HABQTlib.Data

This module contains data types and helper functions for working with quantum state vectors and density matrices.

Documentation

type Dim = Int

Dimension of Hilbert space.

type Rank = Int

Rank of mixed state.

type NumberOfParticles = Int

Number of particles per rank.

type QBitNum = Int

Number of quantum bits.

type Weight = Double

Weight associated with a particle.

type MHMCiter = Int

Number of MHMC iterations to perform when resampling.

type OptIter = Int

Number of optimisation steps to perform when searching for optimal measurment.

data OutputVerb

Output verbosity settings.

Constructors

NoOutput

No stdout output

FidOutput

Only output fidelities and weights of hierarchical mean estimates

FullOutput

Full output, including resampling diagnostic information

Instances

Eq OutputVerb

Methods

(==) :: OutputVerb -> OutputVerb -> Bool

(/=) :: OutputVerb -> OutputVerb -> Bool

Ord OutputVerb

Methods

compare :: OutputVerb -> OutputVerb -> Ordering

(<) :: OutputVerb -> OutputVerb -> Bool

(<=) :: OutputVerb -> OutputVerb -> Bool

(>) :: OutputVerb -> OutputVerb -> Bool

(>=) :: OutputVerb -> OutputVerb -> Bool

max :: OutputVerb -> OutputVerb -> OutputVerb

min :: OutputVerb -> OutputVerb -> OutputVerb

Show OutputVerb

Methods

showsPrec :: Int -> OutputVerb -> ShowS

show :: OutputVerb -> String

showList :: [OutputVerb] -> ShowS

newtype DensityMatrix

Density matrix are stored as hmatrix matrices of complex doubles.

Constructors

DensityMatrix

Fields

• getDensityMatrix :: Matrix (Complex Double)

Instances

Eq DensityMatrix

Methods

(==) :: DensityMatrix -> DensityMatrix -> Bool

(/=) :: DensityMatrix -> DensityMatrix -> Bool

Show DensityMatrix

Methods

showsPrec :: Int -> DensityMatrix -> ShowS

show :: DensityMatrix -> String

showList :: [DensityMatrix] -> ShowS

Generic DensityMatrix

Associated Types

type Rep DensityMatrix :: * -> *

Methods

from :: DensityMatrix -> Rep DensityMatrix x

to :: Rep DensityMatrix x -> DensityMatrix

Newtype DensityMatrix

Associated Types

type O DensityMatrix :: *

Methods

pack :: O DensityMatrix -> DensityMatrix

unpack :: DensityMatrix -> O DensityMatrix

type Rep DensityMatrix

type Rep DensityMatrix = D1 * (MetaData "DensityMatrix" "HABQTlib.Data" "HABQT-0.1.0.0-9QLE6iKEmCvEwMEGENDi9h" True) (C1 * (MetaCons "DensityMatrix" PrefixI True) (S1 * (MetaSel (Just Symbol "getDensityMatrix") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Matrix (Complex Double)))))

type O DensityMatrix

type O DensityMatrix = GO (Rep DensityMatrix)

truncateRank :: Rank -> WeighedDensityMatrix -> WeighedDensityMatrix

Set smallest eigenvalues of a weighed density matrix to zero until specified rank is reached.

newtype PureStateVector

Pure state vectors are stored as hmatrix matrices of complex doubles. Such matrices only have one column.

Constructors

PureStateVector

Fields

• getStateVector :: Matrix (Complex Double)

Instances

Eq PureStateVector

Methods

(==) :: PureStateVector -> PureStateVector -> Bool

(/=) :: PureStateVector -> PureStateVector -> Bool

Show PureStateVector

Methods

showsPrec :: Int -> PureStateVector -> ShowS

show :: PureStateVector -> String

showList :: [PureStateVector] -> ShowS

Generic PureStateVector

Associated Types

type Rep PureStateVector :: * -> *

Methods

from :: PureStateVector -> Rep PureStateVector x

to :: Rep PureStateVector x -> PureStateVector

Newtype PureStateVector

Associated Types

type O PureStateVector :: *

Methods

pack :: O PureStateVector -> PureStateVector

unpack :: PureStateVector -> O PureStateVector

type Rep PureStateVector

type Rep PureStateVector = D1 * (MetaData "PureStateVector" "HABQTlib.Data" "HABQT-0.1.0.0-9QLE6iKEmCvEwMEGENDi9h" True) (C1 * (MetaCons "PureStateVector" PrefixI True) (S1 * (MetaSel (Just Symbol "getStateVector") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Matrix (Complex Double)))))

type O PureStateVector

type O PureStateVector = GO (Rep PureStateVector)

pureStateLikelihood :: PureStateVector -> DensityMatrix -> Double

Probability of obtaining a measurement result when projecting a system in mixed state determined by a density matrix onto a pure state.

svToDM :: PureStateVector -> DensityMatrix

Calculate the density matrix of a given pure state.

newtype WeighedDensityMatrix

Weighed density matrix where weight is stored separately as first coordinate of a tuple.

