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, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, subtract, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = ScalarMult(frac(one, Exp(two, subtract(frac(Add(t, one), two), frac(t, two)))), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)))
sub_expr3 = ExprRange(sub_expr1, 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()
expr = ExprTuple(TensorProd(sub_expr2, TensorProd(sub_expr3)), TensorProd(sub_expr2, sub_expr3))

expr:

# 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(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes} \left(\left(\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)\right) {\otimes}  \left(\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)\right) {\otimes}  \ldots {\otimes}  \left(\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)\right)\right), \left(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right)\right){\otimes} \left(\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)\right) {\otimes}  \left(\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)\right) {\otimes}  \ldots {\otimes}  \left(\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)\right)\right)

stored_expr.style_options()

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',)

# display the expression information
stored_expr.expr_info()

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