Expression of type ExprTuple ¶

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, ExprTuple, Variable, VertExprArray, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _ket_u, _phase, _psi_t_ket, _s
from proveit.physics.quantum.circuits import 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 = MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(Neg(t), one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr4, one, t), ExprRange(sub_expr1, sub_expr4, sub_expr2, sub_expr3).with_wrapping_at(2,6)])))

# 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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
& \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
& \qout{\vdots} \\
& \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
& \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multiqout{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle}
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

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

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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