-
Notifications
You must be signed in to change notification settings - Fork 1
Functions for finite size systems: Low level functions: Problems with discrete approximation of the derivative
kchabuda edited this page Jul 17, 2021
·
1 revision
fin2_FoM_FoMD_optbd(n,d,bc,ch,chp,epsilon,cini=None,a0ini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True,bdpsimax=100,alwaysbdpsimax=False)
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS and also a check of convergence with increasing bond dimensions. Function for finite size systems. Version with two channels separated by epsilon.
Parameters:
n: number of sites in TN d: dimension of the local Hilbert space (dimension of the physical index) bc: boundary conditions, 'O' for OBC, 'P' for PBC ch: MPO for a quantum channel at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC chp: MPO for a quantum channel at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC epsilon: value of a separation between estimated parameters encoded in ch and chp, float cini: initial MPO for the SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC a0ini: initial MPS for the initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC imprecision: expected imprecision of the end results, default value is 10**-2 bdlmax: maximal value of bd for SLD MPO, default value is 100 alwaysbdlmax: boolean value, True if the maximal value of bd for SLD MPO has to be reached, otherwise False (default value) lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False bdpsimax: maximal value of bd for the initial wave function MPS, default value is 100 alwaysbdpsimax: boolean value, True if the maximal value of bd for initial wave function MPS has to be reached, otherwise False (default value)
Returns:
result: optimal value of FoM/FoMD resultm: matrix describing FoM/FoMD as a function of bd of respectively SLD MPO [rows] and the initial wave function MPS [columns] c: optimal MPO for SLD a0: optimal MPS for initial wave function
fin2_FoM_optbd(n,d,bc,a,b,epsilon,cini=None,imprecision=10**-2,bdlmax=100,alwaysbdlmax=False,lherm=True)
Optimization of FoM over SLD MPO and also check of convergence in bond dimension. Function for finite size systems. Version with two states separated by epsilon.
Parameters:
n: number of sites in TN d: dimension of local Hilbert space (dimension of physical index) bc: boundary conditions, 'O' for OBC, 'P' for PBC a: MPO for the density matrix at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC b: MPO for the density matrix at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC epsilon: value of a separation between estimated parameters encoded in a and b, float cini: initial MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC imprecision: expected imprecision of the end results, default value is 10**-2 bdlmax: maximal value of bd for SLD MPO, default value is 100 alwaysbdlmax: boolean value, True if maximal value of bd for SLD MPO have to be reached, otherwise False (default value) lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
result: optimal value of FoM resultv: vector describing FoM as a function of bd of the SLD MPO c: optimal MPO for SLD
fin2_FoMD_optbd(n,d,bc,c2d,cd,cpd,epsilon,a0ini=None,imprecision=10**-2,bdpsimax=100,alwaysbdpsimax=False)
Optimization of FoMD over initial wave function MPS and also check of convergence when increasing the bond dimension. Function for finite size systems. Version with two dual SLDs separated by epsilon.
Parameters:
n: number of sites in TN d: dimension of local Hilbert space (dimension of physical index) bc: boundary conditions, 'O' for OBC, 'P' for PBC c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC epsilon: value of a separation between estimated parameters encoded in cd and cpd, float a0ini: initial MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC imprecision: expected imprecision of the end results, default value is 10**-2 bdpsimax: maximal value of bd for initial wave function MPS, default value is 100 alwaysbdpsimax: boolean value, True if maximal value of bd for initial wave function MPS have to be reached, otherwise False (default value)
Returns:
result: optimal value of FoMD resultv: vector describing FoMD in function of bd of initial wave function MPS a0: optimal MPS for initial wave function
fin2_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,epsilon,imprecision=10**-2,lherm=True)
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS. Function for finite size systems. Version with two channels separated by epsilon.
Parameters:
n: number of sites in TN d: dimension of local Hilbert space (dimension of physical index) bc: boundary conditions, 'O' for OBC, 'P' for PBC c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,d,n) for PBC a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d,n) for PBC ch: MPO for quantum channel at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC chp: MPO for quantum channel at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d**2,d**2) for OBC (bd can vary between sites), or ndarray of a shape (bd,bd,d**2,d**2,n) for PBC epsilon: value of a separation between estimated parameters encoded in ch and chp, float imprecision: expected imprecision of the end results, default value is 10**-2 lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fval: optimal value of FoM/FoMD c: optimal MPO for SLD a0: optimal MPS for initial wave function
fin2_FoM_OBC_optm(a,b,epsilon,c,imprecision=10**-2,lherm=True)
Optimization of FoM over MPO for SLD. Function for finite size systems with OBC. Version with two states separated by epsilon.
