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 ExprRange, ExprTuple, U, Variable, VertExprArray, s, t
from proveit.numbers import Add, Exp, Interval, Mod, Mult, Round, four, frac, one, pi, two
from proveit.physics.quantum import I, NumKet, Z, ket_plus, var_ket_u
from proveit.physics.quantum.QPE import QPE, phase, two_pow_t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit
from proveit.statistics import Prob

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, one)
sub_expr3 = Add(t, s)
sub_expr4 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ExprTuple(frac(four, Exp(pi, two)), Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr4), one, s)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(two_pow_t, phase)), two_pow_t), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = sub_expr4), one, s)]))))

# 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(\frac{4}{\pi^{2}}, \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\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: 3 operands: 4
2	Operation	operator: 5 operand: 9
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Literal
8	Operation	operator: 100 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 102
11	Literal
12	ExprTuple	14, 15, 16, 17
13	Literal
14	ExprTuple	18, 19
15	ExprTuple	20, 21
16	ExprTuple	22, 23
17	ExprTuple	24, 25
18	ExprRange	lambda_map: 26 start_index: 88 end_index: 103
19	ExprRange	lambda_map: 27 start_index: 88 end_index: 89
20	ExprRange	lambda_map: 28 start_index: 88 end_index: 103
21	ExprRange	lambda_map: 28 start_index: 77 end_index: 78
22	ExprRange	lambda_map: 29 start_index: 88 end_index: 103
23	ExprRange	lambda_map: 30 start_index: 88 end_index: 89
24	ExprRange	lambda_map: 31 start_index: 88 end_index: 103
25	ExprRange	lambda_map: 32 start_index: 88 end_index: 89
26	Lambda	parameter: 76 body: 33
27	Lambda	parameter: 76 body: 34
28	Lambda	parameter: 76 body: 35
29	Lambda	parameter: 76 body: 36
30	Lambda	parameter: 76 body: 37
31	Lambda	parameter: 76 body: 38
32	Lambda	parameter: 76 body: 40
33	Operation	operator: 62 operands: 41
34	Operation	operator: 48 operands: 42
35	Operation	operator: 48 operands: 43
36	Operation	operator: 44 operands: 45
37	Operation	operator: 63 operands: 46
38	Operation	operator: 48 operands: 47
39	ExprTuple	76
40	Operation	operator: 48 operands: 49
41	NamedExprs	state: 50
42	NamedExprs	element: 51 targets: 59
43	NamedExprs	element: 52 targets: 53
44	Literal
45	NamedExprs	basis: 54
46	NamedExprs	operation: 55
47	NamedExprs	element: 56 targets: 57
48	Literal
49	NamedExprs	element: 58 targets: 59
50	Operation	operator: 60 operand: 72
51	Operation	operator: 62 operands: 69
52	Operation	operator: 63 operands: 64
53	Operation	operator: 70 operands: 65
54	Literal
55	Literal
56	Operation	operator: 68 operands: 66
57	Operation	operator: 70 operands: 67
58	Operation	operator: 68 operands: 69
59	Operation	operator: 70 operands: 71
60	Literal
61	ExprTuple	72
62	Literal
63	Literal
64	NamedExprs	operation: 73 part: 76
65	ExprTuple	88, 78
66	NamedExprs	state: 74 part: 76
67	ExprTuple	88, 103
68	Literal
69	NamedExprs	state: 75 part: 76
70	Literal
71	ExprTuple	77, 78
72	Literal
73	Operation	operator: 79 operands: 80
74	Operation	operator: 81 operands: 82
75	Variable
76	Variable
77	Operation	operator: 84 operands: 83
78	Operation	operator: 84 operands: 85
79	Literal
80	ExprTuple	86, 103
81	Literal
82	ExprTuple	87, 103
83	ExprTuple	103, 88
84	Literal
85	ExprTuple	103, 89
86	Variable
87	Operation	operator: 90 operands: 91
88	Literal
89	Variable
90	Literal
91	ExprTuple	92, 98
92	Operation	operator: 93 operand: 95
93	Literal
94	ExprTuple	95
95	Operation	operator: 96 operands: 97
96	Literal
97	ExprTuple	98, 99
98	Operation	operator: 100 operands: 101
99	Variable
100	Literal
101	ExprTuple	102, 103
102	Literal
103	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 ¶