Expression of type Lambda

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 Conditional, ExprRange, Lambda, Variable, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, Mult, NaturalPos, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, _psi_t_ket

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(t, Conditional(Equals(_psi_t_ket, 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())), InSet(t, NaturalPos)))

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())

t \mapsto \left\{\lvert \psi_{t} \rangle = \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) \textrm{ if } t \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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