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, Not, 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(Not(Equals(_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())

(\lnot \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) = \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: 7 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 6
3	Literal
4	Literal
5	ExprTuple	6
6	Operation	operator: 7 operands: 8
7	Literal
8	ExprTuple	9, 10
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	15, 16, 17, 14
12	Literal
13	ExprTuple	15, 16, 17, 18
14	ExprTuple	19, 27
15	ExprTuple	20, 21
16	ExprTuple	22, 23
17	ExprTuple	24, 25
18	ExprTuple	26, 27
19	ExprRange	lambda_map: 28 start_index: 98 end_index: 99
20	ExprRange	lambda_map: 29 start_index: 98 end_index: 99
21	ExprRange	lambda_map: 30 start_index: 98 end_index: 100
22	ExprRange	lambda_map: 31 start_index: 98 end_index: 99
23	ExprRange	lambda_map: 31 start_index: 85 end_index: 86
24	ExprRange	lambda_map: 32 start_index: 98 end_index: 99
25	ExprRange	lambda_map: 33 start_index: 98 end_index: 100
26	ExprRange	lambda_map: 34 start_index: 98 end_index: 99
27	ExprRange	lambda_map: 35 start_index: 98 end_index: 100
28	Lambda	parameter: 84 body: 36
29	Lambda	parameter: 84 body: 37
30	Lambda	parameter: 84 body: 38
31	Lambda	parameter: 84 body: 39
32	Lambda	parameter: 84 body: 40
33	Lambda	parameter: 84 body: 41
34	Lambda	parameter: 84 body: 42
35	Lambda	parameter: 84 body: 44
36	Operation	operator: 53 operands: 45
37	Operation	operator: 69 operands: 46
38	Operation	operator: 53 operands: 47
39	Operation	operator: 53 operands: 48
40	Operation	operator: 49 operands: 50
41	Operation	operator: 70 operands: 51
42	Operation	operator: 53 operands: 52
43	ExprTuple	84
44	Operation	operator: 53 operands: 54
45	NamedExprs	element: 55 targets: 63
46	NamedExprs	state: 56
47	NamedExprs	element: 57 targets: 65
48	NamedExprs	element: 58 targets: 59
49	Literal
50	NamedExprs	basis: 60
51	NamedExprs	operation: 61
52	NamedExprs	element: 62 targets: 63
53	Literal
54	NamedExprs	element: 64 targets: 65
55	Operation	operator: 75 operands: 66
56	Operation	operator: 67 operand: 80
57	Operation	operator: 69 operands: 76
58	Operation	operator: 70 operands: 71
59	Operation	operator: 77 operands: 72
60	Literal
61	Literal
62	Operation	operator: 75 operands: 73
63	Operation	operator: 77 operands: 74
64	Operation	operator: 75 operands: 76
65	Operation	operator: 77 operands: 78
66	NamedExprs	state: 79 part: 84
67	Literal
68	ExprTuple	80
69	Literal
70	Literal
71	NamedExprs	operation: 81 part: 84
72	ExprTuple	98, 86
73	NamedExprs	state: 82 part: 84
74	ExprTuple	98, 99
75	Literal
76	NamedExprs	state: 83 part: 84
77	Literal
78	ExprTuple	85, 86
79	Operation	operator: 90 operands: 87
80	Literal
81	Operation	operator: 88 operands: 89
82	Operation	operator: 90 operands: 91
83	Literal
84	Variable
85	Operation	operator: 93 operands: 92
86	Operation	operator: 93 operands: 94
87	ExprTuple	95, 99
88	Literal
89	ExprTuple	96, 99
90	Literal
91	ExprTuple	97, 99
92	ExprTuple	99, 98
93	Literal
94	ExprTuple	99, 100
95	Variable
96	Literal
97	Variable
98	Literal
99	Literal
100	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 ¶