Expression of type QcircuitEquiv ¶

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, 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 = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)]
sub_expr8 = [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)]
expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([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_expr7, sub_expr8)), Qcircuit(vert_expr_array = VertExprArray([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)], sub_expr7, 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())

\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}

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(1)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

	core type	sub-expressions
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 10, 11
6	Literal
7	ExprTuple	9, 10, 11
8	ExprTuple	12, 13
9	ExprTuple	14, 15
10	ExprTuple	16, 17
11	ExprTuple	18, 19
12	ExprRange	lambda_map: 20 start_index: 79 end_index: 83
13	ExprRange	lambda_map: 21 start_index: 79 end_index: 80
14	ExprRange	lambda_map: 22 start_index: 79 end_index: 83
15	ExprRange	lambda_map: 22 start_index: 69 end_index: 70
16	ExprRange	lambda_map: 23 start_index: 79 end_index: 83
17	ExprRange	lambda_map: 24 start_index: 79 end_index: 80
18	ExprRange	lambda_map: 25 start_index: 79 end_index: 83
19	ExprRange	lambda_map: 26 start_index: 79 end_index: 80
20	Lambda	parameter: 68 body: 27
21	Lambda	parameter: 68 body: 28
22	Lambda	parameter: 68 body: 29
23	Lambda	parameter: 68 body: 30
24	Lambda	parameter: 68 body: 31
25	Lambda	parameter: 68 body: 32
26	Lambda	parameter: 68 body: 34
27	Operation	operator: 41 operands: 35
28	Operation	operator: 41 operands: 36
29	Operation	operator: 41 operands: 37
30	Operation	operator: 41 operands: 38
31	Operation	operator: 57 operands: 39
32	Operation	operator: 41 operands: 40
33	ExprTuple	68
34	Operation	operator: 41 operands: 42
35	NamedExprs	element: 43 targets: 50
36	NamedExprs	element: 44 targets: 52
37	NamedExprs	element: 45 targets: 46
38	NamedExprs	element: 47 targets: 50
39	NamedExprs	operation: 48
40	NamedExprs	element: 49 targets: 50
41	Literal
42	NamedExprs	element: 51 targets: 52
43	Operation	operator: 54 operands: 53
44	Operation	operator: 54 operands: 62
45	Operation	operator: 54 operands: 55
46	Operation	operator: 63 operands: 56
47	Operation	operator: 57 operands: 58
48	Literal
49	Operation	operator: 61 operands: 59
50	Operation	operator: 63 operands: 60
51	Operation	operator: 61 operands: 62
52	Operation	operator: 63 operands: 64
53	NamedExprs	state: 77 part: 68
54	Literal
55	NamedExprs	state: 65 part: 68
56	ExprTuple	79, 70
57	Literal
58	NamedExprs	operation: 66 part: 68
59	NamedExprs	state: 67 part: 68
60	ExprTuple	79, 83
61	Literal
62	NamedExprs	state: 78 part: 68
63	Literal
64	ExprTuple	69, 70
65	Operation	operator: 71 operands: 72
66	Operation	operator: 73 operand: 83
67	Literal
68	Variable
69	Operation	operator: 75 operands: 74
70	Operation	operator: 75 operands: 76
71	Literal
72	ExprTuple	77, 78
73	Literal
74	ExprTuple	83, 79
75	Literal
76	ExprTuple	83, 80
77	Operation	operator: 81 operand: 83
78	Literal
79	Literal
80	Literal
81	Literal
82	ExprTuple	83
83	Literal

Expression of type QcircuitEquiv¶

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

Expression of type QcircuitEquiv ¶

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