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 = Neg(t)
sub_expr3 = Add(t, one)
sub_expr4 = Add(t, _s)
sub_expr5 = TensorProd(_psi_t_ket, _ket_u)
sub_expr6 = Interval(one, sub_expr4)
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)))), Add(sub_expr2, one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr4)), one, _s).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray([MultiQubitElem(element = Output(state = sub_expr5, part = one), targets = sub_expr6), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = Add(sub_expr1, t)), targets = sub_expr6), Add(sub_expr2, two), zero), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = sub_expr1), targets = sub_expr6), sub_expr3, sub_expr4).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{2}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\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, 12
8	ExprRange	lambda_map: 13 start_index: 14 end_index: 76
9	ExprRange	lambda_map: 15 start_index: 87 end_index: 68
10	Operation	operator: 32 operands: 16
11	ExprRange	lambda_map: 17 start_index: 18 end_index: 76
12	ExprRange	lambda_map: 19 start_index: 50 end_index: 53
13	Lambda	parameter: 100 body: 20
14	Operation	operator: 61 operands: 21
15	Lambda	parameter: 100 body: 22
16	NamedExprs	element: 23 targets: 39
17	Lambda	parameter: 100 body: 24
18	Operation	operator: 61 operands: 25
19	Lambda	parameter: 100 body: 26
20	Operation	operator: 44 operands: 27
21	ExprTuple	31, 87
22	Operation	operator: 32 operands: 28
23	Operation	operator: 44 operands: 29
24	Operation	operator: 32 operands: 30
25	ExprTuple	31, 96
26	Operation	operator: 32 operands: 33
27	NamedExprs	state: 34
28	NamedExprs	element: 35 targets: 36
29	NamedExprs	state: 52 part: 87
30	NamedExprs	element: 37 targets: 39
31	Operation	operator: 98 operand: 79
32	Literal
33	NamedExprs	element: 38 targets: 39
34	Operation	operator: 71 operands: 40
35	Operation	operator: 44 operands: 41
36	Operation	operator: 46 operands: 42
37	Operation	operator: 44 operands: 43
38	Operation	operator: 44 operands: 45
39	Operation	operator: 46 operands: 47
40	ExprTuple	48, 49
41	NamedExprs	state: 67 part: 100
42	ExprTuple	50, 53
43	NamedExprs	state: 52 part: 51
44	Literal
45	NamedExprs	state: 52 part: 100
46	Literal
47	ExprTuple	87, 53
48	Operation	operator: 80 operands: 54
49	Operation	operator: 55 operands: 56
50	Operation	operator: 61 operands: 57
51	Operation	operator: 61 operands: 58
52	Operation	operator: 59 operands: 60
53	Operation	operator: 61 operands: 62
54	ExprTuple	87, 63
55	Literal
56	ExprTuple	64, 65
57	ExprTuple	79, 87
58	ExprTuple	100, 79
59	Literal
60	ExprTuple	66, 67
61	Literal
62	ExprTuple	79, 68
63	Operation	operator: 94 operands: 69
64	Operation	operator: 83 operand: 76
65	Operation	operator: 71 operands: 72
66	Operation	operator: 73 operand: 79
67	Literal
68	Literal
69	ExprTuple	96, 75
70	ExprTuple	76
71	Literal
72	ExprTuple	77, 78
73	Literal
74	ExprTuple	79
75	Operation	operator: 80 operands: 81
76	Literal
77	Operation	operator: 94 operands: 82
78	Operation	operator: 83 operand: 87
79	Variable
80	Literal
81	ExprTuple	87, 96
82	ExprTuple	85, 86
83	Literal
84	ExprTuple	87
85	Literal
86	Operation	operator: 88 operands: 89
87	Literal
88	Literal
89	ExprTuple	96, 90, 91, 92, 93
90	Literal
91	Literal
92	Operation	operator: 94 operands: 95
93	Literal
94	Literal
95	ExprTuple	96, 97
96	Literal
97	Operation	operator: 98 operand: 100
98	Literal
99	ExprTuple	100
100	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 ¶