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))), 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(\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)

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