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 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(one, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = sub_expr4)
sub_expr6 = MultiQubitElem(element = Output(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = sub_expr4)
expr = 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 = Interval(sub_expr2, sub_expr3)), one, _s)], [ExprRange(sub_expr1, sub_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [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)]))).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 + \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}

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