceuanEstimation.RLD` — Method.
RLD(ρ::Matrix{T}, dρ::Vector{Matrix{T}}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
Calculate the right logarrithmic derivatives (RLDs). The RLD operator is defined as \(\partial_{a}\rho=\rho \mathcal{R}_a\), where \(\rho\) is the parameterized density matrix.
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.rep: Representation of the RLD operator. Options can be: "original" (default) and "eigen".eps: Machine epsilon.
QuanEstimation.NM — Method.¶
NM(;max_episode::Int=1000, p_num::Int=10, nelder_mead=missing, ar::Number=1.0, ae::Number=2.0, ac::Number=0.5, as0::Number=0.5, seed::Number=1234)
State optimization algorithm: NM.
max_episode: The number of populations.p_num: The number of the input states.nelder_mead: Initial guesses of the optimization variables.ar: Reflection constant.ae: Expansion constant.ac: Constraction constant.as0: Shrink constant.
QuanEstimation.PSO — Method.¶
PSO(;max_episode::Union{T,Vector{T}} where {T<:Int}=[1000, 100], p_num::Number=10, ini_particle=missing, c0::Number=1.0, c1::Number=2.0, c2::Number=2.0, seed::Number=1234)
Optimization algorithm: PSO.
max_episode: The number of episodes, it accepts both integer and array with two elements.p_num: The number of particles.ini_particle: Initial guesses of the optimization variables.c0: The damping factor that assists convergence, also known as inertia weight.c1: The exploitation weight that attracts the particle to its best previous position, also known as cognitive learning factor.c2: The exploitation weight that attracts the particle to the best position in the neighborhood, also known as social learning factor.
sourced: Lower and upper bounds of the control coefficients.
*seed`: Random seed.
QuanEstimation.QFIM_obj — Method.¶
QFIM_obj(;W=missing, eps=GLOBAL_EPS, LDtype::Symbol=:SLD)
Choose QFI [\(\mathrm{Tr}(WF^{-1})\)] as the objective function with \(W\) the weight matrix and \(F\) the QFIM.
W: Weight matrix.eps: Machine epsilon.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are:SLD(default),:RLDand:LLD.
QuanEstimation.RI — Method.¶
RI(;max_episode::Int=300, seed::Number=1234)
State optimization algorithm: RI.
max_episode: The number of episodes.
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.rep: Representation of the SLD operator. Options can be: "original" (default) and "eigen" .eps: Machine epsilon.
QuanEstimation.RLD — Method.¶
RLD(ρ::Matrix{T}, dρ::Vector{Matrix{T}}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
Calculate the right logarrithmic derivatives (RLDs). The RLD operator is defined as \(\partial_{a}\rho=\rho \mathcal{R}_a\), where \(\rho\) is the parameterized density matrix.
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.rep: Representation of the RLD operator. Options can be: "original" (default) and "eigen".eps: Machine epsilon.
sourcetoticBound/CramerRao.jl#L22-L27' class='documenter-source'>
QuanEstimation.RLD — Method.¶
RLD(ρ::Matrix{T}, dρ::Matrix{T}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
When applied to the case of single parameter.
QuanEstimation.SCMopt — Type.¶
SCMopt(psi=missing, ctrl=missing, M=missing, ctrl_bound=[-Inf, Inf], seed=1234)
State, control and measurement optimization.
psi: Guessed probe state.ctrl: Guessed control coefficients.M: Guessed projective measurement (a set of basis).ctrl_bound: Lower and upper bounds of the control coefficients.seed: Random seed.
source2abe67017d7c9564bc9d/src/OptScenario/OptScenario.jl#L35-L42' class='documenter-source'>
QuanEstimation.SCopt — Type.¶
SCopt(psi=missing, ctrl=missing, ctrl_bound=[-Inf, Inf], seed=1234)
State and control optimization.
psi: Guessed probe state.ctrl: Guessed control coefficients.ctrl_bound: Lower and upper bounds of the control coefficients.seed: Random seed.
