Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

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, U, m
from proveit.linear_algebra import Unitary
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, one, two
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import unitary_gate_op
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Lambda([U, var_ket_psi], Conditional(Equals(Prob(unitary_gate_op), one), And(InSet(U, Unitary(Exp(two, m))), InSet(var_ket_psi, m_ket_domain))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(U, \lvert \psi \rangle\right) \mapsto \left\{\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \gate{U} & \qout{U \thinspace \lvert \psi \rangle}
} \end{array}\right) = 1 \textrm{ if } U \in \textrm{U}\left(2^{m}\right) ,  \lvert \psi \rangle \in \mathbb{C}^{2^{m}}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 64 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 61
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operand: 16
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	16
13	ExprTuple	65, 17
14	Literal
15	ExprTuple	66, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operand: 29
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	25, 26, 27
21	Literal
22	ExprTuple	29
23	Literal
24	ExprTuple	28, 29
25	ExprTuple	30
26	ExprTuple	31
27	ExprTuple	32
28	Literal
29	Operation	operator: 33 operands: 34
30	ExprRange	lambda_map: 35 start_index: 61 end_index: 62
31	ExprRange	lambda_map: 36 start_index: 61 end_index: 62
32	ExprRange	lambda_map: 37 start_index: 61 end_index: 62
33	Literal
34	ExprTuple	38, 62
35	Lambda	parameter: 60 body: 39
36	Lambda	parameter: 60 body: 40
37	Lambda	parameter: 60 body: 42
38	Literal
39	Operation	operator: 45 operands: 43
40	Operation	operator: 45 operands: 44
41	ExprTuple	60
42	Operation	operator: 45 operands: 46
43	NamedExprs	element: 47 targets: 50
44	NamedExprs	element: 48 targets: 50
45	Literal
46	NamedExprs	element: 49 targets: 50
47	Operation	operator: 51 operands: 52
48	Operation	operator: 53 operands: 54
49	Operation	operator: 55 operands: 56
50	Operation	operator: 57 operands: 58
51	Literal
52	NamedExprs	state: 66 part: 60
53	Literal
54	NamedExprs	operation: 65 part: 60
55	Literal
56	NamedExprs	state: 59 part: 60
57	Literal
58	ExprTuple	61, 62
59	Operation	operator: 63 operands: 64
60	Variable
61	Literal
62	Variable
63	Literal
64	ExprTuple	65, 66
65	Variable
66	Variable