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, 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 = Add(Neg(t), one)
expr = Equals(Len(operands = [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = Add(sub_expr1, t)), targets = Interval(one, Add(t, _s))), sub_expr2, zero)]), Add(zero, Neg(sub_expr2), one))

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}~\left(-t + 1\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 + 2\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(0 - \left(-t + 1\right) + 1\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: 5 operands: 6
4	Operation	operator: 34 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	11, 9, 29
8	ExprRange	lambda_map: 10 start_index: 15 end_index: 11
9	Operation	operator: 26 operand: 15
10	Lambda	parameter: 38 body: 14
11	Literal
12	ExprTuple	15
13	ExprTuple	38
14	Operation	operator: 16 operands: 17
15	Operation	operator: 34 operands: 18
16	Literal
17	NamedExprs	element: 19 targets: 20
18	ExprTuple	21, 29
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 42
22	Literal
23	NamedExprs	state: 27 part: 28
24	Literal
25	ExprTuple	29, 30
26	Literal
27	Operation	operator: 31 operands: 32
28	Operation	operator: 34 operands: 33
29	Literal
30	Operation	operator: 34 operands: 35
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	38, 42
34	Literal
35	ExprTuple	42, 39
36	Operation	operator: 40 operand: 42
37	Literal
38	Variable
39	Literal
40	Literal
41	ExprTuple	42
42	Variable