QuanEstimation.SLD — Method.¶
SLD(ρ::Matrix{T}, dρ::Vector{Matrix{T}}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
Calculate the symmetric logarrithmic derivatives (SLDs). The SLD operator \(L_a\) is defined as\(\partial_{a}\rho=\frac{1}{2}(\rho L_{a}+L_{a}\rho)\), where \(\rho\) is the parameterized density matrix.
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.rep: Representation of the SLD operator. Options can be: "original" (default) and "eigen" .eps: Machine epsilon.
x: The regimes of the parameters for the integral.p: The prior distribution.rho0: Density matrix.tspan: The experimental results obtained in practice.H: Free Hamiltonian with respect to the values in x.dH: Derivatives of the free Hamiltonian with respect to the unknown parameters to be estimated.dyn_method: Setting the method for solving the Lindblad dynamics. Options are: "expm" and "ode".method: Choose the method for updating the tunable parameters (u). Options are: "FOP" and "MI".savefile: Whether or not to save all the posterior distributions.max_episode: The number of episodes.eps: Machine epsilon.Hc: Control Hamiltonians.ctrl: Control coefficients.decay: Decay operators and the corresponding decay rates.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).W: Whether or not to save all the posterior distributions.
QuanEstimation.SLD — Method.¶
SLD(ρ::Matrix{T}, dρ::Matrix{T}; rep="original", eps=GLOBAL_EPS) where {T<:Complex}
When applied to the case of single parameter.
QuanEstimation.SMopt — Type.¶
SMopt(psi=missing, M=missing, seed=1234)
State and control optimization.
psi: Guessed probe state.M: Guessed projective measurement (a set of basis).seed: Random seed.
x: The regimes of the parameters for the integral.p: The prior distribution.rho0: Density matrix.K: Kraus operator(s) with respect to the values in x.dK: Derivatives of the Kraus operator(s) with respect to the unknown parameters to be estimated.method: Choose the method for updating the tunable parameters (u). Options are: "FOP" and "MI".savefile: Whether or not to save all the posterior distributions.max_episode: The number of episodes.eps: Machine epsilon.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).W: Whether or not to save all the posterior distributions.
QuanEstimation.StateOpt — Method.¶
StateOpt(psi=missing, seed=1234)
State optimization.
psi: Guessed probe state.seed: Random seed.
sourceether or not to save all the posterior distributions.
QuanEstimation.autoGRAPE — Method.¶
autoGRAPE(;max_episode=300, epsilon=0.01, beta1=0.90, beta2=0.99, Adam::Bool=true)
Control optimization algorithm: auto-GRAPE.
max_episode: The number of episodes.epsilon: Learning rate.beta1: The exponential decay rate for the first moment estimates.beta2: The exponential decay rate for the second moment estimates.Adam: Whether or not to use Adam for updating control coefficients.
source9023de2abe67017d7c9564bc9d/src/Common/BayesEstimation.jl#L363-L373' class='documenter-source'>
QuanEstimation.Adapt — Method.¶
Adapt(x::AbstractVector, p, rho0::AbstractMatrix, tspan, H, dH; dyn_method=:Expm, method="FOP", savefile=false, max_episode::Int=1000, eps::Float64=1e-8, Hc=missing, ctrl=missing, decay=missing, M=missing, W=missing)
In QuanEstimation, the Hamiltonian of the adaptive system should be written as \(H(\textbf{x}+\textbf{u})\) with \(\textbf{x}\) the unknown parameters and \(\textbf{u}\) the tunable parameters. The tunable parameters \(\textbf{u}\) are used to let the Hamiltonian work at the optimal point \(\textbf{x}_{\mathrm{opt}}\).
x: The regimes of the parameters for the integral.p: The prior distribution.rho0: Density matrix.tspan: The experimental results obtained in practice.H: Free Hamiltonian with respect to the values in x.dH: Derivatives of the free Hamiltonian with respect to the unknown parameters to be estimated.dyn_method: Setting the method for solving the Lindblad dynamics. Options are: "expm" and "ode".method: Choose the method for updating the tunable parameters (u). Options are: "FOP" and "MI".savefile: Whether or not to save all the posterior distributions.max_episode: The number of episodes.eps: Machine epsilon.Hc: Control Hamiltonians.ctrl: Control coefficients.decay: Decay operators and the corresponding decay rates.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).W: Whether or not to save all the posterior distributions.
