logo

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 IndexedVar, Lambda, N, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Interval, one
from proveit.physics.quantum.circuits import Input, MultiQubitElem
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = Lambda(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(A_1_to_m), part = sub_expr1), targets = Interval(one, IndexedVar(N, m))))
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())
{_{-}b} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~{_{-}b}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array}
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 12
body: 2
1ExprTuple12
2Operationoperator: 3
operands: 4
3Literal
4NamedExprselement: 5
targets: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8NamedExprsstate: 11
part: 12
9Literal
10ExprTuple20, 13
11Operationoperator: 14
operands: 15
12Variable
13IndexedVarvariable: 16
index: 21
14Literal
15ExprTuple18
16Variable
17ExprTuple21
18ExprRangelambda_map: 19
start_index: 20
end_index: 21
19Lambdaparameter: 25
body: 22
20Literal
21Variable
22IndexedVarvariable: 23
index: 25
23Variable
24ExprTuple25
25Variable