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
from proveit.linear_algebra import ScalarMult
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import Qmult, m_ket_domain, normalized_var_ket_u, var_ket_u, varphi
from proveit.physics.quantum.circuits import phase_kickback_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(var_ket_u, Conditional(Forall(instance_param_or_params = [varphi], instance_expr = Equals(Prob(phase_kickback_circuit), one), condition = Equals(Qmult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, varphi)), var_ket_u))), And(InSet(var_ket_u, m_ket_domain), normalized_var_ket_u))))

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 u \rangle \mapsto \left\{\forall_{\varphi~|~\left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)}~\left(\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \control{} \qw \qwx[1] & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U} & \qout{\lvert u \rangle}
} \end{array}\right) = 1\right) \textrm{ if } \lvert u \rangle \in \mathbb{C}^{2^{m}} ,  \left \|\lvert u \rangle\right \| = 1\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: 96 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 124 body: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 22 operands: 16
12	ExprTuple	124
13	Conditional	value: 17 condition: 18
14	Literal
15	ExprTuple	96, 19
16	ExprTuple	20, 118
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 26 operand: 96
21	ExprTuple	28, 118
22	Literal
23	ExprTuple	29, 30
24	Literal
25	ExprTuple	31, 32
26	Literal
27	ExprTuple	96
28	Operation	operator: 33 operand: 39
29	Operation	operator: 35 operands: 36
30	Operation	operator: 101 operands: 37
31	Literal
32	Operation	operator: 112 operands: 38
33	Literal
34	ExprTuple	39
35	Literal
36	ExprTuple	92, 96
37	ExprTuple	107, 96
38	ExprTuple	121, 109
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43, 44
42	ExprTuple	45, 46
43	ExprTuple	47, 48
44	ExprTuple	49, 50
45	Operation	operator: 82 operands: 51
46	ExprRange	lambda_map: 52 start_index: 118 end_index: 57
47	Operation	operator: 73 operands: 53
48	ExprRange	lambda_map: 54 start_index: 118 end_index: 57
49	Operation	operator: 88 operands: 55
50	ExprRange	lambda_map: 56 start_index: 118 end_index: 57
51	NamedExprs	state: 58
52	Lambda	parameter: 97 body: 59
53	NamedExprs	element: 60 targets: 61
54	Lambda	parameter: 97 body: 62
55	NamedExprs	state: 63
56	Lambda	parameter: 97 body: 65
57	Operation	operator: 103 operands: 66
58	Operation	operator: 114 operand: 75
59	Operation	operator: 73 operands: 68
60	Literal
61	Operation	operator: 69 operand: 121
62	Operation	operator: 73 operands: 71
63	Operation	operator: 101 operands: 72
64	ExprTuple	97
65	Operation	operator: 73 operands: 74
66	ExprTuple	109, 118
67	ExprTuple	75
68	NamedExprs	element: 76 targets: 81
69	Literal
70	ExprTuple	121
71	NamedExprs	element: 77 targets: 81
72	ExprTuple	78, 79
73	Literal
74	NamedExprs	element: 80 targets: 81
75	Literal
76	Operation	operator: 82 operands: 89
77	Operation	operator: 83 operands: 84
78	Operation	operator: 110 operands: 85
79	Operation	operator: 86 operands: 87
80	Operation	operator: 88 operands: 89
81	Operation	operator: 90 operands: 91
82	Literal
83	Literal
84	NamedExprs	operation: 92 part: 97
85	ExprTuple	118, 93
86	Literal
87	ExprTuple	94, 95
88	Literal
89	NamedExprs	state: 96 part: 97
90	Literal
91	ExprTuple	121, 98
92	Variable
93	Operation	operator: 112 operands: 99
94	Operation	operator: 114 operand: 106
95	Operation	operator: 101 operands: 102
96	Variable
97	Variable
98	Operation	operator: 103 operands: 104
99	ExprTuple	121, 105
100	ExprTuple	106
101	Literal
102	ExprTuple	107, 108
103	Literal
104	ExprTuple	109, 121
105	Operation	operator: 110 operands: 111
106	Literal
107	Operation	operator: 112 operands: 113
108	Operation	operator: 114 operand: 118
109	Variable
110	Literal
111	ExprTuple	118, 121
112	Literal
113	ExprTuple	116, 117
114	Literal
115	ExprTuple	118
116	Literal
117	Operation	operator: 119 operands: 120
118	Literal
119	Literal
120	ExprTuple	121, 122, 123, 124
121	Literal
122	Literal
123	Literal
124	Variable