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 Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = 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))), Neg(t), 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}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t} \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 - 1} \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
3	ExprRange	lambda_map: 4 start_index: 5 end_index: 23
4	Lambda	parameter: 46 body: 6
5	Operation	operator: 44 operand: 9
6	Operation	operator: 20 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Variable
10	Operation	operator: 26 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	33, 15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 40 operands: 18
16	Operation	operator: 29 operand: 23
17	Operation	operator: 20 operands: 21
18	ExprTuple	42, 22
19	ExprTuple	23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 40 operands: 28
25	Operation	operator: 29 operand: 33
26	Literal
27	ExprTuple	33, 42
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33
31	Literal
32	Operation	operator: 34 operands: 35
33	Literal
34	Literal
35	ExprTuple	42, 36, 37, 38, 39
36	Literal
37	Literal
38	Operation	operator: 40 operands: 41
39	Literal
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Variable