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 I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _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 = Interval(one, _t)
sub_expr3 = Add(_t, one)
sub_expr4 = Add(_t, _s)
sub_expr5 = Interval(sub_expr3, sub_expr4)
sub_expr6 = MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr7 = [ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]
sub_expr8 = [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)]
sub_expr9 = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]
sub_expr10 = [ExprRange(sub_expr1, sub_expr6, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr4).with_wrapping_at(2,6)]
expr = ExprTuple(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr7)), Qcircuit(vert_expr_array = VertExprArray(sub_expr10))), QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr7, sub_expr8, sub_expr9)), Qcircuit(vert_expr_array = VertExprArray(sub_expr10, sub_expr8, sub_expr9))).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{
\qin{\lvert \psi_{t} \rangle} & { /^{t} } \qw \\
\qin{\lvert u \rangle} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & { /^{t} } \qw \\
\ghostqin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw
} \end{array}\right), \begin{array}{c} \begin{array}{l} \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) \\  \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\multiqin{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\ghostqin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} & { /^{s} } \qw & \qout{\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: 16
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15
11	ExprTuple	16
12	ExprTuple	15, 17, 18
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: 86 end_index: 90
20	ExprRange	lambda_map: 28 start_index: 86 end_index: 87
21	ExprRange	lambda_map: 29 start_index: 86 end_index: 90
22	ExprRange	lambda_map: 29 start_index: 76 end_index: 77
23	ExprRange	lambda_map: 30 start_index: 86 end_index: 90
24	ExprRange	lambda_map: 31 start_index: 86 end_index: 87
25	ExprRange	lambda_map: 32 start_index: 86 end_index: 90
26	ExprRange	lambda_map: 33 start_index: 86 end_index: 87
27	Lambda	parameter: 75 body: 34
28	Lambda	parameter: 75 body: 35
29	Lambda	parameter: 75 body: 36
30	Lambda	parameter: 75 body: 37
31	Lambda	parameter: 75 body: 38
32	Lambda	parameter: 75 body: 39
33	Lambda	parameter: 75 body: 41
34	Operation	operator: 48 operands: 42
35	Operation	operator: 48 operands: 43
36	Operation	operator: 48 operands: 44
37	Operation	operator: 48 operands: 45
38	Operation	operator: 64 operands: 46
39	Operation	operator: 48 operands: 47
40	ExprTuple	75
41	Operation	operator: 48 operands: 49
42	NamedExprs	element: 50 targets: 57
43	NamedExprs	element: 51 targets: 59
44	NamedExprs	element: 52 targets: 53
45	NamedExprs	element: 54 targets: 57
46	NamedExprs	operation: 55
47	NamedExprs	element: 56 targets: 57
48	Literal
49	NamedExprs	element: 58 targets: 59
50	Operation	operator: 61 operands: 60
51	Operation	operator: 61 operands: 69
52	Operation	operator: 61 operands: 62
53	Operation	operator: 70 operands: 63
54	Operation	operator: 64 operands: 65
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	NamedExprs	state: 84 part: 75
61	Literal
62	NamedExprs	state: 72 part: 75
63	ExprTuple	86, 77
64	Literal
65	NamedExprs	operation: 73 part: 75
66	NamedExprs	state: 74 part: 75
67	ExprTuple	86, 90
68	Literal
69	NamedExprs	state: 85 part: 75
70	Literal
71	ExprTuple	76, 77
72	Operation	operator: 78 operands: 79
73	Operation	operator: 80 operand: 90
74	Literal
75	Variable
76	Operation	operator: 82 operands: 81
77	Operation	operator: 82 operands: 83
78	Literal
79	ExprTuple	84, 85
80	Literal
81	ExprTuple	90, 86
82	Literal
83	ExprTuple	90, 87
84	Operation	operator: 88 operand: 90
85	Literal
86	Literal
87	Literal
88	Literal
89	ExprTuple	90
90	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 ¶