Expression of type Conditional ¶

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, 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 = Conditional(Equals(Prob(phase_kickback_circuit), one), Equals(Qmult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, varphi)), var_ket_u)))

# 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\{\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..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 93
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operand: 14
7	Operation	operator: 11 operands: 12
8	Operation	operator: 76 operands: 13
9	Literal
10	ExprTuple	14
11	Literal
12	ExprTuple	67, 71
13	ExprTuple	82, 71
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18, 19
17	ExprTuple	20, 21
18	ExprTuple	22, 23
19	ExprTuple	24, 25
20	Operation	operator: 57 operands: 26
21	ExprRange	lambda_map: 27 start_index: 93 end_index: 32
22	Operation	operator: 48 operands: 28
23	ExprRange	lambda_map: 29 start_index: 93 end_index: 32
24	Operation	operator: 63 operands: 30
25	ExprRange	lambda_map: 31 start_index: 93 end_index: 32
26	NamedExprs	state: 33
27	Lambda	parameter: 72 body: 34
28	NamedExprs	element: 35 targets: 36
29	Lambda	parameter: 72 body: 37
30	NamedExprs	state: 38
31	Lambda	parameter: 72 body: 40
32	Operation	operator: 78 operands: 41
33	Operation	operator: 89 operand: 50
34	Operation	operator: 48 operands: 43
35	Literal
36	Operation	operator: 44 operand: 96
37	Operation	operator: 48 operands: 46
38	Operation	operator: 76 operands: 47
39	ExprTuple	72
40	Operation	operator: 48 operands: 49
41	ExprTuple	84, 93
42	ExprTuple	50
43	NamedExprs	element: 51 targets: 56
44	Literal
45	ExprTuple	96
46	NamedExprs	element: 52 targets: 56
47	ExprTuple	53, 54
48	Literal
49	NamedExprs	element: 55 targets: 56
50	Literal
51	Operation	operator: 57 operands: 64
52	Operation	operator: 58 operands: 59
53	Operation	operator: 85 operands: 60
54	Operation	operator: 61 operands: 62
55	Operation	operator: 63 operands: 64
56	Operation	operator: 65 operands: 66
57	Literal
58	Literal
59	NamedExprs	operation: 67 part: 72
60	ExprTuple	93, 68
61	Literal
62	ExprTuple	69, 70
63	Literal
64	NamedExprs	state: 71 part: 72
65	Literal
66	ExprTuple	96, 73
67	Variable
68	Operation	operator: 87 operands: 74
69	Operation	operator: 89 operand: 81
70	Operation	operator: 76 operands: 77
71	Variable
72	Variable
73	Operation	operator: 78 operands: 79
74	ExprTuple	96, 80
75	ExprTuple	81
76	Literal
77	ExprTuple	82, 83
78	Literal
79	ExprTuple	84, 96
80	Operation	operator: 85 operands: 86
81	Literal
82	Operation	operator: 87 operands: 88
83	Operation	operator: 89 operand: 93
84	Variable
85	Literal
86	ExprTuple	93, 96
87	Literal
88	ExprTuple	91, 92
89	Literal
90	ExprTuple	93
91	Literal
92	Operation	operator: 94 operands: 95
93	Literal
94	Literal
95	ExprTuple	96, 97, 98, 99
96	Literal
97	Literal
98	Literal
99	Variable

Expression of type Conditional¶

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

Expression of type Conditional ¶

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