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, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _ket_u, _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))), Add(Neg(t), one), zero).with_decreasing_order(), _ket_u)

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 - 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) {\otimes} \lvert u \rangle

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	ExprRange	lambda_map: 5 start_index: 6 end_index: 27
4	Literal
5	Lambda	parameter: 50 body: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 24 operands: 10
8	Literal
9	ExprTuple	11, 37
10	ExprTuple	12, 13
11	Operation	operator: 48 operand: 18
12	Operation	operator: 30 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	18
15	ExprTuple	37, 19
16	Literal
17	ExprTuple	20, 21
18	Variable
19	Operation	operator: 44 operands: 22
20	Operation	operator: 33 operand: 27
21	Operation	operator: 24 operands: 25
22	ExprTuple	46, 26
23	ExprTuple	27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 30 operands: 31
27	Literal
28	Operation	operator: 44 operands: 32
29	Operation	operator: 33 operand: 37
30	Literal
31	ExprTuple	37, 46
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37
35	Literal
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	46, 40, 41, 42, 43
40	Literal
41	Literal
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Variable