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Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, k
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, NaturalPos, one
from proveit.physics.quantum import var_ket_psi
from proveit.physics.quantum.circuits import MultiQubitElem, Output
In [2]:
# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Equals(MultiQubitElem(element = Output(state = var_ket_psi, part = one), targets = Interval(k, k)), Output(state = var_ket_psi)), InSet(k, NaturalPos)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
k \mapsto \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle~\mbox{part}~1~\mbox{on}~\{k~\ldotp \ldotp~k\}} 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle} 
} \end{array} \textrm{ if } k \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 23
body: 2
1ExprTuple23
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple23, 11
9Operationoperator: 12
operands: 13
10Operationoperator: 17
operands: 14
11Literal
12Literal
13NamedExprselement: 15
targets: 16
14NamedExprsstate: 21
15Operationoperator: 17
operands: 18
16Operationoperator: 19
operands: 20
17Literal
18NamedExprsstate: 21
part: 22
19Literal
20ExprTuple23, 23
21Variable
22Literal
23Variable