QuanEstimation.Adapt — Method.¶
Adapt(x::AbstractVector, p, rho0::AbstractMatrix, K, dK; method="FOP", savefile=false, max_episode::Int=1000, eps::Float64=1e-8, M=missing, W=missing)
In QuanEstimation, the Hamiltonian of the adaptive system should be written as \(H(\textbf{x}+\textbf{u})\) with \(\textbf{x}\) the unknown parameters and \(\textbf{u}\) the tunable parameters. The tunable parameters \(\textbf{u}\) are used to let the Hamiltonian work at the optimal point \(\textbf{x}_{\mathrm{opt}}\).
x: The regimes of the parameters for the integral.p: The prior distribution.rho0: Density matrix.K: Kraus operator(s) with respect to the values in x.dK: Derivatives of the Kraus operator(s) with respect to the unknown parameters to be estimated.method: Choose the method for updating the tunable parameters (u). Options are: "FOP" and "MI".savefile: Whether or not to save all the posterior distributions.max_episode: The number of episodes.eps: Machine epsilon.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).W: Whether or not to save all the posterior distributions.
QuanEstimation.BCB — Method.¶
BCB(x, p, rho; W=missing, eps=GLOBAL_EPS)
Calculation of the minimum Bayesian cost with a quadratic cost function.
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.W: Weight matrix.eps: Machine epsilon.
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are "SLD" (default), "RLD" and "LLD".eps: Machine epsilon.
QuanEstimation.BCFIM — Method.¶
BCFIM(x::AbstractVector, p, rho, drho; M=missing, eps=GLOBAL_EPS)
Calculation of the Bayesian classical Fisher information (BCFI) and the Bayesian classical Fisher information matrix (BCFIM) of the form \(\mathcal{I}_{\mathrm{Bayes}}=\int p(\textbf{x})\mathcal{I}\mathrm{d}\textbf{x}\) with \(\mathcal{I}\) the CFIM and \(p(\textbf{x})\) the prior distribution.
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).eps: Machine epsilon.
sourcers obtained via the maximum a posteriori probability (MAP).
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.y: The experimental results obtained in practice.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).savefile: Whether or not to save all the posterior distributions.
QuanEstimation.BCRB — Method.¶
BCRB(x::AbstractVector, p, dp, rho, drho; M=missing, b=missing, db=missing, btype=1, eps=GLOBAL_EPS)
Calculation of the Bayesian Cramer-Rao bound (BCRB).
x: The regimes of the parameters for the integral.p: The prior distribution.dp: Derivatives of the prior distribution with respect to the unknown parameters to be estimated. For example, dp[0] is the derivative vector on the first parameter.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).b: Vector of biases of the form \(\textbf{b}=(b(x_0),b(x_1),\dots)^{\mathrm{T}}\).db: Derivatives of b on the unknown parameters to be estimated, It should be expressed as \(\textbf{b}'=(\partial_0 b(x_0),\partial_1 b(x_1),\dots)^{\mathrm{T}}\).btype: Types of the BCRB. Options are 1, 2 and 3.eps: Machine epsilon.
sourcearameterized density matrix.
* M: A set of POVM.
* W: Weight matrix.
* eps: Machine epsilon.
