Expression of type Equals

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.core_expr_types import Len
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Neg, one, two, zero
from proveit.physics.quantum.QPE import _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = TensorProd(_psi_t_ket, _ket_u)
sub_expr3 = Interval(one, Add(t, _s))
expr = Equals(Len(operands = [MultiQubitElem(element = Output(state = sub_expr2, part = one), targets = sub_expr3), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr2, part = Add(sub_expr1, t)), targets = sub_expr3), Add(Neg(t), two), zero)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, t)]))

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(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 2\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 3\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)| = |\left(1, 2, \ldots, t\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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

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