Ας υποθέσουμε οτι μπορούσατε να είχατε 1 απο τα 3 πράγματα:
Μετά βίας να βγάζετε τον μήνα αλλά να εχετε οικογένεια , καλούς φίλους και σχέση
Να βγάζατε 3κ στην αθήνα το μήνα αλλα να μην ειχατε σχεση , να είχατε 1 μόνο φίλο και οικογένεια
Να βγάζετε 7κ αθήνα το μήνα αλλά να μην έχετε ούτε καλό οικογενειακό περιβάλλον , ούτε σχέση ούτε φίλους.
Τι θα διαλέγατε?
Πηγες λενε για 25+7 καλα οτι να ναι να πουληθει ο Ντελιας για ουτε 30 εκ ρευστο.Αχ ρε Σαββιδη μας την εκανες την ζημια γκαντσλφ.
Αντε να παιξει ο Λουσε στην θεση του όΚωνσταντελια τωρα με την Μπραν.Η να παμε 4-1-4-1 με κορυφη Μυθου αναγκαστικα και 3 επιτελικους χαφ.
Μηπως να αγπρασουμε την αρχοκη ενδεκαδα τπυ ΟΦΗ?
Πούλησε τον Σαββίδη να μας κάνεις την τιμή να φύγεις από τον ΠΑΟΚ!!
I have friends and we have tried playing lol in a coordinated environment as a 5 man platinum team.If we were allowed to play solo as 5 people would we be able to reach diamond?Thx.
Im into lattice based cryptography.Two matrices represent the same space if a) they are of the same order , b) they have the same determinant.
My goal is to create using python a random matrix with determinant c as public key and map it into a identity matrix of the same dimension as the private key.
Now suppose we had a identity matrix.For the 2x2 case the determinant is 1 while for higher dimension identity matrices is there a general pattern for the determinant?
I want to code a python a function which both creates the public key and the private key for lattice based cryptography.But its been a while since I have studied about it and I cant find the video which made me understand it so can you help me remember it?
Suppose we start with a basis of vectors and those vectors are pretty small for conveniency. Lets say we take [{1,0},{0,1}].The smallest distance vector to point 1,1 lets say is {1,0}+{0,1}.Now we change basis to something much more difficult and we ask the same question find (smallest) coefficients a and b for the new basis such as we point to 1,1.Now all good. The new basis vector is the public key and the 2x2 matrix to give us the basis vectors 1,0 and 0,1 is the private key because with 1,0 and 0,1 we can easily calculate the smallest vector problem. My issue is if we wanted to send a message what exactly will be what we encode okay but is the encoding related to the coefficients in both basises?
Hi.I am on my way to create my own Qiskit. Here is the code
import numpy as np
class Circuit:
notGate = np.array([[0,1],[1,0]])
identityGate = np.array([[1,0],[0,1]])
hadamardGate = 1/np.sqrt(2)*np.array([[1,1],[1,-1]])
zetaGate = np.array([[1,0],[0,-1]])
listOfMatrices = []
def __init__(self):
self.initState = 1/np.sqrt(8)*np.array([[1],[1],[1],[1],[1],[1],[1],[1]])
def addNotControlledGate(self,gateName1,gateName2,gateName3):
g1 = gateName1
match g1:
case 'N':
gate1 = self.notGate
case 'I':
gate1 = self.identityGate
case 'H':
gate1 = self.hadamardGate
case 'Z':
gate1 = self.zetaGate
g2 = gateName2
match g2:
case 'N':
gate2 = self.notGate
case 'I':
gate2 = self.identityGate
case 'H':
gate2 = self.hadamardGate
case 'Z':
gate2 = self.zetaGate
g3 = gateName3
match g3:
case 'N':
gate3 = self.notGate
case 'I':
gate3 = self.identityGate
case 'H':
gate3 = self.hadamardGate
case 'Z':
gate3 = self.zetaGate
gate12 = np.kron(gate1,gate2)
gateOverall = np.kron(gate12,gate3)
print(gateOverall)
self.listOfMatrices.append(gateOverall)
return gateOverall
def addControlledGate(self,control,target,gateName):
g1 = gateName
match g1:
case 'N':
gate1 = self.notGate
