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, ExprRange, ExprTuple, IndexedVar, Lambda, U, Variable, t
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import And, Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import var_ket_u, varphi
from proveit.physics.quantum.circuits import phase_kickback_on_register_circuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(varphi, sub_expr1)
expr = ExprTuple(Lambda([ExprRange(sub_expr1, sub_expr2, one, t)], Conditional(Equals(Prob(phase_kickback_on_register_circuit), one), And(ExprRange(sub_expr1, Equals(MatrixMult(IndexedVar(U, sub_expr1), var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, sub_expr2)), var_ket_u)), one, t)))))

# 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(\varphi_{1}, \varphi_{2}, \ldots, \varphi_{t}\right) \mapsto \left\{\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert + \rangle} & \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qout{\vdots} \\
\qin{\lvert + \rangle} & \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \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_{t}} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U_{1}} & \gate{U_{2}} & \gate{\cdots} & \gate{U_{t}} & \qout{\lvert u \rangle}
} \end{array}\right) = 1 \textrm{ if } \left(\left(U_{1} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert u \rangle\right)\right) \land  \left(\left(U_{2} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert u \rangle\right)\right) \land  \ldots \land  \left(\left(U_{t} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{t}} \cdot \lvert u \rangle\right)\right)\right..\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	4
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 126 end_index: 125
5	Operation	operator: 86 operands: 8
6	Operation	operator: 9 operands: 10
7	Lambda	parameter: 135 body: 132
8	ExprTuple	11, 126
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operand: 16
12	ExprRange	lambda_map: 15 start_index: 126 end_index: 125
13	Literal
14	ExprTuple	16
15	Lambda	parameter: 135 body: 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 86 operands: 20
18	Literal
19	ExprTuple	21, 22, 23
20	ExprTuple	24, 25
21	ExprTuple	26, 27
22	ExprRange	lambda_map: 28 start_index: 126 end_index: 125
23	ExprTuple	29, 30
24	Operation	operator: 31 operands: 32
25	Operation	operator: 104 operands: 33
26	ExprRange	lambda_map: 34 start_index: 126 end_index: 125
27	ExprRange	lambda_map: 35 start_index: 126 end_index: 109
28	Lambda	parameter: 108 body: 36
29	ExprRange	lambda_map: 37 start_index: 126 end_index: 125
30	ExprRange	lambda_map: 38 start_index: 126 end_index: 109
31	Literal
32	ExprTuple	39, 73
33	ExprTuple	112, 73
34	Lambda	parameter: 135 body: 40
35	Lambda	parameter: 135 body: 41
36	ExprTuple	42, 43
37	Lambda	parameter: 135 body: 44
38	Lambda	parameter: 135 body: 45
39	IndexedVar	variable: 99 index: 135
40	Operation	operator: 59 operands: 46
41	Operation	operator: 84 operands: 47
42	ExprRange	lambda_map: 48 start_index: 126 end_index: 125
43	ExprRange	lambda_map: 49 start_index: 126 end_index: 109
44	Operation	operator: 64 operands: 50
45	Operation	operator: 84 operands: 51
46	NamedExprs	state: 52
47	NamedExprs	element: 53 targets: 70
48	Lambda	parameter: 135 body: 54
49	Lambda	parameter: 135 body: 55
50	NamedExprs	state: 56
51	NamedExprs	element: 57 targets: 70
52	Operation	operator: 119 operand: 66
53	Operation	operator: 59 operands: 65
54	Operation	operator: 60 operands: 61
55	Operation	operator: 84 operands: 62
56	Operation	operator: 104 operands: 63
57	Operation	operator: 64 operands: 65
58	ExprTuple	66
59	Literal
60	Literal
61	ExprTuple	67, 68
62	NamedExprs	element: 69 targets: 70
63	ExprTuple	71, 72
64	Literal
65	NamedExprs	state: 73 part: 135
66	Literal
67	Conditional	value: 74 condition: 75
68	Conditional	value: 76 condition: 77
69	Operation	operator: 87 operands: 78
70	Operation	operator: 79 operands: 80
71	Operation	operator: 115 operands: 81
72	Operation	operator: 82 operands: 83
73	Variable
74	Operation	operator: 84 operands: 85
75	Operation	operator: 86 operands: 90
76	Operation	operator: 87 operands: 88
77	Operation	operator: 89 operands: 90
78	NamedExprs	operation: 91 part: 135
79	Literal
80	ExprTuple	114, 92
81	ExprTuple	126, 93
82	Literal
83	ExprTuple	94, 95
84	Literal
85	NamedExprs	element: 96 targets: 97
86	Literal
87	Literal
88	NamedExprs	operation: 98
89	Literal
90	ExprTuple	108, 135
91	IndexedVar	variable: 99 index: 108
92	Operation	operator: 121 operands: 101
93	Operation	operator: 117 operands: 102
94	Operation	operator: 119 operand: 111
95	Operation	operator: 104 operands: 105
96	Literal
97	Operation	operator: 106 operand: 114
98	Literal
99	Variable
100	ExprTuple	108
101	ExprTuple	125, 109
102	ExprTuple	129, 110
103	ExprTuple	111
104	Literal
105	ExprTuple	112, 113
106	Literal
107	ExprTuple	114
108	Variable
109	Variable
110	Operation	operator: 115 operands: 116
111	Literal
112	Operation	operator: 117 operands: 118
113	Operation	operator: 119 operand: 126
114	Operation	operator: 121 operands: 122
115	Literal
116	ExprTuple	126, 129
117	Literal
118	ExprTuple	123, 124
119	Literal
120	ExprTuple	126
121	Literal
122	ExprTuple	125, 126
123	Literal
124	Operation	operator: 127 operands: 128
125	Variable
126	Literal
127	Literal
128	ExprTuple	129, 130, 131, 132
129	Literal
130	Literal
131	Literal
132	IndexedVar	variable: 133 index: 135
133	Variable
134	ExprTuple	135
135	Variable

Expression of type ExprTuple¶

from the theory of proveit.physics.quantum.circuits¶

Expression of type ExprTuple ¶

from the theory of proveit.physics.quantum.circuits ¶