Expression of type TensorProd

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, 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}")
expr = TensorProd(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))), TensorProd(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:

# 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(\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)

stored_expr.style_options()

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',)

# display the expression information
stored_expr.expr_info()

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