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 Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import Qmult, 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(varphi, Conditional(Equals(Prob(phase_kickback_circuit), one), Equals(Qmult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, varphi)), 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(\varphi \mapsto \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 \textrm{ if } \left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)\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: 102 body: 3
2	ExprTuple	102
3	Conditional	value: 4 condition: 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 96
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operand: 17
10	Operation	operator: 14 operands: 15
11	Operation	operator: 79 operands: 16
12	Literal
13	ExprTuple	17
14	Literal
15	ExprTuple	70, 74
16	ExprTuple	85, 74
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21, 22
20	ExprTuple	23, 24
21	ExprTuple	25, 26
22	ExprTuple	27, 28
23	Operation	operator: 60 operands: 29
24	ExprRange	lambda_map: 30 start_index: 96 end_index: 35
25	Operation	operator: 51 operands: 31
26	ExprRange	lambda_map: 32 start_index: 96 end_index: 35
27	Operation	operator: 66 operands: 33
28	ExprRange	lambda_map: 34 start_index: 96 end_index: 35
29	NamedExprs	state: 36
30	Lambda	parameter: 75 body: 37
31	NamedExprs	element: 38 targets: 39
32	Lambda	parameter: 75 body: 40
33	NamedExprs	state: 41
34	Lambda	parameter: 75 body: 43
35	Operation	operator: 81 operands: 44
36	Operation	operator: 92 operand: 53
37	Operation	operator: 51 operands: 46
38	Literal
39	Operation	operator: 47 operand: 99
40	Operation	operator: 51 operands: 49
41	Operation	operator: 79 operands: 50
42	ExprTuple	75
43	Operation	operator: 51 operands: 52
44	ExprTuple	87, 96
45	ExprTuple	53
46	NamedExprs	element: 54 targets: 59
47	Literal
48	ExprTuple	99
49	NamedExprs	element: 55 targets: 59
50	ExprTuple	56, 57
51	Literal
52	NamedExprs	element: 58 targets: 59
53	Literal
54	Operation	operator: 60 operands: 67
55	Operation	operator: 61 operands: 62
56	Operation	operator: 88 operands: 63
57	Operation	operator: 64 operands: 65
58	Operation	operator: 66 operands: 67
59	Operation	operator: 68 operands: 69
60	Literal
61	Literal
62	NamedExprs	operation: 70 part: 75
63	ExprTuple	96, 71
64	Literal
65	ExprTuple	72, 73
66	Literal
67	NamedExprs	state: 74 part: 75
68	Literal
69	ExprTuple	99, 76
70	Variable
71	Operation	operator: 90 operands: 77
72	Operation	operator: 92 operand: 84
73	Operation	operator: 79 operands: 80
74	Variable
75	Variable
76	Operation	operator: 81 operands: 82
77	ExprTuple	99, 83
78	ExprTuple	84
79	Literal
80	ExprTuple	85, 86
81	Literal
82	ExprTuple	87, 99
83	Operation	operator: 88 operands: 89
84	Literal
85	Operation	operator: 90 operands: 91
86	Operation	operator: 92 operand: 96
87	Variable
88	Literal
89	ExprTuple	96, 99
90	Literal
91	ExprTuple	94, 95
92	Literal
93	ExprTuple	96
94	Literal
95	Operation	operator: 97 operands: 98
96	Literal
97	Literal
98	ExprTuple	99, 100, 101, 102
99	Literal
100	Literal
101	Literal
102	Variable