Constructors

WeighedDensityMatrix

Fields

• getWDM :: (Weight, DensityMatrix)

Instances

Eq WeighedDensityMatrix

Methods

(==) :: WeighedDensityMatrix -> WeighedDensityMatrix -> Bool

(/=) :: WeighedDensityMatrix -> WeighedDensityMatrix -> Bool

Show WeighedDensityMatrix

Methods

showsPrec :: Int -> WeighedDensityMatrix -> ShowS

show :: WeighedDensityMatrix -> String

showList :: [WeighedDensityMatrix] -> ShowS

Generic WeighedDensityMatrix

Associated Types

type Rep WeighedDensityMatrix :: * -> *

Methods

from :: WeighedDensityMatrix -> Rep WeighedDensityMatrix x

to :: Rep WeighedDensityMatrix x -> WeighedDensityMatrix

Newtype WeighedDensityMatrix

Associated Types

type O WeighedDensityMatrix :: *

Methods

pack :: O WeighedDensityMatrix -> WeighedDensityMatrix

unpack :: WeighedDensityMatrix -> O WeighedDensityMatrix

type Rep WeighedDensityMatrix

type Rep WeighedDensityMatrix = D1 * (MetaData "WeighedDensityMatrix" "HABQTlib.Data" "HABQT-0.1.0.0-9QLE6iKEmCvEwMEGENDi9h" True) (C1 * (MetaCons "WeighedDensityMatrix" PrefixI True) (S1 * (MetaSel (Just Symbol "getWDM") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Weight, DensityMatrix))))

type O WeighedDensityMatrix

type O WeighedDensityMatrix = GO (Rep WeighedDensityMatrix)

mkWDM :: Weight -> DensityMatrix -> WeighedDensityMatrix

A shorter alias for curried WeighedDensityMatrix constructor.

mkWDM1 :: DensityMatrix -> WeighedDensityMatrix

Alias for mkWDM 1.

newtype WeighedPureStateVector

Weighed state vector where weight is stored separately as first coordinate of a tuple.

Constructors

WeighedPureStateVector

Fields

• getWSV :: (Weight, PureStateVector)

Instances

Eq WeighedPureStateVector

Methods

(==) :: WeighedPureStateVector -> WeighedPureStateVector -> Bool

(/=) :: WeighedPureStateVector -> WeighedPureStateVector -> Bool

Show WeighedPureStateVector

Methods

showsPrec :: Int -> WeighedPureStateVector -> ShowS

show :: WeighedPureStateVector -> String

showList :: [WeighedPureStateVector] -> ShowS

Generic WeighedPureStateVector

Associated Types

type Rep WeighedPureStateVector :: * -> *

Methods

from :: WeighedPureStateVector -> Rep WeighedPureStateVector x

to :: Rep WeighedPureStateVector x -> WeighedPureStateVector

Newtype WeighedPureStateVector

Associated Types

type O WeighedPureStateVector :: *

Methods

pack :: O WeighedPureStateVector -> WeighedPureStateVector

unpack :: WeighedPureStateVector -> O WeighedPureStateVector

type Rep WeighedPureStateVector

type Rep WeighedPureStateVector = D1 * (MetaData "WeighedPureStateVector" "HABQTlib.Data" "HABQT-0.1.0.0-9QLE6iKEmCvEwMEGENDi9h" True) (C1 * (MetaCons "WeighedPureStateVector" PrefixI True) (S1 * (MetaSel (Just Symbol "getWSV") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Weight, PureStateVector))))

type O WeighedPureStateVector

type O WeighedPureStateVector = GO (Rep WeighedPureStateVector)

(<+>) :: WeighedDensityMatrix -> WeighedDensityMatrix -> WeighedDensityMatrix infix 8

Given two weighed density matrixes, compute their mixture. Associative operation.

fidelity :: PureStateVector -> PureStateVector -> Double

Fidelity (probability of measurement) between pure states.

fidelityDM :: DensityMatrix -> DensityMatrix -> Double

Fidelity (probability of measurement) between mixed states.

validSV :: PureStateVector -> Validation [String] PureStateVector

Check whether a pure state vector is properly normed.

validDM :: DensityMatrix -> Validation [String] DensityMatrix

Verify that density matrix is Hermitian and has trace 1.

validPartNum :: NumberOfParticles -> Validation [String] NumberOfParticles

Verify that particle number is a positive integer.

validRank :: Rank -> Validation [String] Rank

Verify that rank is a positive integer. Setting rank to be higher than the dimension of space creates poinless performance overhead, but isn't prevented by validation.

validMHMCiter :: MHMCiter -> Validation [String] MHMCiter

Verify that number of MHMC iterations is a positive integer.

validOptIter :: OptIter -> Validation [String] OptIter

Verify that number of POVM optimisation iterations is positive.

validQBitN :: QBitNum -> Validation [String] QBitNum

Verify that number of quantum bits is positive.