A random walk in the density matrix space of a Hilbert state space of a quantum system (elementary rotation jumps; faster) More...
#include <tomographer/densedm/tspacellhwalker.h>
Inheritance diagram for Tomographer::DenseDM::TSpace::LLHMHWalkerLight< DenseLLHType_, RngType_, LoggerType_ >: Collaboration diagram for Tomographer::DenseDM::TSpace::LLHMHWalkerLight< DenseLLHType_, RngType_, LoggerType_ >:Public Types | |
| enum | |
| see MHWalker Interface More... | |
| typedef DenseLLHType_ | DenseLLHType |
| The DenseLLH interface object type. | |
| typedef RngType_ | RngType |
| The random number generator type. | |
| typedef LoggerType_ | LoggerType |
| The logger type. | |
| typedef DenseLLHType::DMTypes | DMTypes |
| The data types of our problem. | |
| typedef DenseLLHType::LLHValueType | LLHValueType |
| The loglikelihood function value type (see DenseLLH Interface e.g. IndepMeasLLH) | |
| typedef DMTypes::MatrixType | MatrixType |
| The matrix type for a density operator on our quantum system. | |
| typedef DMTypes::VectorParamType | VectorParamType |
| Type of an X-parameterization of a density operator (see X Parameterization) | |
| typedef DMTypes::RealScalar | RealScalar |
The real scalar corresponding to our data types. Usually a double. | |
| typedef DMTypes::ComplexScalar | ComplexScalar |
The complex real scalar corresponding to our data types. Usually a std::complex<double>. | |
| typedef LLHMHWalkerLightParams< RealScalar > | WalkerParams |
| The real scalar type for the step size — this scalar type is the only parameter we need (see MHWalker Interface) | |
| typedef MatrixType | PointType |
| Provided for MHRandomWalk. A point in our random walk = a density matrix. | |
| typedef LLHValueType | FnValueType |
| Provided for MHRandomWalk. The function value type is the loglikelihood value type. | |
Public Member Functions | |
| LLHMHWalkerLight (const MatrixType &startpt, const DenseLLHType &llh, RngType &rng, LoggerType &baselogger) | |
| Constructor which just initializes the given fields. More... | |
| void | init () |
| Provided for MHRandomWalk. Initializes some fields and prepares for a random walk. More... | |
| const MatrixType & | startPoint () |
| Return the starting point given in the constructor, or a random start point. | |
| void | thermalizingDone () |
| Callback for after thermalizing is done. No-op. | |
| void | done () |
| Callback for after random walk is finished. No-op. | |
| LLHValueType | fnLogVal (const MatrixType &T) const |
| Calculate the logarithm of the Metropolis-Hastings function value. More... | |
| MatrixType | jumpFn (const MatrixType &cur_T, WalkerParams params) |
| Decides of a new point to jump to for the random walk. | |
Detailed Description
template<typename DenseLLHType_, typename RngType_, typename LoggerType_>
class Tomographer::DenseDM::TSpace::LLHMHWalkerLight< DenseLLHType_, RngType_, LoggerType_ >
A random walk in the density matrix space of a Hilbert state space of a quantum system (elementary rotation jumps; faster)
The random walk explores the density operators on a Hilbert space of a given dimension, according to the distribution given by the likelihood function on the Hilbert-schmidt uniform prior.
In contrast to LLHMHWalker, the random jumps of this MHWalker is not a uniform random unitary jump, rather, it is a jump in a random elementary direction. The stationary distribution of the Markov chain is the same, so the same distribution is explored, but because less calculations are involved this method can be much faster.
- Since
- Added in Tomographer 5.0
- Template Parameters
-
DenseLLHType A type satisfying the DenseLLH Interface RngType A std::randomrandom number generator (such as std::mt19937)LoggerType A logger type (see Logging and Loggers)
Definition at line 342 of file tspacellhwalker.h.
Member Enumeration Documentation
§ anonymous enum
| anonymous enum |
| Enumerator | |
|---|---|
| UseFnSyntaxType | We will calculate the log-likelihood function, which is the logarithm of the Metropolis-Hastings function we should be calculating. |
Definition at line 379 of file tspacellhwalker.h.
Constructor & Destructor Documentation
§ LLHMHWalkerLight()
|
inline |
Constructor which just initializes the given fields.
The llh object is responsible for calculating the log-likelihood function of the tomography experiment (see class documentation).
The startpt argument specifies the starting point for the random walk (matrix in T Parameterization). If you provide a zero startpt here, then a random starting point will be chosen using the rng random number generator to generate a random point on the sphere.
Definition at line 411 of file tspacellhwalker.h.
Member Function Documentation
§ fnLogVal()
|
inline |
Calculate the logarithm of the Metropolis-Hastings function value.
- Returns
- the log-likelihood, which is computed via the DenseLLH object.
Definition at line 480 of file tspacellhwalker.h.
§ init()
|
inline |
Provided for MHRandomWalk. Initializes some fields and prepares for a random walk.
- Note
- If the startpt given to the constructor is zero (or has very small norm), then a uniformly random starting point is chosen. The starting point is chosen randomly according to the Haar-invariant measure on the state space. This corresponds to choosing a uniform point on the sphere corresponding to the T-parameterization of the density matrices.
Definition at line 433 of file tspacellhwalker.h.
The documentation for this class was generated from the following file:
- tomographer/densedm/tspacellhwalker.h (v5.3)