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)]), t).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} |\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)| \\  = t \end{array} \end{array}

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.	()	(1)	('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, 43
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 17 operands: 8
7	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
8	NamedExprs	element: 12 targets: 22
9	Lambda	parameter: 39 body: 14
10	Operation	operator: 35 operands: 15
11	Literal
12	Operation	operator: 24 operands: 16
13	ExprTuple	39
14	Operation	operator: 17 operands: 18
15	ExprTuple	19, 20
16	NamedExprs	state: 28 part: 30
17	Literal
18	NamedExprs	element: 21 targets: 22
19	Operation	operator: 23 operand: 43
20	Literal
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	NamedExprs	state: 28 part: 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 35 operands: 34
30	Literal
31	Operation	operator: 35 operands: 36
32	Literal
33	ExprTuple	37, 38
34	ExprTuple	39, 43
35	Literal
36	ExprTuple	43, 40
37	Operation	operator: 41 operand: 43
38	Literal
39	Variable
40	Literal
41	Literal
42	ExprTuple	43
43	Variable