case 'I':
gate1 = self.identityGate
case 'H':
gate1 = self.hadamardGate
case 'Z':
gate1 = self.zetaGate
zeroprefixgate = np.array([[1,0],[0,0]])
oneprefixgate = np.array([[0,0],[0,1]])
if control ==1:
if target == 2:
gate11 = np.kron(oneprefixgate,gate1)
gateOverall11 = np.kron(gate11,self.identityGate)
gate00 = np.kron(zeroprefixgate,self.identityGate)
gateOverall00 = np.kron(gate00,self.identityGate)
elif target == 3:
gate11 = np.kron(oneprefixgate,self.identityGate)
gateOverall11 = np.kron(gate11,gate1)
gate00 = np.kron(zeroprefixgate,self.identityGate)
gateOverall00 = np.kron(gate00,self.identityGate)
elif control ==2:
if target == 1:
gate11 = np.kron(gate1,oneprefixgate)
gateOverall11 = np.kron(gate11,self.identityGate)
gate00 = np.kron(self.identityGate,zeroprefixgate)
gateOverall00 = np.kron(gate00,self.identityGate)
elif target == 3:
gate11 = np.kron(self.identityGate,oneprefixgate)
gateOverall11 = np.kron(gate11, gate1)
gate00 = np.kron(self.identityGate,zeroprefixgate)
gateOverall00 = np.kron(gate00,self.identityGate)
elif control == 3:
if target == 1:
gate11 = np.kron(gate1,self.identityGate)
gateOverall11 = np.kron(gate11,oneprefixgate)
gate00 = np.kron(self.identityGate,self.identityGate)
gateOverall00 = np.kron(gate00,zeroprefixgate)
elif target == 2:
gate11 = np.kron(self.identityGate,gate1)
gateOverall11 = np.kron(gate11,oneprefixgate)
gate00 = np.kron(self.identityGate,self.identityGate)
gateOverall00 = np.kron(gate00,zeroprefixgate)
gateOverall = gateOverall00+gateOverall11
print(gateOverall)
self.listOfMatrices.append(gateOverall)
return gateOverall
def getState(self, i):
if i < 0:
return np.identity(8)
if i == 0:
return self.listOfMatrices[0]
x = self.listOfMatrices[i] @ self.getState(i - 1)
print(x)
return x
def getNormalisationFactorOfInitialState(self):
counter = 0
for i in range(len(self.initState)):
if self.initState[i] == 0:
continue
else:
counter+=1
print(counter)
return counter
def getFinalVector(self):
x = self.getState(1)
y = self.initState
z = x @ y
print(z)
return z
def measure(self):
x = self.getFinalVector()
y = np.abs(x)
z = np.square(y)
print(z)
I want to now add a phase gate but im unsure on how to do it.My function addControlledGate and addNotControlledGate takes 3 arguments , but I want the user to be able to select what phase the phase gate will have.How to do it?Thx.
Hi.I noticed that in Dihedral groups the 2d irrep(s) which show up(at least for D3,D5,D7...)contain a specific frequency of cyclic rotations.So this means that they can be solved by a QFT of a cyclic group.The issue is that we don't know beforehand which cyclic group that is.So I decided to try run a QPEto find the eigenvalues of that particular group and therefore find the phase but the problem here is that we don't know what U is.U must be unitary it must create orthogonal vectors after they are applied to columns which only contain the s generator of the dihedral group.If we find U then the HSP of a dihedral group becomes algorithmically valid.So let's dig into deeper.The s generators are sr^k if we could find k from information available only after the QFT then then any dihedral group becomes algorithmically useful.I have tried taking the orthogonal vectors (1,0),(ω^k,ω^-k) and (ω^-k,ω^k) but there doesn't seem to exist a 2x2 matrix which after u change the basis towards it you have 2 pairs of orthogonal vectors.So I was thinking about choosing a 3x3 matrix but I don't know if that would make any difference.What does reddit think of this?