QuanEstimation.BQCRB — Method.¶
BQCRB(x::AbstractVector, p, dp, rho, drho; b=missing, db=missing, LDtype=:SLD, btype=1, eps=GLOBAL_EPS)
Calculation of the Bayesian quantum Cramer-Rao bound (BQCRB).
x: The regimes of the parameters for the integral.p: The prior distribution.dp: Derivatives of the prior distribution with respect to the unknown parameters to be estimated. For example, dp[0] is the derivative vector on the first parameter.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.b: Vector of biases of the form \(\textbf{b}=(b(x_0),b(x_1),\dots)^{\mathrm{T}}\).db: Derivatives of b on the unknown parameters to be estimated, It should be expressed as \(\textbf{b}'=(\partial_0 b(x_0),\partial_1 b(x_1),\dots)^{\mathrm{T}}\).LDtype: Types of QFI (QFIM) can be set as the objective function. Options are "SLD" (default), "RLD" and "LLD".btype: Types of the BCRB. Options are 1, 2 and 3.eps: Machine epsilon.
QuanEstimation.BQFIM — Method.¶
BQFIM(x::AbstractVector, p, rho, drho; LDtype=:SLD, eps=GLOBAL_EPS)
Calculation of the Bayesian quantum Fisher information (BQFI) and the Bayesian quantum Fisher information matrix (BQFIM) of the form \(\mathcal{F}_{\mathrm{Bayes}}=\int p(\textbf{x})\mathcal{F}\mathrm{d}\textbf{x}\) with \(\mathcal{F}\) the QFIM of all types and \(p(\textbf{x})\) the prior distribution.
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are "SLD" (default), "RLD" and "LLD".eps: Machine epsilon.
QuanEstimation.Bayes — Method.¶
Bayes(x, p, rho, y; M=missing, savefile=false)
Bayesian estimation. The prior distribution is updated via the posterior distribution obtained by the Bayes' rule and the estimated value of parameters obtained via the maximum a posteriori probability (MAP).
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.y: The experimental results obtained in practice.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).savefile: Whether or not to save all the posterior distributions.
QuanEstimation.BayesCost — Method.¶
BayesCost(x, p, xest, rho, M; W=missing, eps=GLOBAL_EPS)
Calculation of the average Bayesian cost with a quadratic cost function.
x: The regimes of the parameters for the integral.p: The prior distribution.xest: The estimators.rho: Parameterized density matrix.M: A set of POVM.W: Weight matrix.eps: Machine epsilon.
QuanEstimation.CFIM — Method.¶
CFIM(ρ::Matrix{T}, dρ::Vector{Matrix{T}}, M; eps=GLOBAL_EPS) where {T<:Complex}
Calculate the classical Fisher information matrix (CFIM).
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).eps: Machine epsilon.
QuanEstimation.CFIM — Method.¶
CFIM(ρ::Matrix{T}, dρ::Vector{Matrix{T}}; M=nothing, eps=GLOBAL_EPS) where {T<:Complex}
When the set of POVM is not given. Calculate the CFIM with SIC-POVM. The SIC-POVM is generated from the Weyl-Heisenberg covariant SIC-POVM fiducial state which can be downloaded from here.
QuanEstimation.CFIM — Method.¶
CFIM(ρ::Matrix{T}, dρ::Matrix{T}, M; eps=GLOBAL_EPS) where {T<:Complex}
When applied to the case of single parameter. Calculate the classical Fisher information (CFI).
QuanEstimation.CFIM — Method.¶
CFIM(ρ::Matrix{T}, dρ::Matrix{T}; eps=GLOBAL_EPS) where {T<:Complex}
When applied to the case of single parameter and the set of POVM is not given. Calculate the CFI with SIC-POVM.
QuanEstimation.FIM — Method.¶
FIM(p::Vector{R}, dp::Vector{R}; eps=GLOBAL_EPS) where {R<:Real}
Calculation of the classical Fisher information matrix for classical scenarios.
p: The probability distribution.dp: Derivatives of the probability distribution on the unknown parameters to be estimated. For example, dp[0] is the derivative vector on the first parameter.eps: Machine epsilon.
QuanEstimation.FIM — Method.¶
FIM(p::Vector{R}, dp::Vector{R}; eps=GLOBAL_EPS) where {R<:Real}
When applied to the case of single parameter and the set of POVM is not given. Calculate the classical Fisher information for classical scenarios.
sourceuanEstimation.NHB` — Method.
