Expression of type ExprTuple

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 ExprTuple, Lambda, Variable
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _s, _t
from proveit.physics.quantum.circuits import Gate, Input, MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
sub_expr3 = Interval(one, _t)
sub_expr4 = Lambda(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)))
expr = ExprTuple(sub_expr4, sub_expr4, Lambda(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr3)), Lambda(sub_expr1, Gate(operation = I).with_implicit_representation()), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr3)), Lambda(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2))))

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({_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{{\mathrm {FT}}^{\dag}_{t}~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \Psi \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~{_{-}a}~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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