Quantum.Synthesis.GridProblems

1-dimensional grid problems

General solutions

gridpoints

gridpoints_parity

Randomized solutions

gridpoint_random

gridpoint_random_parity

Scaled solutions

gridpoints_scaled

gridpoints_scaled_parity

2-dimensional grid problems

Representation of convex sets

type Point r

point_fromDRootTwo

type Operator a

data Ellipse r

type CharFun

type LineIntersector r

data ConvexSet r

Specific convex sets

unitdisk

rectangle

General solutions

gridpoints2

Scaled solutions

gridpoints2_scaled

gridpoints2_increasing

Implementation details

Positive operators and ellipses

toOperator

fromOperator

op_fromDRootTwo

operator_from_bz

operator_to_bz

operator_to_bl2z

det

operator_skew

uprightness

States

type OperatorPair a

skew

bias

Grid operators

opR

opA

opA_inv

opA_power

opB

opB_inv

opB_power

opK

opX

opZ

opS

opS_inv

opS_power

Action of grid operators on states

action

Shifts

shift_sigma

shift_tau

shift_state

Skew reduction

lemma_A

lemma_B

lemma_A_l2

lemma_B_l2

step_lemma

reduction

to_upright

Action of special grid operators on convex sets

point_transform

ellipse_transform

charfun_transform

lineintersector_transform

convex_transform

Bounding boxes

boundingbox_ellipse

boundingbox

Auxiliary functions

within

fatten_interval

lambda

lambda_inv

lambdapower

signpower

floorlog

logBase_double

iprod

point_sub

special_inverse