-
Notifications
You must be signed in to change notification settings - Fork 1
Functions for finite size systems: Low level functions: Problems with exact derivative
kchabuda edited this page Jul 17, 2021
·
1 revision
fin_FoM_FoMD_optbd(n,d,bc,ch,chp,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 check of convergence in bond dimensions. Function for finite size systems.
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 ch: MPO for quantum channel, 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 generalized derivative of quantum channel, 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 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 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 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 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 FoM/FoMD resultm: matrix describing FoM/FoMD in function of bd of respectively SLD MPO [rows] and initial wave function MPS [columns] c: optimal MPO for SLD a0: optimal MPS for initial wave function
fin_FoM_optbd(n,d,bc,a,b,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.
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 density matrix, 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 generalized derivative of density matrix, 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 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 in function of bd of SLD MPO c: optimal MPO for SLD
fin_FoMD_optbd(n,d,bc,c2d,cpd,a0ini=None,imprecision=10**-2,bdpsimax=100,alwaysbdpsimax=False)
Optimization of FoMD over initial wave function MPS and also check of convergence in bond dimension. Function for finite size systems.
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, 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 generalized derivative of 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 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
fin_FoM_FoMD_optm(n,d,bc,c,a0,ch,chp,imprecision=10**-2,lherm=True)
Iterative optimization of FoM/FoMD over SLD MPO and initial wave function MPS. Function for finite size systems.
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, 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 generalized derivative of quantum channel, 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 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
fin_FoM_OBC_optm(a,b,c,imprecision=10**-2,lherm=True)
Optimization of FoM over MPO for SLD. Function for finite size systems with OBC.
Parameters:
a: MPO for density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) b: MPO for generalized derivative of density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) c: MPO for 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
fin_FoM_PBC_optm(a,b,c,imprecision=10**-2,lherm=True)
Optimization of FoM over MPO for SLD. Function for finite size systems with PBC.
Parameters:
a: MPO for density matrix, expected ndarray of a shape (bd,bd,d,d,n) b: MPO for generalized derivative of density matrix, expected ndarray of a shape (bd,bd,d,d,n) c: MPO for 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
fin_FoMD_OBC_optm(c2d,cpd,a0,imprecision=10**-2)
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with OBC.
Parameters:
c2d: MPO for square of dual of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) cpd: MPO for dual of generalized derivative of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) 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) 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
fin_FoMD_PBC_optm(c2d,cpd,a0,imprecision=10**-2)
Optimization of FoMD over MPS for initial wave function. Function for finite size systems with PBC.
Parameters:
c2d: MPO for square of dual of SLD, expected ndarray of a shape (bd,bd,d,d,n) cpd: MPO for dual of generalized derivative of SLD, expected ndarray of a shape (bd,bd,d,d,n) 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
fin_FoM_OBC_val(a,b,c)
Calculate the value of FoM. Function for finite size systems with OBC.
Parameters:
a: MPO for density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) b: MPO for generalized derivative of density matrix, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) 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
fin_FoM_PBC_val(a,b,c)
Calculate the value of FoM. Function for finite size systems with PBC.
Parameters:
a: MPO for a density matrix, expected ndarray of a shape (bd,bd,d,d,n) b: MPO for generalized derivative of a density matrix, expected ndarray of a shape (bd,bd,d,d,n) c: MPO for the SLD, expected ndarray of a shape (bd,bd,d,d,n)
Returns:
fomval: value of FoM
fin_FoMD_OBC_val(c2d,cpd,a0)
Calculate value of FoMD. Function for finite size systems with OBC.
Parameters:
c2d: MPO for square of dual of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) cpd: MPO for dual of generalized derivative of SLD, expected list of length n of ndarrays of a shape (bd,bd,d,d) (bd can vary between sites) 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
fin_FoMD_PBC_val(c2d,cpd,a0)
Calculate the value of FoMD. Function for finite size systems with PBC.
Parameters:
c2d: MPO for square of dual of the SLD, expected ndarray of a shape (bd,bd,d,d,n) cpd: MPO for dual of generalized derivative of the SLD, expected ndarray of a shape (bd,bd,d,d,n) a0: MPS for the 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