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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 A, B, Lambda, S, k
from proveit.logic import Equals
from proveit.physics.quantum.circuits import MultiQubitElem, Output
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B, S], Equals(Equals(MultiQubitElem(element = Output(state = A, part = k), targets = S), MultiQubitElem(element = Output(state = B, part = k), targets = S)), Equals(A, B)))
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())
\left(A, B, S\right) \mapsto \left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{A~\mbox{part}~k~\mbox{on}~S} 
} \end{array} = \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{B~\mbox{part}~k~\mbox{on}~S} 
} \end{array}\right) = \left(A = B\right)\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple20, 21, 16
2Operationoperator: 7
operands: 3
3ExprTuple4, 5
4Operationoperator: 7
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple20, 21
9Operationoperator: 12
operands: 11
10Operationoperator: 12
operands: 13
11NamedExprselement: 14
targets: 16
12Literal
13NamedExprselement: 15
targets: 16
14Operationoperator: 18
operands: 17
15Operationoperator: 18
operands: 19
16Variable
17NamedExprsstate: 20
part: 22
18Literal
19NamedExprsstate: 21
part: 22
20Variable
21Variable
22Variable