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
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 QPE, _Psi_circuit, _Psi_ket, _U, _ket_u, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output, Qcircuit, QcircuitEquiv

# 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 = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = sub_expr5)
sub_expr7 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr5)
sub_expr8 = [ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3).with_wrapping_at(2,6)]
expr = ExprTuple(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_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)])), Qcircuit(vert_expr_array = VertExprArray(sub_expr8))), QcircuitEquiv(_Psi_circuit, Qcircuit(vert_expr_array = VertExprArray([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)], [ExprRange(sub_expr1, sub_expr7, one, _t), ExprRange(sub_expr1, sub_expr7, sub_expr2, sub_expr3)], sub_expr8))).with_wrapping_at(1))

# 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(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qout{\lvert \Psi \rangle} \\
& \qout{\lvert u \rangle}
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multiqout{1}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle}
} \end{array}\right), \begin{array}{c} \begin{array}{l} \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}\right) \\  \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \multiqout{4}{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \ghostqout{\lvert \Psi \rangle {\otimes} \lvert u \rangle}
} \end{array}\right) \end{array} \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	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 13 operand: 15
7	Operation	operator: 13 operand: 18
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15
11	ExprTuple	18
12	ExprTuple	16, 17, 15
13	Literal
14	ExprTuple	16, 17, 18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprRange	lambda_map: 27 start_index: 82 end_index: 86
20	ExprRange	lambda_map: 28 start_index: 82 end_index: 87
21	ExprRange	lambda_map: 29 start_index: 82 end_index: 86
22	ExprRange	lambda_map: 30 start_index: 82 end_index: 87
23	ExprRange	lambda_map: 31 start_index: 82 end_index: 86
24	ExprRange	lambda_map: 31 start_index: 70 end_index: 74
25	ExprRange	lambda_map: 32 start_index: 82 end_index: 86
26	ExprRange	lambda_map: 32 start_index: 70 end_index: 74
27	Lambda	parameter: 73 body: 33
28	Lambda	parameter: 73 body: 34
29	Lambda	parameter: 73 body: 35
30	Lambda	parameter: 73 body: 36
31	Lambda	parameter: 73 body: 37
32	Lambda	parameter: 73 body: 39
33	Operation	operator: 45 operands: 40
34	Operation	operator: 45 operands: 41
35	Operation	operator: 60 operands: 42
36	Operation	operator: 45 operands: 43
37	Operation	operator: 45 operands: 44
38	ExprTuple	73
39	Operation	operator: 45 operands: 46
40	NamedExprs	element: 47 targets: 48
41	NamedExprs	element: 49 targets: 52
42	NamedExprs	state: 50
43	NamedExprs	element: 51 targets: 52
44	NamedExprs	element: 53 targets: 55
45	Literal
46	NamedExprs	element: 54 targets: 55
47	Operation	operator: 65 operands: 56
48	Operation	operator: 67 operands: 57
49	Operation	operator: 65 operands: 61
50	Operation	operator: 58 operand: 69
51	Operation	operator: 60 operands: 61
52	Operation	operator: 67 operands: 62
53	Operation	operator: 63 operands: 64
54	Operation	operator: 65 operands: 66
55	Operation	operator: 67 operands: 68
56	NamedExprs	state: 84 part: 73
57	ExprTuple	82, 86
58	Literal
59	ExprTuple	69
60	Literal
61	NamedExprs	state: 85 part: 73
62	ExprTuple	70, 74
63	Literal
64	NamedExprs	operation: 71 part: 73
65	Literal
66	NamedExprs	state: 72 part: 73
67	Literal
68	ExprTuple	82, 74
69	Literal
70	Operation	operator: 80 operands: 75
71	Operation	operator: 76 operands: 77
72	Operation	operator: 78 operands: 79
73	Variable
74	Operation	operator: 80 operands: 81
75	ExprTuple	86, 82
76	Literal
77	ExprTuple	83, 86
78	Literal
79	ExprTuple	84, 85
80	Literal
81	ExprTuple	86, 87
82	Literal
83	Literal
84	Literal
85	Literal
86	Literal
87	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 ¶