NHB(ρ::AbstractMatrix, dρ::AbstractVector, W::AbstractMatrix)
Nagaoka-Hayashi bound (NHB) via the semidefinite program (SDP).
ρ: Density matrix.dρ: Derivatives of the density matrix on the unknown parameters to be estimated. For example, drho[0] is the derivative vector on the first parameter.W: Weight matrix.
QuanEstimation.FI_Expt — Method.¶
FI_Expt(y1, y2, dx; ftype=:norm)
Calculate the classical Fisher information (CFI) based on the experiment data.
y1: Experimental data obtained at the truth value (x).y1: Experimental data obtained at x+dx.dx: A known small drift of the parameter.ftype: The distribution the data follows. Options are: norm, gamma, rayleigh, and poisson.
QuanEstimation.HCRB — Method.¶
HCRB(ρ::AbstractMatrix, dρ::AbstractVector, C::AbstractMatrix; eps=GLOBAL_EPS)
Caltulate the Holevo Cramer-Rao bound (HCRB) via the semidefinite program (SDP).
ρ: Density matrix.dρ: Derivatives of the density matrix on the unknown parameters to be estimated. For example, drho[0] is the derivative vector on the first parameter.W: Weight matrix.eps: Machine epsilon.
source class='documenter-source'>
QuanEstimation.MLE — Method.¶
MLE(x, rho, y; M=missing, savefile=false)
Bayesian estimation. The estimated value of parameters obtained via the maximum likelihood estimation (MLE).
x: The regimes of the parameters for the integral.rho: Parameterized density matrix.y: The experimental results obtained in practice.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).savefile: Whether or not to save all the posterior distributions.
QuanEstimation.MeasurementOpt — Method.¶
MeasurementOpt(mtype=:Projection, kwargs...)
Measurement optimization.
mtype: The type of scenarios for the measurement optimization. Options are:Projection(default),:LCand:Rotation.kwargs...: keywords and the correponding default vaules.mtype=:Projection,mtype=:LCandmtype=:Rotation, thekwargs...areM=missing,B=missing, POVM_basis=missing, ands=missing, POVM_basis=missing, respectively.
QuanEstimation.NHB — Method.¶
NHB(ρ::AbstractMatrix, dρ::AbstractVector, W::AbstractMatrix)
Nagaoka-Hayashi bound (NHB) via the semidefinite program (SDP).
ρ: Density matrix.dρ: Derivatives of the density matrix on the unknown parameters to be estimated. For example, drho[0] is the derivative vector on the first parameter.W: Weight matrix.
QuanEstimation.OBB — Method.¶
OBB(x::AbstractVector, p, dp, rho, drho, d2rho; LDtype=:SLD, eps=GLOBAL_EPS)
Calculation of the Bayesian version of Cramer-Rao bound introduced by Van Trees (VTB).
x: The regimes of the parameters for the integral.p: The prior distribution.dp: Derivatives of the prior distribution with respect to the unknown parameters to be estimated. For example, dp[0] is the derivative vector on the first parameter.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.d2rho: Second order Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are "SLD" (default), "RLD" and "LLD".eps: Machine epsilon.
QuanEstimation.QFIM — Method.¶
QFIM(ρ::Matrix{T}, dρ::Vector{Matrix{T}}; LDtype=:SLD, exportLD::Bool= false, eps=GLOBAL_EPS) where {T<:Complex}
When applied to the case of single parameter. Calculation of the quantum Fisher information (QFI) for all types.
QuanEstimation.QFIM — Method.¶
QFIM(ρ::Matrix{T}, dρ::Matrix{T}; LDtype=:SLD, exportLD::Bool= false, eps=GLOBAL_EPS) where {T<:Complex}
Calculation of the quantum Fisher information (QFI) for all types.
