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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 Lambda, k
from proveit.logic import Equals, Forall
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(var_ket_psi, Forall(instance_param_or_params = [k], instance_expr = Equals(MultiQubitElem(element = Output(state = var_ket_psi, part = one), targets = Interval(k, k)), Output(state = var_ket_psi)), domain = 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())
\lvert \psi \rangle \mapsto \left[\forall_{k \in \mathbb{N}^+}~\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}\right)\right]
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 26
body: 2
1ExprTuple26
2Operationoperator: 3
operand: 5
3Literal
4ExprTuple5
5Lambdaparameter: 28
body: 7
6ExprTuple28
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operands: 11
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14, 15
12Literal
13ExprTuple28, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 22
operands: 19
16Literal
17Literal
18NamedExprselement: 20
targets: 21
19NamedExprsstate: 26
20Operationoperator: 22
operands: 23
21Operationoperator: 24
operands: 25
22Literal
23NamedExprsstate: 26
part: 27
24Literal
25ExprTuple28, 28
26Variable
27Literal
28Variable