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, 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 = ExprTuple(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(\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..\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	parameters: 65 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 62
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operand: 17
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprTuple	17
14	ExprTuple	66, 18
15	Literal
16	ExprTuple	67, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operand: 30
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	26, 27, 28
22	Literal
23	ExprTuple	30
24	Literal
25	ExprTuple	29, 30
26	ExprTuple	31
27	ExprTuple	32
28	ExprTuple	33
29	Literal
30	Operation	operator: 34 operands: 35
31	ExprRange	lambda_map: 36 start_index: 62 end_index: 63
32	ExprRange	lambda_map: 37 start_index: 62 end_index: 63
33	ExprRange	lambda_map: 38 start_index: 62 end_index: 63
34	Literal
35	ExprTuple	39, 63
36	Lambda	parameter: 61 body: 40
37	Lambda	parameter: 61 body: 41
38	Lambda	parameter: 61 body: 43
39	Literal
40	Operation	operator: 46 operands: 44
41	Operation	operator: 46 operands: 45
42	ExprTuple	61
43	Operation	operator: 46 operands: 47
44	NamedExprs	element: 48 targets: 51
45	NamedExprs	element: 49 targets: 51
46	Literal
47	NamedExprs	element: 50 targets: 51
48	Operation	operator: 52 operands: 53
49	Operation	operator: 54 operands: 55
50	Operation	operator: 56 operands: 57
51	Operation	operator: 58 operands: 59
52	Literal
53	NamedExprs	state: 67 part: 61
54	Literal
55	NamedExprs	operation: 66 part: 61
56	Literal
57	NamedExprs	state: 60 part: 61
58	Literal
59	ExprTuple	62, 63
60	Operation	operator: 64 operands: 65
61	Variable
62	Literal
63	Variable
64	Literal
65	ExprTuple	66, 67
66	Variable
67	Variable