ρ: Density matrix.dρ: Derivatives of the density matrix with respect to the unknown parameters to be estimated. For example, drho[1] is the derivative vector with respect to the first parameter.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are:SLD(default),:RLDand:LLD.exportLD: export logarithmic derivatives apart from F.eps: Machine epsilon.
QuanEstimation.QFIM_Gauss — Method.¶
QFIM_Gauss(R̄::V, dR̄::VV, D::M, dD::VM) where {V,VV,M,VM<:AbstractVecOrMat}
Calculate the SLD based quantum Fisher information matrix (QFIM) with gaussian states.
R̄: First-order moment.dR̄: Derivatives of the first-order moment with respect to the unknown parameters to be estimated. For example, dR[1] is the derivative vector on the first parameter.D: Second-order moment.dD: Derivatives of the second-order moment with respect to the unknown parameters to be estimated.eps: Machine epsilon.
QuanEstimation.QFIM_Kraus — Method.¶
QFIM_Kraus(ρ0::AbstractMatrix, K::AbstractVector, dK::AbstractVector; LDtype=:SLD, exportLD::Bool=false, eps=GLOBAL_EPS)
Calculation of the quantum Fisher information (QFI) and quantum Fisher information matrix (QFIM) with Kraus operator(s) for all types.
ρ0: Density matrix.K: Kraus operator(s).dK: Derivatives of the Kraus operator(s) on the unknown parameters to be estimated. For example, dK[0] is the derivative vector on the first parameter.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are:SLD(default),:RLDand:LLD.exportLD: Whether or not to export the values of logarithmic derivatives. If set True then the the values of logarithmic derivatives will be exported.eps: Machine epsilon.
source, e.g. QFIM, CFIM, HCRB, etc.
QuanEstimation.QVTB — Method.¶
QVTB(x::AbstractVector, p, dp, rho, drho; LDtype=:SLD, eps=GLOBAL_EPS)
Calculation of the Bayesian version of Cramer-Rao bound in troduced by Van Trees (VTB).
x: The regimes of the parameters for the integral.p: The prior distribution.dp: Derivatives of the prior distribution with respect to the unknown parameters to be estimated. For example, dp[0] is the derivative vector on the first parameter.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.LDtype: Types of QFI (QFIM) can be set as the objective function. Options are "SLD" (default), "RLD" and "LLD".eps: Machine epsilon.
QuanEstimation.QZZB — Method.¶
QZZB(x::AbstractVector, p::AbstractVector, rho::AbstractVecOrMat; eps=GLOBAL_EPS)
Calculation of the quantum Ziv-Zakai bound (QZZB).
x: The regimes of the parameters for the integral.p: The prior distribution.rho: Parameterized density matrix.eps: Machine epsilon.
source9564bc9d/src/Parameterization/Kraus/KrausDynamics.jl#L20-L25' class='documenter-source'>
QuanEstimation.SIC — Method.¶
SIC(dim::Int64)
Generation of a set of rank-one symmetric informationally complete positive operator-valued measure (SIC-POVM).
dim: The dimension of the system.
Note: SIC-POVM is calculated by the Weyl-Heisenberg covariant SIC-POVM fiducial state which can be downloaded from here.
QuanEstimation.SpinSqueezing — Method.¶
SpinSqueezing(ρ::AbstractMatrix; basis="Dicke", output="KU")
Calculate the spin squeezing parameter for the input density matrix. The basis can be "Dicke" for the Dicke basis, or "Pauli" for the Pauli basis. The output can be both "KU"(for spin squeezing defined by Kitagawa and Ueda) and "WBIMH"(for spin squeezing defined by Wineland et al.).
QuanEstimation.TargetTime — Method.¶
TargetTime(f::Number, tspan::AbstractVector, func::Function, args...; kwargs...)
Calculate the minimum time to reach a precision limit of given level. The func can be any objective function during the control optimization, e.g. QFIM, CFIM, HCRB, etc.
