Nathaniel: Fixed scaling of probability vector

2025-03-28T12:53:41Z

Fixed scaling of probability vector

← Older revision		Revision as of 12:53, 28 March 2025
Line 58:		Line 58:
	The following code generates a Pauli channel with Kraus operators $\left\{\tfrac{1}{\sqrt{15}}I,\tfrac{2}{\sqrt{15}}X,\tfrac{3}{\sqrt{15}}Y,\tfrac{4}{\sqrt{15}}Z\right\}$, where $I,X,Y,Z$ are the usual [[Pauli\|Pauli operators]]:		The following code generates a Pauli channel with Kraus operators $\left\{\tfrac{1}{\sqrt{15}}I,\tfrac{2}{\sqrt{15}}X,\tfrac{3}{\sqrt{15}}Y,\tfrac{4}{\sqrt{15}}Z\right\}$, where $I,X,Y,Z$ are the usual [[Pauli\|Pauli operators]]:
	<syntaxhighlight>		<syntaxhighlight>
	>> Phi = full(PauliChannel([1,2,3,4]/15))		>> Phi = full(PauliChannel([1,2,3,4]/10))

	Phi =		Phi =

	0.~~3333~~ 0 0 -0.~~2000~~		0.5000 0 0 -0.3000
	0 0.~~3333~~ -0.~~0667~~ 0		0 0.5000 -0.1000 0
	0 -0.~~0667~~ 0.~~3333~~ 0		0 -0.1000 0.5000 0
	-0.~~2000~~ 0 0 0.~~3333~~		-0.3000 0 0 0.5000

	>> celldisp(KrausOperators(Phi)) % look at its Kraus operators		>> celldisp(KrausOperators(Phi)) % look at its Kraus operators
Line 71:		Line 71:
	ans{1} =		ans{1} =

	-0.~~5164 0.~~0000		-0.6325 0
	0 0.~~5164~~		0 0.6325


Line 78:		Line 78:
	ans{2} =		ans{2} =

	-0.~~0000 0.4472~~		0 -0.5477
	~~-0.4472 -~~0.0000		0.5477 0


Line 85:		Line 85:
	ans{3} =		ans{3} =

	-0.~~0000~~ 0.~~3651~~		0 -0.4472
	~~0.3651 -0.~~0000		-0.4472 0


Line 92:		Line 92:
	ans{4} =		ans{4} =

	-0.~~2582 -0.~~0000		-0.3162 0
	0 -0.~~2582~~		0 -0.3162
	</syntaxhighlight>		</syntaxhighlight>

	{{SourceCode\|name=PauliChannel}}		{{SourceCode\|name=PauliChannel}}

Nathaniel: Created page with "{{Function |name=PauliChannel |desc=Generates a Pauli channel |rel=Pauli |cat=Superoperators |upd=December 16, 2014}} `'''PauliChan..."`

2015-01-14T19:46:27Z Created page with "{{Function |name=PauliChannel |desc=Generates a Pauli channel |rel=Pauli |cat=Superoperators |upd=December 16, 2014}} <tt>'''PauliChan..." New page {{Function |name=PauliChannel |desc=Generates a Pauli channel |rel=[[Pauli]] |cat=[[List of functions#Superoperators|Superoperators]] |upd=December 16, 2014}} <tt>'''PauliChannel'''</tt> is a [[List of functions|function]] that generates the Choi matrix of a Pauli channel (either a random Pauli channel on a specified number of qubits, or a specific Pauli channel requested by the user). The output of this function is sparse. ==Syntax== * <tt>PHI = PauliChannel(P)</tt> ==Argument descriptions== * <tt>P</tt>: Either a positive integer, indicating that the user wants a randomly-generated <tt>P</tt>-qubit Pauli channel. Otherwise, <tt>P</tt> should be a probability vector of length $4^q$ for some integer $q \geq 1$, whose entries specify the weights of the Pauli operators in the channel's Kraus decomposition. More specifically, the weight of the $j$-th Pauli operator (in lexicographical order) in the Kraus operator representation of this channel will be $\sqrt{P(j)}$. ==Examples== ===A random 1-qubit Pauli channel=== The following code returns the Choi matrix a randomly-generated 1-qubit Pauli channel: <syntaxhighlight> >> Phi = full(PauliChannel(1)) % generate the random Pauli channel Phi = 0.5737 0 0 0.1346 0 0.4263 0.3196 0 0 0.3196 0.4263 0 0.1346 0 0 0.5737 >> celldisp(KrausOperators(Phi)) % look at its Kraus operators ans{1} = 0 0.6107 0.6107 0 ans{2} = 0.5951 0 0 0.5951 ans{3} = 0.4686 0 0 -0.4686 ans{4} = 0 0.2310 -0.2310 0 </syntaxhighlight> ===A specific Pauli channel=== The following code generates a Pauli channel with Kraus operators $\left\{\tfrac{1}{\sqrt{15}}I,\tfrac{2}{\sqrt{15}}X,\tfrac{3}{\sqrt{15}}Y,\tfrac{4}{\sqrt{15}}Z\right\}$, where $I,X,Y,Z$ are the usual [[Pauli|Pauli operators]]: <syntaxhighlight> >> Phi = full(PauliChannel([1,2,3,4]/15)) Phi = 0.3333 0 0 -0.2000 0 0.3333 -0.0667 0 0 -0.0667 0.3333 0 -0.2000 0 0 0.3333 >> celldisp(KrausOperators(Phi)) % look at its Kraus operators ans{1} = -0.5164 0.0000 0 0.5164 ans{2} = -0.0000 0.4472 -0.4472 -0.0000 ans{3} = -0.0000 0.3651 0.3651 -0.0000 ans{4} = -0.2582 -0.0000 0 -0.2582 </syntaxhighlight> {{SourceCode|name=PauliChannel}}

PauliChannel - Revision history

Nathaniel: Fixed scaling of probability vector

Nathaniel: Created page with "{{Function |name=PauliChannel |desc=Generates a Pauli channel |rel=Pauli |cat=Superoperators |upd=December 16, 2014}} '''PauliChan..."

Nathaniel: Created page with "{{Function |name=PauliChannel |desc=Generates a Pauli channel |rel=Pauli |cat=Superoperators |upd=December 16, 2014}} `'''PauliChan..."`