Expression of type ExprTuple ¶

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

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, ConditionalSet, ExprRange, ExprTuple, Variable, VertExprArray, t
from proveit.linear_algebra import MatrixExp, ScalarMult, VecAdd
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import CONTROL, ket0, ket1, ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _phase, _s
from proveit.physics.quantum.circuits import Gate, Igate, Input, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr3 = Add(t, one)
sub_expr4 = Add(t, _s)
sub_expr5 = Add(sub_expr2, t)
sub_expr6 = Interval(sub_expr3, sub_expr4)
sub_expr7 = Add(Neg(t), one)
sub_expr8 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr9 = [ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr6), one, _s)]
sub_expr10 = [ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), sub_expr7, zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr6), one, _s)]
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray(sub_expr9, ExprRange(sub_expr2, [ExprRange(sub_expr1, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr5, sub_expr1)), Conditional(Igate, NotEquals(sub_expr5, sub_expr1))), one, t).with_case_simplification(), ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = MatrixExp(_U, Exp(two, Neg(sub_expr2))), part = sub_expr1), targets = sub_expr6), one, _s)], sub_expr7, zero).with_decreasing_order(), sub_expr10)), Qcircuit(vert_expr_array = VertExprArray(sub_expr9, [ExprRange(sub_expr1, sub_expr8, one, t), ExprRange(sub_expr1, sub_expr8, sub_expr3, sub_expr4)], sub_expr10)))

# 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(\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 2^{t - 1} \cdot \varphi} \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 2^{t - 2} \cdot \varphi} \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 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U^{2^{t - 1}}} & \gate{U^{2^{t - 2}}} & \gate{\cdots} & \gate{U^{2^{0}}} & \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\vdots} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

	core type	sub-expressions
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	7, 6, 9
4	Literal
5	ExprTuple	7, 8, 9
6	ExprRange	lambda_map: 10 start_index: 22 end_index: 110
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprTuple	15, 16
10	Lambda	parameter: 130 body: 17
11	ExprRange	lambda_map: 18 start_index: 126 end_index: 125
12	ExprRange	lambda_map: 19 start_index: 126 end_index: 108
13	ExprRange	lambda_map: 20 start_index: 126 end_index: 125
14	ExprRange	lambda_map: 20 start_index: 113 end_index: 88
15	ExprRange	lambda_map: 21 start_index: 22 end_index: 110
16	ExprRange	lambda_map: 23 start_index: 126 end_index: 108
17	ExprTuple	24, 25
18	Lambda	parameter: 141 body: 26
19	Lambda	parameter: 141 body: 27
20	Lambda	parameter: 141 body: 28
21	Lambda	parameter: 141 body: 29
22	Operation	operator: 120 operands: 30
23	Lambda	parameter: 141 body: 31
24	ExprRange	lambda_map: 32 start_index: 126 end_index: 125
25	ExprRange	lambda_map: 33 start_index: 126 end_index: 108
26	Operation	operator: 53 operands: 34
27	Operation	operator: 80 operands: 35
28	Operation	operator: 80 operands: 36
29	Operation	operator: 57 operands: 37
30	ExprTuple	38, 126
31	Operation	operator: 80 operands: 39
32	Lambda	parameter: 141 body: 40
33	Lambda	parameter: 141 body: 41
34	NamedExprs	state: 42
35	NamedExprs	element: 43 targets: 62
36	NamedExprs	element: 44 targets: 45
37	NamedExprs	state: 46
38	Operation	operator: 139 operand: 125
39	NamedExprs	element: 48 targets: 62
40	Operation	operator: 49 operands: 50
41	Operation	operator: 80 operands: 51
42	Operation	operator: 118 operand: 63
43	Operation	operator: 53 operands: 58
44	Operation	operator: 83 operands: 54
45	Operation	operator: 73 operands: 55
46	Operation	operator: 101 operands: 56
47	ExprTuple	125
48	Operation	operator: 57 operands: 58
49	Literal
50	ExprTuple	59, 60
51	NamedExprs	element: 61 targets: 62
52	ExprTuple	63
53	Literal
54	NamedExprs	operation: 64 part: 141
55	ExprTuple	126, 88
56	ExprTuple	65, 66
57	Literal
58	NamedExprs	state: 67 part: 141
59	Conditional	value: 68 condition: 69
60	Conditional	value: 70 condition: 71
61	Operation	operator: 83 operands: 72
62	Operation	operator: 73 operands: 74
63	Literal
64	Operation	operator: 75 operands: 76
65	Operation	operator: 115 operands: 77
66	Operation	operator: 78 operands: 79
67	Literal
68	Operation	operator: 80 operands: 81
69	Operation	operator: 82 operands: 86
70	Operation	operator: 83 operands: 84
71	Operation	operator: 85 operands: 86
72	NamedExprs	operation: 87 part: 141
73	Literal
74	ExprTuple	113, 88
75	Literal
76	ExprTuple	106, 125
77	ExprTuple	126, 89
78	Literal
79	ExprTuple	90, 91
80	Literal
81	NamedExprs	element: 92 targets: 93
82	Literal
83	Literal
84	NamedExprs	operation: 94
85	Literal
86	ExprTuple	95, 141
87	Operation	operator: 96 operands: 97
88	Operation	operator: 120 operands: 98
89	Operation	operator: 135 operands: 99
90	Operation	operator: 118 operand: 110
91	Operation	operator: 101 operands: 102
92	Literal
93	Operation	operator: 103 operand: 113
94	Literal
95	Operation	operator: 120 operands: 105
96	Literal
97	ExprTuple	106, 107
98	ExprTuple	125, 108
99	ExprTuple	137, 109
100	ExprTuple	110
101	Literal
102	ExprTuple	111, 112
103	Literal
104	ExprTuple	113
105	ExprTuple	130, 125
106	Literal
107	Operation	operator: 135 operands: 114
108	Literal
109	Operation	operator: 115 operands: 116
110	Literal
111	Operation	operator: 135 operands: 117
112	Operation	operator: 118 operand: 126
113	Operation	operator: 120 operands: 121
114	ExprTuple	137, 122
115	Literal
116	ExprTuple	126, 137
117	ExprTuple	123, 124
118	Literal
119	ExprTuple	126
120	Literal
121	ExprTuple	125, 126
122	Operation	operator: 139 operand: 130
123	Literal
124	Operation	operator: 128 operands: 129
125	Variable
126	Literal
127	ExprTuple	130
128	Literal
129	ExprTuple	137, 131, 132, 133, 134
130	Variable
131	Literal
132	Literal
133	Operation	operator: 135 operands: 136
134	Literal
135	Literal
136	ExprTuple	137, 138
137	Literal
138	Operation	operator: 139 operand: 141
139	Literal
140	ExprTuple	141
141	Variable

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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