QuanEstimation.VTB — Method.¶
VTB(x::AbstractVector, p, dp, rho, drho; M=missing, eps=GLOBAL_EPS)
Calculation of the Bayesian version of Cramer-Rao bound introduced by Van Trees (VTB).
x: The regimes of the parameters for the integral.p: The prior distribution.dp: Derivatives of the prior distribution with respect to the unknown parameters to be estimated. For example, dp[0] is the derivative vector on the first parameter.rho: Parameterized density matrix.drho: Derivatives of the parameterized density matrix (rho) with respect to the unknown parameters to be estimated.M: A set of positive operator-valued measure (POVM). The default measurement is a set of rank-one symmetric informationally complete POVM (SIC-POVM).eps: Machine epsilon.
QuanEstimation.evolve — Method.¶
evolve(dynamics::Kraus{dm})
Evolution of density matrix under time-independent Hamiltonian without noise and controls.
QuanEstimation.evolve — Method.¶
evolve(dynamics::Kraus{ket})
Evolution of pure states under time-independent Hamiltonian without noise and controls
tspan: Time length for the evolution.ρ0: Initial state (density matrix).H0: Free Hamiltonian.dH: Derivatives of the free Hamiltonian with respect to the unknown parameters to be estimated. For example, dH[0] is the derivative vector on the first parameter.decay: Decay operators and the corresponding decay rates. Its input rule is decay=[[\(\Gamma_1\), \(\gamma_1\)], [\(\Gamma_2\), \(\gamma_2\)],...], where \(\Gamma_1\) \((\Gamma_2)\) represents the decay operator and \(\gamma_1\) \((\gamma_2)\) is the corresponding decay rate.Hc: Control Hamiltonians.ctrl: Control coefficients.
QuanEstimation.expm — Method.¶
expm(tspan::AbstractVector, ρ0::AbstractMatrix, H0::AbstractMatrix, dH::AbstractMatrix; decay::Union{AbstractVector, Missing}=missing, Hc::Union{AbstractVector, Missing}=missing, ctrl::Union{AbstractVector, Missing}=missing)
When applied to the case of single parameter.
QuanEstimation.expm — Method.¶
expm(tspan::AbstractVector, ρ0::AbstractMatrix, H0::AbstractMatrix, dH::AbstractVector; decay::Union{AbstractVector, Missing}=missing, Hc::Union{AbstractVector, Missing}=missing, ctrl::Union{AbstractVector, Missing}=missing)
The dynamics of a density matrix is of the form \(\partial_t\rho=-i[H,\rho]+\sum_i \gamma_i\left(\Gamma_i\rho\Gamma^{\dagger}_i-\frac{1}{2}\left\{\rho,\Gamma^{\dagger}_i \Gamma_i \right\}\right)\), where \(\rho\) is the evolved density matrix, \(H\) is the Hamiltonian of the system, \(\Gamma_i\) and \(\gamma_i\) are the \(i\mathrm{th}\) decay operator and the corresponding decay rate.
tspan: Time length for the evolution.ρ0: Initial state (density matrix).H0: Free Hamiltonian.dH: Derivatives of the free Hamiltonian with respect to the unknown parameters to be estimated. For example, dH[0] is the derivative vector on the first parameter.decay: Decay operators and the corresponding decay rates. Its input rule is decay=[[\(\Gamma_1\), \(\gamma_1\)], [\(\Gamma_2\), \(\gamma_2\)],...], where \(\Gamma_1\) \((\Gamma_2)\) represents the decay operator and \(\gamma_1\) \((\gamma_2)\) is the corresponding decay rate.Hc: Control Hamiltonians.ctrl: Control coefficients.
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QuanEstimation.mintime — Method.¶
mintime(f::Number, opt::ControlOpt, alg::AbstractAlgorithm, obj::AbstractObj, dynamics::AbstractDynamics; savefile::Bool=false, method::String="binary")
Search of the minimum time to reach a given value of the objective function.
f: The given value of the objective function.opt: Control Optimization.alg: Optimization algorithms, options areauto-GRAPE,GRAPE,PSO,DEandDDPG.obj: Objective function, options areQFIM_obj,CFIM_objandHCRB_obj.dynamics: Lindblad dynamics.savefile: Whether or not to save all the control coeffients.method: Methods for searching the minimum time to reach the given value of the objective function. Options arebinaryandforward.system: control system.
