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Tomographer
v5.3
Tomographer C++ Framework Documentation
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C++ types needed to store a quantum state as a dense matrix. More...
#include <tomographer/densedm/dmtypes.h>
Public Types | |
| typedef RealScalar_ | RealScalar |
Real scalar type, given in template parameter. Usually double is fine. | |
| typedef std::complex< RealScalar > | ComplexScalar |
| The corresponding complex scalar type. | |
| typedef Eigen::Matrix< ComplexScalar, FixedDim, FixedDim, Eigen::Matrix< ComplexScalar, FixedDim, FixedDim >::Options, MaxFixedDim_, MaxFixedDim_ > | MatrixType |
| Matrix type, to store the density operator as a dense matrix. | |
| typedef const Eigen::Ref< const MatrixType > & | MatrixTypeConstRef |
| Shorthand for a const reference to a MatrixType-like Eigen object. | |
| typedef Eigen::Matrix< RealScalar, FixedDim2, 1 > | VectorParamType |
| Real vector with dim*dim elements. | |
| typedef const Eigen::Ref< const VectorParamType > & | VectorParamTypeConstRef |
| Shorthand for a const reference to a VectorParamType-like Eigen object. | |
| typedef Eigen::Matrix< RealScalar, FixedNdof, 1 > | VectorParamNdofType |
| Real vector with dim*dim-1 elements. More... | |
| typedef const Eigen::Ref< const VectorParamNdofType > & | VectorParamNdofTypeConstRef |
| Shorthand for a const reference to a VectorParamNdofType-like Eigen object. | |
Public Member Functions | |
| template<ENABLED_IF( !IsDynamicDim) > | |
| DMTypes () | |
| Constructor [only for statically-fixed dim]. More... | |
| DMTypes (Eigen::Index d) | |
| Constructor [works for both static or dynamic dim]. More... | |
| Eigen::Index | dim () const |
| get the dimension of the quantum system (dimension of the Hilbert space) More... | |
| Eigen::Index | dim2 () const |
| get the square of the dimension of the quantum system More... | |
| Eigen::Index | ndof () const |
| get the square of the dimension of the quantum system, minus one More... | |
| template<ENABLED_IF( !IsDynamicDim) > | |
| MatrixType::ConstantReturnType | initMatrixType () const |
| Zero initializer for a MatrixType [implementation for static dimension]. More... | |
| template<ENABLED_IF( IsDynamicDim) > | |
| MatrixType::ConstantReturnType | initMatrixType () const |
| Zero initializer for MatrixType [implementation for dynamic dimension]. More... | |
| template<ENABLED_IF( !IsDynamicDim) > | |
| VectorParamType::ConstantReturnType | initVectorParamType () const |
| Zero initializer for a VectorParamType [implementation for static dimension]. More... | |
| template<ENABLED_IF( IsDynamicDim) > | |
| VectorParamType::ConstantReturnType | initVectorParamType () const |
| Zero initializer for VectorParamType [implementation for dynamic dimension]. More... | |
| template<ENABLED_IF( !IsDynamicDim) > | |
| VectorParamNdofType::ConstantReturnType | initVectorParamNdofType () const |
| Zero initializer for a VectorParamNdofType [implementation for static dimension]. More... | |
| template<ENABLED_IF( IsDynamicDim) > | |
| VectorParamNdofType::ConstantReturnType | initVectorParamNdofType () const |
| Zero initializer for VectorParamNdofType [implementation for dynamic dimension]. More... | |
Static Public Member Functions | |
| static ComplexScalar | cplx (RealScalar a, RealScalar b) |
| Utility to initialize a complex number using the current scalar type. | |
Static Public Attributes | |
| static constexpr bool | IsDynamicDim = (FixedDim_ == Eigen::Dynamic) |
| Whether the dimension is specified dynamically at run-time or statically at compile-time. | |
| static constexpr int | FixedDim = FixedDim_ |
| The fixed dimension of the quantum system, or Eigen::Dynamic. | |
| static constexpr int | FixedDim2 = ((FixedDim!=Eigen::Dynamic) ? FixedDim*FixedDim : Eigen::Dynamic) |
| The square of the dimension of the quantum system, or Eigen::Dynamic. | |
| static constexpr int | FixedNdof = ((FixedDim2!=Eigen::Dynamic) ? FixedDim2-1 : Eigen::Dynamic) |
| The square of the dimension of the quantum system minus one, or Eigen::Dynamic. | |
C++ types needed to store a quantum state as a dense matrix.