Πάμε για τη ρεβάνς μήπως αν και δεν νομίζω.Οχι ότι η Άντερλεχτ έδειξε το αλλά τέλος πάντων.Ο μύθου είναι αχρηστος.Η ομάδα θέλει ενίσχυση για το πρωτάθλημα.Ευρωπη φέτος τπτ.
Η Λεφσκι κερδισε την Καιρατ 1-0 και παει με προβαδισμα στην ρεβανς.Ποιον θελουν οι οπαδοι της ΑΕΚ να πετυχουν και ποιον θελουμε εμεις να πετυχουμε αν γινει το θαυμα της χρονιας και αποκλεισουμε την Αντερλεχτ?
Δεν ξέρω σαν πολύ να ζοριστήκαμε με την Ντινάμο ,τώρα θα δουμε με την Άντερλεχτ πως θα πάει η ομάδα.
Πήραμε την πρόκριση σήμερα με Κωνσταντελια αλλά έχουμε πρόβλημα στο μεσοεπιθετικά.Την Άντερλεχτ δεν την περνάμε.Ας ελπίσουμε καλή κλήρωση στο Conference
I am a quantum computing nerd and one of the issues we encounter when trying to solve the HSP for nonabellian groups is that the 2d irreps are a matrix and therefore the states |0>+|1> mix.I wanted to take a step back and go back to linear algebra to try and solve this issue.Suppose in the simplest case you have a matrix 2x2.If the off diagonal elements are non 0 and if you have a vector (a,b) where a and b are coordinates in orthogonal directions then there is mixing of coordinates between a,b under that 2x2 matrix.
The 2x2 irrep of the nonabellian group D3(min order) unfortunately has this mixing due to the s generator.
I have 2 questions:Can a 2x2 matrix with offdiagonal elements represent every point in space(my intuition is yes)and if thats true does this mean that there is a unknown transform(idc which is only that there is)that takes 2 nonorthogonal vectors or signals which can produce any vector and signal?Thanks
I am a quantum computing nerd and one of the issues we encounter when trying to solve the HSP for nonabellian groups is that the 2d irreps are a matrix and therefore the states |0>+|1> mix.I wanted to take a step back and go back to linear algebra to try and solve this issue.Suppose in the simplest case you have a matrix 2x2.If the off diagonal elements are non 0 and if you have a vector (a,b) where a and b are coordinates in orthogonal directions then there is mixing of coordinates between a,b under that 2x2 matrix.
The 2x2 irrep of the nonabellian group D3(min order) unfortunately has this mixing due to the s generator.
I have 2 questions:Can a 2x2 matrix with offdiagonal elements represent every point in space(my intuition is yes)and if thats true does this mean that there is a unknown transform(idc which is only that there is)that takes 2 nonorthogonal vectors or signals which can produce any vector and signal?Thanks
Hello what do people do nowadays?The # of players in the games I was playing 10 years ago has been significantly reduced and other services seem to be failing , lacking in people.What do people do nowadays?
In assymetric cryptography we have 2 keys one which encrypts your message and one which decrypts your message.What makes assymetric cryptography more secure than symmetric cryptography is that in assymetric cryptography not any key is exchanged in any way shape or form ,only the encrypted message so encrypted message so if a 3rd party wants to spy on your message , he cannot do it , he will receive a bunch of nonsense.
I want to ask something else.Many keys can decrypt the same ecrypting keys so my question are different decrypting keys which can decrypt the same message related mathematically?I think so because im a QC nerd and I know that Shor breaks RSA encryption based on the fact that the encrypting key , encrypts data based on the modulus operation and quantum computers are really good at finding periods which is what a mod operation creates but im not entirely sure about the rest of the field.
A 1d irrep is easy to view .It is analogous to a scaling factor in vector calculus.If you had a vector of (a,b) a 1d irrep does what a scalar does , it multiplies the vector with a scalar k(a,b).How does a 2d irrep work?How can we visualise them?
I am asking because I am working on the HSP for nonabelian groups and for most nonabelian groups where for any hidden subgroup with a 2d irrep , weak Fourier sampling is not enough. So I thought maybe I can solve this graphically rather than arithmetically.