Expression of type ExprTuple

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, ExprTuple, Lambda
from proveit.core_expr_types import U_1_to_i, V_1_to_j
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import one
from proveit.physics.quantum import m_ket_domain, var_ket_psi
from proveit.physics.quantum.circuits import circuit_Ui_Vj, circuit_Ui_psi_m, circuit_psi_m_Vj
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(var_ket_psi, Conditional(Forall(instance_param_or_params = [U_1_to_i, V_1_to_j], instance_expr = Implies(Equals(Prob(circuit_Ui_psi_m), one), Equals(Prob(circuit_Ui_Vj), Prob(circuit_psi_m_Vj)).with_wrapping_at(2)).with_wrapping_at(2)).with_wrapping(), 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(\lvert \psi \rangle \mapsto \left\{\begin{array}{l}\forall_{U_{1}, U_{2}, \ldots, U_{i}, V_{1}, V_{2}, \ldots, V_{j}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{i} \\ \downarrow\end{array}} & \qout{\lvert \psi \rangle}
} \end{array}\right) = 1\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{\begin{array}{c} \uparrow \\U_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\U_{i} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\V_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\V_{2} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\V_{j} \\ \downarrow\end{array}} & \qw
} \end{array}\right) =  \\ \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \gate{\begin{array}{c} \uparrow \\V_{1} \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\\cdots \\ \downarrow\end{array}} & \gate{\begin{array}{c} \uparrow \\V_{j} \\ \downarrow\end{array}} & { /^{m} } \qw
} \end{array}\right) \end{array} \end{array}\right) \end{array} \end{array}\right)\end{array} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2^{m}}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 72 body: 3
2	ExprTuple	72
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	72, 11
10	Lambda	parameters: 12 body: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	43, 45
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	Operation	operator: 22 operands: 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	ExprTuple	27, 75
24	ExprTuple	28, 74
25	Literal
26	ExprTuple	29, 30
27	Literal
28	Operation	operator: 33 operand: 35
29	Operation	operator: 33 operand: 36
30	Operation	operator: 33 operand: 37
31	ExprTuple	35
32	ExprTuple	36
33	Literal
34	ExprTuple	37
35	Operation	operator: 40 operands: 38
36	Operation	operator: 40 operands: 39
37	Operation	operator: 40 operands: 41
38	ExprTuple	43, 42
39	ExprTuple	43, 45
40	Literal
41	ExprTuple	44, 45
42	ExprTuple	46
43	ExprRange	lambda_map: 47 start_index: 74 end_index: 48
44	ExprTuple	49
45	ExprRange	lambda_map: 50 start_index: 74 end_index: 51
46	ExprRange	lambda_map: 52 start_index: 74 end_index: 75
47	Lambda	parameter: 73 body: 53
48	Variable
49	ExprRange	lambda_map: 54 start_index: 74 end_index: 75
50	Lambda	parameter: 73 body: 55
51	Variable
52	Lambda	parameter: 73 body: 56
53	IndexedVar	variable: 57 index: 73
54	Lambda	parameter: 73 body: 58
55	IndexedVar	variable: 59 index: 73
56	Operation	operator: 62 operands: 61
57	Variable
58	Operation	operator: 62 operands: 63
59	Variable
60	ExprTuple	73
61	NamedExprs	element: 64 targets: 66
62	Literal
63	NamedExprs	element: 65 targets: 66
64	Operation	operator: 67 operands: 69
65	Operation	operator: 68 operands: 69
66	Operation	operator: 70 operands: 71
67	Literal
68	Literal
69	NamedExprs	state: 72 part: 73
70	Literal
71	ExprTuple	74, 75
72	Variable
73	Variable
74	Literal
75	Variable