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.numbers import Add, Interval, one
from proveit.physics.quantum import I, ket_plus
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import QPE1, _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, _t)
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = QcircuitEquiv(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_expr5), one, _s)], [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr4), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)])), _Psi_circuit).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}_1\left(U, t\right)} & \multigate{3}{{\mathrm {FT}}^{\dag}_{t}} & \multiqout{3}{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghost{{\mathrm {FT}}^{\dag}_{t}} & \ghostqout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw & \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{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) \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	10, 8, 9, 12
6	Literal
7	ExprTuple	10, 11, 12
8	ExprTuple	13, 14
9	ExprTuple	15, 16
10	ExprTuple	17, 18
11	ExprTuple	19, 20
12	ExprTuple	21, 22
13	ExprRange	lambda_map: 23 start_index: 92 end_index: 93
14	ExprRange	lambda_map: 23 start_index: 81 end_index: 82
15	ExprRange	lambda_map: 24 start_index: 92 end_index: 93
16	ExprRange	lambda_map: 25 start_index: 92 end_index: 94
17	ExprRange	lambda_map: 26 start_index: 92 end_index: 93
18	ExprRange	lambda_map: 27 start_index: 92 end_index: 94
19	ExprRange	lambda_map: 28 start_index: 92 end_index: 93
20	ExprRange	lambda_map: 28 start_index: 81 end_index: 82
21	ExprRange	lambda_map: 29 start_index: 92 end_index: 93
22	ExprRange	lambda_map: 30 start_index: 92 end_index: 94
23	Lambda	parameter: 80 body: 31
24	Lambda	parameter: 80 body: 32
25	Lambda	parameter: 80 body: 33
26	Lambda	parameter: 80 body: 34
27	Lambda	parameter: 80 body: 35
28	Lambda	parameter: 80 body: 36
29	Lambda	parameter: 80 body: 37
30	Lambda	parameter: 80 body: 39
31	Operation	operator: 47 operands: 40
32	Operation	operator: 47 operands: 41
33	Operation	operator: 65 operands: 42
34	Operation	operator: 64 operands: 43
35	Operation	operator: 47 operands: 44
36	Operation	operator: 47 operands: 45
37	Operation	operator: 47 operands: 46
38	ExprTuple	80
39	Operation	operator: 47 operands: 48
40	NamedExprs	element: 49 targets: 55
41	NamedExprs	element: 50 targets: 57
42	NamedExprs	operation: 51
43	NamedExprs	state: 52
44	NamedExprs	element: 53 targets: 59
45	NamedExprs	element: 54 targets: 55
46	NamedExprs	element: 56 targets: 57
47	Literal
48	NamedExprs	element: 58 targets: 59
49	Operation	operator: 65 operands: 60
50	Operation	operator: 65 operands: 61
51	Literal
52	Operation	operator: 62 operand: 76
53	Operation	operator: 64 operands: 71
54	Operation	operator: 65 operands: 66
55	Operation	operator: 72 operands: 67
56	Operation	operator: 70 operands: 68
57	Operation	operator: 72 operands: 69
58	Operation	operator: 70 operands: 71
59	Operation	operator: 72 operands: 73
60	NamedExprs	operation: 74 part: 80
61	NamedExprs	operation: 75 part: 80
62	Literal
63	ExprTuple	76
64	Literal
65	Literal
66	NamedExprs	operation: 77 part: 80
67	ExprTuple	92, 82
68	NamedExprs	state: 78 part: 80
69	ExprTuple	92, 93
70	Literal
71	NamedExprs	state: 79 part: 80
72	Literal
73	ExprTuple	81, 82
74	Operation	operator: 83 operands: 87
75	Operation	operator: 84 operand: 93
76	Literal
77	Operation	operator: 86 operands: 87
78	Literal
79	Literal
80	Variable
81	Operation	operator: 89 operands: 88
82	Operation	operator: 89 operands: 90
83	Literal
84	Literal
85	ExprTuple	93
86	Literal
87	ExprTuple	91, 93
88	ExprTuple	93, 92
89	Literal
90	ExprTuple	93, 94
91	Literal
92	Literal
93	Literal
94	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 ¶