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.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 = Add(t, _s)
sub_expr3 = Neg(t)
sub_expr4 = TensorProd(_psi_t_ket, _ket_u)
sub_expr5 = Interval(one, sub_expr2)
sub_expr6 = MultiQubitElem(element = Output(state = sub_expr4, part = Add(sub_expr1, t)), targets = sub_expr5)
sub_expr7 = ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr4, part = sub_expr1), targets = sub_expr5), Add(t, one), sub_expr2).with_wrapping_at(2,6)
expr = Equals([MultiQubitElem(element = Output(state = sub_expr4, part = one), targets = sub_expr5), ExprRange(sub_expr1, sub_expr6, Add(sub_expr3, two), zero), sub_expr7], [ExprRange(sub_expr1, sub_expr6, Add(sub_expr3, one), zero), sub_expr7]).with_wrapping_at(2)

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},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 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}~t + 2~\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}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) =  \\ \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},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 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}~t + 2~\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}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \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.	()	(2)	('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	ExprTuple	5, 6, 8
4	ExprTuple	7, 8
5	Operation	operator: 27 operands: 9
6	ExprRange	lambda_map: 11 start_index: 10 end_index: 13
7	ExprRange	lambda_map: 11 start_index: 12 end_index: 13
8	ExprRange	lambda_map: 14 start_index: 15 end_index: 41
9	NamedExprs	element: 16 targets: 32
10	Operation	operator: 45 operands: 17
11	Lambda	parameter: 47 body: 18
12	Operation	operator: 45 operands: 19
13	Literal
14	Lambda	parameter: 47 body: 21
15	Operation	operator: 45 operands: 22
16	Operation	operator: 34 operands: 23
17	ExprTuple	26, 24
18	Operation	operator: 27 operands: 25
19	ExprTuple	26, 40
20	ExprTuple	47
21	Operation	operator: 27 operands: 28
22	ExprTuple	53, 40
23	NamedExprs	state: 39 part: 40
24	Literal
25	NamedExprs	element: 29 targets: 32
26	Operation	operator: 30 operand: 53
27	Literal
28	NamedExprs	element: 31 targets: 32
29	Operation	operator: 34 operands: 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	NamedExprs	state: 39 part: 38
34	Literal
35	NamedExprs	state: 39 part: 47
36	Literal
37	ExprTuple	40, 41
38	Operation	operator: 45 operands: 42
39	Operation	operator: 43 operands: 44
40	Literal
41	Operation	operator: 45 operands: 46
42	ExprTuple	47, 53
43	Literal
44	ExprTuple	48, 49
45	Literal
46	ExprTuple	53, 50
47	Variable
48	Operation	operator: 51 operand: 53
49	Literal
50	Literal
51	Literal
52	ExprTuple	53
53	Variable