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, 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, ket_plus
from proveit.physics.quantum.QPE import QPE1, _U, _ket_u, _phase, _psi_t_ket, _s
from proveit.physics.quantum.circuits import Gate, Input, 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 = Interval(sub_expr2, sub_expr3)
sub_expr5 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = Interval(one, sub_expr3))
sub_expr6 = ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)
sub_expr7 = [ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]
sub_expr8 = [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)]
expr = ExprTuple(Qcircuit(vert_expr_array = VertExprArray(sub_expr7, sub_expr8, [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(Neg(t), one), zero).with_decreasing_order(), sub_expr6])), Qcircuit(vert_expr_array = VertExprArray(sub_expr7, sub_expr8, [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _psi_t_ket, part = sub_expr1), targets = Interval(one, t)), one, t), sub_expr6])))

# 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{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \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)} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\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)} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\vdots} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \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)} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\lvert u \rangle}
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{3}{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \qout{\lvert u \rangle}
} \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 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	7, 8, 6
4	Literal
5	ExprTuple	7, 8, 9
6	ExprTuple	10, 16
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	ExprTuple	15, 16
10	ExprRange	lambda_map: 17 start_index: 18 end_index: 89
11	ExprRange	lambda_map: 19 start_index: 99 end_index: 82
12	ExprRange	lambda_map: 20 start_index: 99 end_index: 83
13	ExprRange	lambda_map: 21 start_index: 99 end_index: 82
14	ExprRange	lambda_map: 21 start_index: 66 end_index: 67
15	ExprRange	lambda_map: 22 start_index: 99 end_index: 82
16	ExprRange	lambda_map: 23 start_index: 99 end_index: 83
17	Lambda	parameter: 112 body: 24
18	Operation	operator: 76 operands: 25
19	Lambda	parameter: 112 body: 26
20	Lambda	parameter: 112 body: 27
21	Lambda	parameter: 112 body: 28
22	Lambda	parameter: 112 body: 29
23	Lambda	parameter: 112 body: 30
24	Operation	operator: 56 operands: 31
25	ExprTuple	32, 99
26	Operation	operator: 50 operands: 33
27	Operation	operator: 37 operands: 34
28	Operation	operator: 37 operands: 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	NamedExprs	state: 39
32	Operation	operator: 110 operand: 82
33	NamedExprs	state: 40
34	NamedExprs	element: 41 targets: 47
35	NamedExprs	element: 42 targets: 43
36	NamedExprs	element: 44 targets: 45
37	Literal
38	NamedExprs	element: 46 targets: 47
39	Operation	operator: 86 operands: 48
40	Operation	operator: 95 operand: 62
41	Operation	operator: 50 operands: 57
42	Operation	operator: 51 operands: 52
43	Operation	operator: 58 operands: 53
44	Operation	operator: 56 operands: 54
45	Operation	operator: 58 operands: 55
46	Operation	operator: 56 operands: 57
47	Operation	operator: 58 operands: 59
48	ExprTuple	60, 61
49	ExprTuple	62
50	Literal
51	Literal
52	NamedExprs	operation: 63 part: 112
53	ExprTuple	99, 67
54	NamedExprs	state: 64 part: 112
55	ExprTuple	99, 82
56	Literal
57	NamedExprs	state: 65 part: 112
58	Literal
59	ExprTuple	66, 67
60	Operation	operator: 92 operands: 68
61	Operation	operator: 69 operands: 70
62	Literal
63	Operation	operator: 71 operands: 72
64	Operation	operator: 73 operand: 82
65	Literal
66	Operation	operator: 76 operands: 75
67	Operation	operator: 76 operands: 77
68	ExprTuple	99, 78
69	Literal
70	ExprTuple	79, 80
71	Literal
72	ExprTuple	81, 82
73	Literal
74	ExprTuple	82
75	ExprTuple	82, 99
76	Literal
77	ExprTuple	82, 83
78	Operation	operator: 106 operands: 84
79	Operation	operator: 95 operand: 89
80	Operation	operator: 86 operands: 87
81	Literal
82	Variable
83	Literal
84	ExprTuple	108, 88
85	ExprTuple	89
86	Literal
87	ExprTuple	90, 91
88	Operation	operator: 92 operands: 93
89	Literal
90	Operation	operator: 106 operands: 94
91	Operation	operator: 95 operand: 99
92	Literal
93	ExprTuple	99, 108
94	ExprTuple	97, 98
95	Literal
96	ExprTuple	99
97	Literal
98	Operation	operator: 100 operands: 101
99	Literal
100	Literal
101	ExprTuple	108, 102, 103, 104, 105
102	Literal
103	Literal
104	Operation	operator: 106 operands: 107
105	Literal
106	Literal
107	ExprTuple	108, 109
108	Literal
109	Operation	operator: 110 operand: 112
110	Literal
111	ExprTuple	112
112	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 ¶