Expression of type Equals ¶

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, n
from proveit.logic import Equals, NotEquals, TRUE
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE, _U, _ket_u, _phase_est_circuit, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit

# 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 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Equals(NotEquals(_phase_est_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_expr5, one, _t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(n, _t), 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)]))), TRUE)

# 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 + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert m \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right) \neq \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert n \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert n \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert n \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert n \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\right) = \top

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.	()	()	('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: 5 operands: 6
4	Literal
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	13, 14, 15, 12
10	Literal
11	ExprTuple	13, 14, 15, 16
12	ExprTuple	17, 25
13	ExprTuple	18, 19
14	ExprTuple	20, 21
15	ExprTuple	22, 23
16	ExprTuple	24, 25
17	ExprRange	lambda_map: 26 start_index: 96 end_index: 97
18	ExprRange	lambda_map: 27 start_index: 96 end_index: 97
19	ExprRange	lambda_map: 28 start_index: 96 end_index: 98
20	ExprRange	lambda_map: 29 start_index: 96 end_index: 97
21	ExprRange	lambda_map: 29 start_index: 83 end_index: 84
22	ExprRange	lambda_map: 30 start_index: 96 end_index: 97
23	ExprRange	lambda_map: 31 start_index: 96 end_index: 98
24	ExprRange	lambda_map: 32 start_index: 96 end_index: 97
25	ExprRange	lambda_map: 33 start_index: 96 end_index: 98
26	Lambda	parameter: 82 body: 34
27	Lambda	parameter: 82 body: 35
28	Lambda	parameter: 82 body: 36
29	Lambda	parameter: 82 body: 37
30	Lambda	parameter: 82 body: 38
31	Lambda	parameter: 82 body: 39
32	Lambda	parameter: 82 body: 40
33	Lambda	parameter: 82 body: 42
34	Operation	operator: 51 operands: 43
35	Operation	operator: 67 operands: 44
36	Operation	operator: 51 operands: 45
37	Operation	operator: 51 operands: 46
38	Operation	operator: 47 operands: 48
39	Operation	operator: 68 operands: 49
40	Operation	operator: 51 operands: 50
41	ExprTuple	82
42	Operation	operator: 51 operands: 52
43	NamedExprs	element: 53 targets: 61
44	NamedExprs	state: 54
45	NamedExprs	element: 55 targets: 63
46	NamedExprs	element: 56 targets: 57
47	Literal
48	NamedExprs	basis: 58
49	NamedExprs	operation: 59
50	NamedExprs	element: 60 targets: 61
51	Literal
52	NamedExprs	element: 62 targets: 63
53	Operation	operator: 73 operands: 64
54	Operation	operator: 65 operand: 78
55	Operation	operator: 67 operands: 74
56	Operation	operator: 68 operands: 69
57	Operation	operator: 75 operands: 70
58	Literal
59	Literal
60	Operation	operator: 73 operands: 71
61	Operation	operator: 75 operands: 72
62	Operation	operator: 73 operands: 74
63	Operation	operator: 75 operands: 76
64	NamedExprs	state: 77 part: 82
65	Literal
66	ExprTuple	78
67	Literal
68	Literal
69	NamedExprs	operation: 79 part: 82
70	ExprTuple	96, 84
71	NamedExprs	state: 80 part: 82
72	ExprTuple	96, 97
73	Literal
74	NamedExprs	state: 81 part: 82
75	Literal
76	ExprTuple	83, 84
77	Operation	operator: 88 operands: 85
78	Literal
79	Operation	operator: 86 operands: 87
80	Operation	operator: 88 operands: 89
81	Literal
82	Variable
83	Operation	operator: 91 operands: 90
84	Operation	operator: 91 operands: 92
85	ExprTuple	93, 97
86	Literal
87	ExprTuple	94, 97
88	Literal
89	ExprTuple	95, 97
90	ExprTuple	97, 96
91	Literal
92	ExprTuple	97, 98
93	Variable
94	Literal
95	Variable
96	Literal
97	Literal
98	Literal

Expression of type Equals¶

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

Expression of type Equals ¶

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