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, Variable, VertExprArray, m
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _phase_est_circuit, _s, _s_wire, _t
from proveit.physics.quantum.circuits import 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 = Interval(one, _t)
sub_expr3 = Interval(Add(_t, one), Add(_t, _s))
expr = ExprTuple(Prob(_phase_est_circuit), Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3), 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(\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 m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \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 m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right), \textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{3}{\lvert \Psi \rangle} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\ghostqin{\lvert \Psi \rangle} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & { /^{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: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12, 14, 15
9	Literal
10	ExprTuple	13, 14, 15
11	ExprTuple	16, 20
12	ExprTuple	17, 18
13	ExprTuple	19, 20
14	ExprTuple	21, 22
15	ExprTuple	23, 24
16	ExprRange	lambda_map: 25 start_index: 93 end_index: 94
17	ExprRange	lambda_map: 26 start_index: 93 end_index: 94
18	ExprRange	lambda_map: 26 start_index: 82 end_index: 83
19	ExprRange	lambda_map: 27 start_index: 93 end_index: 94
20	ExprRange	lambda_map: 28 start_index: 93 end_index: 95
21	ExprRange	lambda_map: 29 start_index: 93 end_index: 94
22	ExprRange	lambda_map: 30 start_index: 93 end_index: 95
23	ExprRange	lambda_map: 31 start_index: 93 end_index: 94
24	ExprRange	lambda_map: 32 start_index: 93 end_index: 95
25	Lambda	parameter: 81 body: 33
26	Lambda	parameter: 81 body: 34
27	Lambda	parameter: 81 body: 35
28	Lambda	parameter: 81 body: 36
29	Lambda	parameter: 81 body: 37
30	Lambda	parameter: 81 body: 38
31	Lambda	parameter: 81 body: 39
32	Lambda	parameter: 81 body: 41
33	Operation	operator: 69 operands: 42
34	Operation	operator: 50 operands: 43
35	Operation	operator: 50 operands: 44
36	Operation	operator: 50 operands: 45
37	Operation	operator: 46 operands: 47
38	Operation	operator: 65 operands: 48
39	Operation	operator: 50 operands: 49
40	ExprTuple	81
41	Operation	operator: 50 operands: 51
42	NamedExprs	state: 52
43	NamedExprs	element: 53 targets: 54
44	NamedExprs	element: 55 targets: 60
45	NamedExprs	element: 56 targets: 62
46	Literal
47	NamedExprs	basis: 57
48	NamedExprs	operation: 58
49	NamedExprs	element: 59 targets: 60
50	Literal
51	NamedExprs	element: 61 targets: 62
52	Operation	operator: 63 operand: 76
53	Operation	operator: 65 operands: 66
54	Operation	operator: 74 operands: 67
55	Operation	operator: 69 operands: 68
56	Operation	operator: 69 operands: 73
57	Literal
58	Literal
59	Operation	operator: 72 operands: 70
60	Operation	operator: 74 operands: 71
61	Operation	operator: 72 operands: 73
62	Operation	operator: 74 operands: 75
63	Literal
64	ExprTuple	76
65	Literal
66	NamedExprs	operation: 77 part: 81
67	ExprTuple	93, 83
68	NamedExprs	state: 78 part: 81
69	Literal
70	NamedExprs	state: 79 part: 81
71	ExprTuple	93, 94
72	Literal
73	NamedExprs	state: 80 part: 81
74	Literal
75	ExprTuple	82, 83
76	Literal
77	Operation	operator: 84 operands: 85
78	Literal
79	Operation	operator: 86 operands: 87
80	Literal
81	Variable
82	Operation	operator: 89 operands: 88
83	Operation	operator: 89 operands: 90
84	Literal
85	ExprTuple	91, 94
86	Literal
87	ExprTuple	92, 94
88	ExprTuple	94, 93
89	Literal
90	ExprTuple	94, 95
91	Literal
92	Variable
93	Literal
94	Literal
95	Literal

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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