The DMTypes template class stores compile-time and run-time information about the types used to represent density operators as dense Eigen objects (storing a matrix explicitly as a list of coefficients in memory, as you'd expect), as well as remembering the dimension of the corresponding Hilbert space. The latter may be fixed either at compile-time or set dynamically at run-time.
If a compile-time dimension is given, then the corresponding Eigen types (see Eigen::Matrix) will be allocated on the stack instead of the heap. For small matrix sizes, you should get a performance increase.
| FixedDim | The dimension of the Hilbert space, if known at compile-time, or Eigen::Dynamic. If Eigen::Dynamic is specified here, the dimension can be specified at run-time to the class's constructor. |
| RealScalar | The type to use as real scalar. The default, double, should be sufficient in most (if not all) cases, but you could try to speed up computations by using float, or be more precise by using long double. |
This class provides several types which are to be used to store matrices acting on the Hilbert space, a vector of real coefficients which can store an X Parameterization of Hermitian such matrices, and a vector of real coefficients of length corresponding to the number of degrees of freedom of a density matrix (e.g. to store a A Parameterization). For each such type, there is an initialization method (e.g. initMatrixType()), which initializes the corresponding object to zero.
Whenever such a type is needed, one calls for example
dim()*dim() real entries, as needed for example to store the X Parameterization of a Hermitian matrix.dim()*dim()-1 real entries, as needed for example to store the A Parameterization of a density matrix.To each of these type corresponds a const-reference type, which is useful to specify function arguments.
| typedef Eigen::Matrix<RealScalar, FixedNdof, 1> Tomographer::DenseDM::DMTypes< FixedDim_, RealScalar_, MaxFixedDim_ >::VectorParamNdofType |
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Constructor [works for both static or dynamic dim].
The dimension fixed at run-time must be specified here, and cannot later be changed.
If the dimension was fixed at compile-time with FixedDim_, then d must equal FixedDim_ (or you'll get an assert failure).
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get the dimension of the quantum system (dimension of the Hilbert space)
If the dimension was fixed at compile-time, then that value is directly returned (and the compiler should be able to optimize this). If the dimension is dynamically set at run-time, then we return that stored value.
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get the square of the dimension of the quantum system
Equivalently, this is the number of complex matrix entries, or the number of real coefficients needed to specify a Hermitian matrix. It is the size of a VectorParamType.
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Zero initializer for a MatrixType [implementation for static dimension].
This function returns an initializer, which when used as constructor argument to MatrixType, initializes it with a zero \( \texttt{dim}\times\texttt{dim} \) matrix.
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Zero initializer for MatrixType [implementation for dynamic dimension].
This function returns an initializer, which when used as constructor argument to MatrixType, initializes it with a zero \( \texttt{dim}\times\texttt{dim} \) matrix.
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Zero initializer for a VectorParamNdofType [implementation for static dimension].
This function returns an initializer, which when used as constructor argument to VectorParamNdofType, initializes it to a zero vector of \( \texttt{dim}^2-1 \) entries.
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Zero initializer for VectorParamNdofType [implementation for dynamic dimension].
This function returns an initializer, which when used as constructor argument to VectorParamNdofType, initializes it to a zero vector of \( \texttt{dim}^2-1 \) entries.
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Zero initializer for a VectorParamType [implementation for static dimension].
This function returns an initializer, which when used as constructor argument to VectorParamType, initializes it to a zero vector of \( \texttt{dim}^2 \) entries.
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Zero initializer for VectorParamType [implementation for dynamic dimension].
This function returns an initializer, which when used as constructor argument to VectorParamType, initializes it to a zero vector of \( \texttt{dim}^2 \) entries.
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get the square of the dimension of the quantum system, minus one
Equivalently, this is the number of degrees of freedom of a density matrix. It is the size of a VectorParamNdofType.