Parameters:
a: MPO for the density matrix at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) b: MPO for the density matrix at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) epsilon: value of a separation between estimated parameters encoded in a and b, float c: MPO for the SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) imprecision: expected imprecision of the end results, default value is 10**-2 lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fomval: optimal value of FoM c: optimal MPO for SLD
fin2_FoM_PBC_optm(a,b,epsilon,c,imprecision=10**-2,lherm=True)
Optimization of FoM over MPO for SLD. Function for finite size systems with PBC. Version with two states separated by epsilon.
Parameters:
a: MPO for the density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d,n) b: MPO for the density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d,n) epsilon: value of a separation between estimated parameters encoded in a and b, float c: MPO for the SLD, expected ndarray of a shape (bd,bd,d,d,n) imprecision: expected imprecision of the end results, default value is 10**-2 lherm: boolean value, True (default value) when Hermitian gauge is imposed on SLD MPO, otherwise False
Returns:
fomval: optimal value of FoM c: optimal MPO for SLD
fin2_FoMD_OBC_optm(c2d,cd,cpd,epsilon,a0,imprecision=10**-2)
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with OBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for the square of the dual of the SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) cd: MPO for the dual of the SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) cpd: MPO for the dual of the SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) epsilon: value of a separation between estimated parameters encoded in cd and cpd, float a0: MPS for the initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD a0: optimal MPS for the initial wave function
fin2_FoMD_PBC_optm(c2d,cd,cpd,epsilon,a0,imprecision=10**-2)
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with PBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n) cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n) cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected ndarray of a shape (bd,bd,d,d,n) epsilon: value of a separation between estimated parameters encoded in cd and cpd, float a0: MPS for initial wave function, expected ndarray of a shape (bd,bd,d,n) imprecision: expected imprecision of the end results, default value is 10**-2
Returns:
fomdval: optimal value of FoMD a0: optimal MPS for initial wave function
fin2_FoM_OBC_val(a,b,epsilon,c)
Calculate value of FoM. Function for finite size systems with OBC. Version with two states separated by epsilon.
Parameters:
a: MPO for density matrix at the value of estimated parameter phi=phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) b: MPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) epsilon: value of a separation between estimated parameters encoded in a and b, float c: MPO for SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
Returns:
fomval: value of FoM
fin2_FoM_PBC_val(a,b,epsilon,c)
Calculate value of FoM. Function for finite size systems with PBC. Version with two states separated by epsilon.
Parameters:
a: MPO for density matrix at the value of estimated parameter phi=phi_0, expected ndarray of a shape (bd,bd,d,d,n) b: MPO for density matrix at the value of estimated parameter phi=phi_0+epsilon, expected ndarray of a shape (bd,bd,d,d,n) epsilon: value of a separation between estimated parameters encoded in a and b, float c: MPO for SLD, expected ndarray of a shape (bd,bd,d,d,n)
Returns:
fomval: value of FoM
fin2_FoMD_OBC_val(c2d,cd,cpd,epsilon,a0)
Calculate value of FoMD. Function for finite size systems with OBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) epsilon: value of a separation between estimated parameters encoded in cd and cpd, float a0: MPS for initial wave function, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites)
Returns:
fomdval: value of FoMD
fin2_FoMD_PBC_val(c2d,cd,cpd,epsilon,a0)
Calculate value of FoMD. Function for finite size systems with PBC. Version with two dual SLDs separated by epsilon.
Parameters:
c2d: MPO for square of dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n) cd: MPO for dual of SLD at the value of estimated parameter phi=-phi_0, expected ndarray of a shape (bd,bd,d,d,n) cpd: MPO for dual of SLD at the value of estimated parameter phi=-(phi_0+epsilon), expected ndarray of a shape (bd,bd,d,d,n) epsilon: value of a separation between estimated parameters encoded in cd and cpd, float a0: MPS for initial wave function, expected ndarray of a shape (bd,bd,d,n)
Returns:
fomdval: value of FoMD
- Home
- Functions for finite size systems
- Functions for infinite size systems
- Auxiliary functions