QuanEstimation.ode — Method.¶
ode(tspan::AbstractVector, ρ0::AbstractMatrix, H0::AbstractMatrix, dH::AbstractMatrix; decay::Union{AbstractVector, Missing}=missing, Hc::Union{AbstractVector, Missing}=missing, ctrl::Union{AbstractVector, Missing}=missing)
When applied to the case of single parameter.
QuanEstimation.ode — Method.¶
ode(tspan::AbstractVector, ρ0::AbstractMatrix, H0::AbstractVector, dH::AbstractVector; decay::Union{AbstractVector, Missing}=missing, Hc::Union{AbstractVector, Missing}=missing, ctrl::Union{AbstractVector, Missing}=missing)
The dynamics of a density matrix is of the form \(\partial_t\rho=-i[H,\rho]+\sum_i \gamma_i\left(\Gamma_i\rho\Gamma^{\dagger}_i-\frac{1}{2}\left\{\rho,\Gamma^{\dagger}_i \Gamma_i \right\}\right)\), where \(\rho\) is the evolved density matrix, \(H\) is the Hamiltonian of the system, \(\Gamma_i\) and \(\gamma_i\) are the \(i\mathrm{th}\) decay operator and the corresponding decay rate.
tspan: Time length for the evolution.ρ0: Initial state (density matrix).H0: Free Hamiltonian.dH: Derivatives of the free Hamiltonian with respect to the unknown parameters to be estimated. For example, dH[0] is the derivative vector on the first parameter.decay: Decay operators and the corresponding decay rates. Its input rule is decay=[[\(\Gamma_1\), \(\gamma_1\)], [\(\Gamma_2\), \(\gamma_2\)],...], where \(\Gamma_1\) \((\Gamma_2)\) represents the decay operator and \(\gamma_1\) \((\gamma_2)\) is the corresponding decay rate.Hc: Control Hamiltonians.ctrl: Control coefficients.
QuanEstimation.offline — Method.¶
offline(apt::Adapt_MZI, alg; target::Symbol=:sharpness, eps = GLOBAL_EPS, seed=1234)
Offline adaptive phase estimation in the MZI.
apt: Adaptive MZI struct which containsx,p, andrho0.alg: The algorithms for searching the optimal tunable phase. Here, DE and PSO are available.target: Setting the target function for calculating the tunable phase. Options are: "sharpness" and "MI".eps: Machine epsilon.seed: Random seed.
QuanEstimation.online — Method.¶
online(apt::Adapt_MZI; target::Symbol=:sharpness, output::String="phi")
Online adaptive phase estimation in the MZI.
apt: Adaptive MZI struct which contains x, p, and rho0.target: Setting the target function for calculating the tunable phase. Options are: "sharpness" and "MI".output: Choose the output variables. Options are: "phi" and "dphi".
QuanEstimation.run — Method.¶
run(opt::AbstractOpt, alg::AbstractAlgorithm, obj::AbstractObj, dynamics::AbstractDynamics; savefile::Bool=false)
Run the optimization problem.
opt: Types of optimization, options areControlOpt,StateOpt,MeasurementOpt,SMopt,SCopt,CMoptandSCMopt.alg: Optimization algorithms, options areauto-GRAPE,GRAPE,AD,PSO,DE, 'NM' andDDPG.obj: Objective function, options areQFIM_obj,CFIM_objandHCRB_obj.dynamics: Lindblad or Kraus parameterization process.savefile: Whether or not to save all the control coeffients.
QuanEstimation.suN_generator — Method.¶
suN_generator(n::Int64)
Generation of the SU(\(N\)) generators with \(N\) the dimension of the system.
N: The dimension of the system.