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, t
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit

# 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 = Interval(one, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = sub_expr5)
sub_expr7 = MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = sub_expr1), targets = sub_expr5)
sub_expr8 = [ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]
sub_expr9 = [ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)]
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr9, [ExprRange(sub_expr1, sub_expr7, one, t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr7, sub_expr2, sub_expr3).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr9, [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi_t_ket, part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{4}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \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)} & \multiqout{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\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, 8, 6
4	Literal
5	ExprTuple	7, 8, 9
6	ExprTuple	10, 11
7	ExprTuple	12, 13
8	ExprTuple	14, 15
9	ExprTuple	16, 17
10	ExprRange	lambda_map: 18 start_index: 76 end_index: 80
11	ExprRange	lambda_map: 18 start_index: 64 end_index: 65
12	ExprRange	lambda_map: 19 start_index: 76 end_index: 80
13	ExprRange	lambda_map: 20 start_index: 76 end_index: 77
14	ExprRange	lambda_map: 21 start_index: 76 end_index: 80
15	ExprRange	lambda_map: 21 start_index: 64 end_index: 65
16	ExprRange	lambda_map: 22 start_index: 76 end_index: 80
17	ExprRange	lambda_map: 23 start_index: 76 end_index: 77
18	Lambda	parameter: 63 body: 24
19	Lambda	parameter: 63 body: 25
20	Lambda	parameter: 63 body: 26
21	Lambda	parameter: 63 body: 27
22	Lambda	parameter: 63 body: 28
23	Lambda	parameter: 63 body: 30
24	Operation	operator: 36 operands: 31
25	Operation	operator: 50 operands: 32
26	Operation	operator: 36 operands: 33
27	Operation	operator: 36 operands: 34
28	Operation	operator: 36 operands: 35
29	ExprTuple	63
30	Operation	operator: 36 operands: 37
31	NamedExprs	element: 38 targets: 42
32	NamedExprs	state: 39
33	NamedExprs	element: 40 targets: 46
34	NamedExprs	element: 41 targets: 42
35	NamedExprs	element: 43 targets: 44
36	Literal
37	NamedExprs	element: 45 targets: 46
38	Operation	operator: 56 operands: 47
39	Operation	operator: 48 operand: 61
40	Operation	operator: 50 operands: 57
41	Operation	operator: 51 operands: 52
42	Operation	operator: 58 operands: 53
43	Operation	operator: 56 operands: 54
44	Operation	operator: 58 operands: 55
45	Operation	operator: 56 operands: 57
46	Operation	operator: 58 operands: 59
47	NamedExprs	state: 60 part: 63
48	Literal
49	ExprTuple	61
50	Literal
51	Literal
52	NamedExprs	operation: 62 part: 63
53	ExprTuple	76, 65
54	NamedExprs	state: 73 part: 63
55	ExprTuple	76, 80
56	Literal
57	NamedExprs	state: 74 part: 63
58	Literal
59	ExprTuple	64, 65
60	Operation	operator: 66 operands: 67
61	Literal
62	Operation	operator: 68 operands: 69
63	Variable
64	Operation	operator: 71 operands: 70
65	Operation	operator: 71 operands: 72
66	Literal
67	ExprTuple	73, 74
68	Literal
69	ExprTuple	75, 80
70	ExprTuple	80, 76
71	Literal
72	ExprTuple	80, 77
73	Operation	operator: 78 operand: 80
74	Literal
75	Literal
76	Literal
77	Literal
78	Literal
79	ExprTuple	80
80	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 ¶