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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _ket_u, _phase, _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 = Neg(t)
sub_expr3 = frac(one, sqrt(two))
expr = ExprTuple(Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1)))), ExprRange(sub_expr1, Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(sub_expr2, two), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, _s))), one, _s).with_wrapping_at(2,6))

# 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{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 3} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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',)

	core type	sub-expressions
0	ExprTuple	1, 2, 3
1	Operation	operator: 22 operands: 4
2	ExprRange	lambda_map: 5 start_index: 6 end_index: 50
3	ExprRange	lambda_map: 7 start_index: 80 end_index: 42
4	NamedExprs	state: 8
5	Lambda	parameter: 81 body: 9
6	Operation	operator: 76 operands: 10
7	Lambda	parameter: 81 body: 11
8	Operation	operator: 46 operands: 12
9	Operation	operator: 22 operands: 13
10	ExprTuple	79, 74
11	Operation	operator: 14 operands: 15
12	ExprTuple	27, 16
13	NamedExprs	state: 17
14	Literal
15	NamedExprs	element: 18 targets: 19
16	Operation	operator: 34 operands: 20
17	Operation	operator: 46 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	ExprTuple	40, 26
21	ExprTuple	27, 28
22	Literal
23	NamedExprs	state: 29 part: 81
24	Literal
25	ExprTuple	30, 31
26	Operation	operator: 46 operands: 32
27	Operation	operator: 54 operands: 33
28	Operation	operator: 34 operands: 35
29	Literal
30	Operation	operator: 76 operands: 36
31	Operation	operator: 76 operands: 37
32	ExprTuple	38, 52
33	ExprTuple	80, 39
34	Literal
35	ExprTuple	40, 41
36	ExprTuple	84, 80
37	ExprTuple	84, 42
38	Operation	operator: 71 operands: 43
39	Operation	operator: 71 operands: 44
40	Operation	operator: 57 operand: 50
41	Operation	operator: 46 operands: 47
42	Literal
43	ExprTuple	60, 48
44	ExprTuple	74, 49
45	ExprTuple	50
46	Literal
47	ExprTuple	51, 52
48	Operation	operator: 63 operands: 53
49	Operation	operator: 54 operands: 55
50	Literal
51	Operation	operator: 71 operands: 56
52	Operation	operator: 57 operand: 80
53	ExprTuple	74, 66, 67, 59, 69
54	Literal
55	ExprTuple	80, 74
56	ExprTuple	60, 61
57	Literal
58	ExprTuple	80
59	Operation	operator: 71 operands: 62
60	Literal
61	Operation	operator: 63 operands: 64
62	ExprTuple	74, 65
63	Literal
64	ExprTuple	74, 66, 67, 68, 69
65	Operation	operator: 82 operand: 73
66	Literal
67	Literal
68	Operation	operator: 71 operands: 72
69	Literal
70	ExprTuple	73
71	Literal
72	ExprTuple	74, 75
73	Operation	operator: 76 operands: 77
74	Literal
75	Operation	operator: 82 operand: 81
76	Literal
77	ExprTuple	79, 80
78	ExprTuple	81
79	Operation	operator: 82 operand: 84
80	Literal
81	Variable
82	Literal
83	ExprTuple	84
84	Variable

Expression of type ExprTuple¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type ExprTuple ¶

from the theory of proveit.physics.quantum.QPE ¶