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, VertExprArray, t
from proveit.linear_algebra import ScalarMult, TensorProd, 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, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, one)
sub_expr3 = Add(t, _s)
sub_expr4 = Add(Neg(t), one)
sub_expr5 = TensorProd(_psi_t_ket, _ket_u)
sub_expr6 = Interval(one, sub_expr3)
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), sub_expr4, zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = Add(sub_expr1, t)), targets = sub_expr6), sub_expr4, zero), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = sub_expr1), targets = sub_expr6), sub_expr2, sub_expr3).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^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
& \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)} \\
& \qout{\vdots} \\
& \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)} \\
& \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multiqout{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \qout{\vdots} \qwx[1] \\
& \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} \qwx[1] \\
& \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{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
1	Operation	operator: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	ExprTuple	10, 11
8	ExprRange	lambda_map: 12 start_index: 15 end_index: 70
9	ExprRange	lambda_map: 13 start_index: 81 end_index: 62
10	ExprRange	lambda_map: 14 start_index: 15 end_index: 70
11	ExprRange	lambda_map: 16 start_index: 44 end_index: 47
12	Lambda	parameter: 94 body: 17
13	Lambda	parameter: 94 body: 18
14	Lambda	parameter: 94 body: 19
15	Operation	operator: 55 operands: 20
16	Lambda	parameter: 94 body: 21
17	Operation	operator: 38 operands: 22
18	Operation	operator: 26 operands: 23
19	Operation	operator: 26 operands: 24
20	ExprTuple	25, 81
21	Operation	operator: 26 operands: 27
22	NamedExprs	state: 28
23	NamedExprs	element: 29 targets: 30
24	NamedExprs	element: 31 targets: 33
25	Operation	operator: 92 operand: 73
26	Literal
27	NamedExprs	element: 32 targets: 33
28	Operation	operator: 65 operands: 34
29	Operation	operator: 38 operands: 35
30	Operation	operator: 40 operands: 36
31	Operation	operator: 38 operands: 37
32	Operation	operator: 38 operands: 39
33	Operation	operator: 40 operands: 41
34	ExprTuple	42, 43
35	NamedExprs	state: 61 part: 94
36	ExprTuple	44, 47
37	NamedExprs	state: 46 part: 45
38	Literal
39	NamedExprs	state: 46 part: 94
40	Literal
41	ExprTuple	81, 47
42	Operation	operator: 74 operands: 48
43	Operation	operator: 49 operands: 50
44	Operation	operator: 55 operands: 51
45	Operation	operator: 55 operands: 52
46	Operation	operator: 53 operands: 54
47	Operation	operator: 55 operands: 56
48	ExprTuple	81, 57
49	Literal
50	ExprTuple	58, 59
51	ExprTuple	73, 81
52	ExprTuple	94, 73
53	Literal
54	ExprTuple	60, 61
55	Literal
56	ExprTuple	73, 62
57	Operation	operator: 88 operands: 63
58	Operation	operator: 77 operand: 70
59	Operation	operator: 65 operands: 66
60	Operation	operator: 67 operand: 73
61	Literal
62	Literal
63	ExprTuple	90, 69
64	ExprTuple	70
65	Literal
66	ExprTuple	71, 72
67	Literal
68	ExprTuple	73
69	Operation	operator: 74 operands: 75
70	Literal
71	Operation	operator: 88 operands: 76
72	Operation	operator: 77 operand: 81
73	Variable
74	Literal
75	ExprTuple	81, 90
76	ExprTuple	79, 80
77	Literal
78	ExprTuple	81
79	Literal
80	Operation	operator: 82 operands: 83
81	Literal
82	Literal
83	ExprTuple	90, 84, 85, 86, 87
84	Literal
85	Literal
86	Operation	operator: 88 operands: 89
87	Literal
88	Literal
89	ExprTuple	90, 91
90	Literal
91	Operation	operator: 92 operand: 94
92	Literal
93	ExprTuple	94
94	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 ¶