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, 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, QcircuitEquiv

# 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 = Interval(one, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE1(_U, t), part = sub_expr1), targets = sub_expr5)
sub_expr7 = MultiQubitElem(element = Output(state = TensorProd(_psi_t_ket, _ket_u), part = sub_expr1), targets = sub_expr5)
sub_expr8 = [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_expr9 = [ExprRange(sub_expr1, sub_expr6, one, t), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)]
sub_expr10 = [ExprRange(sub_expr1, sub_expr7, one, t), ExprRange(sub_expr1, sub_expr7, sub_expr2, sub_expr3).with_wrapping_at(2,6)]
sub_expr11 = [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(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr4), one, _s)]
expr = ExprTuple(QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr11)), Qcircuit(vert_expr_array = VertExprArray(sub_expr10))), QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr9, sub_expr11)), Qcircuit(vert_expr_array = VertExprArray(sub_expr8, sub_expr9, sub_expr10))).with_wrapping_at(1))

# 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(\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}\right) \cong \left(\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}
} \end{array}\right), \begin{array}{c} \begin{array}{l} \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}\right) \\  \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}_1\left(U, t\right)} & \multiqout{4}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \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 {\otimes} \lvert u \rangle} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}_1\left(U, t\right)} & \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle}
} \end{array}\right) \end{array} \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	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 13 operand: 15
7	Operation	operator: 13 operand: 18
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15
11	ExprTuple	18
12	ExprTuple	16, 17, 15
13	Literal
14	ExprTuple	16, 17, 18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	ExprRange	lambda_map: 27 start_index: 28 end_index: 99
20	ExprRange	lambda_map: 29 start_index: 110 end_index: 91
21	ExprRange	lambda_map: 30 start_index: 110 end_index: 102
22	ExprRange	lambda_map: 31 start_index: 110 end_index: 91
23	ExprRange	lambda_map: 32 start_index: 110 end_index: 102
24	ExprRange	lambda_map: 32 start_index: 71 end_index: 74
25	ExprRange	lambda_map: 33 start_index: 110 end_index: 102
26	ExprRange	lambda_map: 33 start_index: 71 end_index: 74
27	Lambda	parameter: 123 body: 34
28	Operation	operator: 83 operands: 35
29	Lambda	parameter: 123 body: 36
30	Lambda	parameter: 123 body: 37
31	Lambda	parameter: 123 body: 38
32	Lambda	parameter: 123 body: 39
33	Lambda	parameter: 123 body: 40
34	Operation	operator: 64 operands: 41
35	ExprTuple	42, 110
36	Operation	operator: 47 operands: 43
37	Operation	operator: 59 operands: 44
38	Operation	operator: 47 operands: 45
39	Operation	operator: 47 operands: 46
40	Operation	operator: 47 operands: 48
41	NamedExprs	state: 49
42	Operation	operator: 121 operand: 102
43	NamedExprs	element: 50 targets: 53
44	NamedExprs	state: 51
45	NamedExprs	element: 52 targets: 53
46	NamedExprs	element: 54 targets: 56
47	Literal
48	NamedExprs	element: 55 targets: 56
49	Operation	operator: 94 operands: 57
50	Operation	operator: 64 operands: 60
51	Operation	operator: 106 operand: 70
52	Operation	operator: 59 operands: 60
53	Operation	operator: 66 operands: 61
54	Operation	operator: 62 operands: 63
55	Operation	operator: 64 operands: 65
56	Operation	operator: 66 operands: 67
57	ExprTuple	68, 69
58	ExprTuple	70
59	Literal
60	NamedExprs	state: 90 part: 123
61	ExprTuple	71, 74
62	Literal
63	NamedExprs	operation: 72 part: 123
64	Literal
65	NamedExprs	state: 73 part: 123
66	Literal
67	ExprTuple	110, 74
68	Operation	operator: 103 operands: 75
69	Operation	operator: 76 operands: 77
70	Literal
71	Operation	operator: 83 operands: 78
72	Operation	operator: 79 operands: 80
73	Operation	operator: 81 operands: 82
74	Operation	operator: 83 operands: 84
75	ExprTuple	110, 85
76	Literal
77	ExprTuple	86, 87
78	ExprTuple	102, 110
79	Literal
80	ExprTuple	88, 102
81	Literal
82	ExprTuple	89, 90
83	Literal
84	ExprTuple	102, 91
85	Operation	operator: 117 operands: 92
86	Operation	operator: 106 operand: 99
87	Operation	operator: 94 operands: 95
88	Literal
89	Operation	operator: 96 operand: 102
90	Literal
91	Literal
92	ExprTuple	119, 98
93	ExprTuple	99
94	Literal
95	ExprTuple	100, 101
96	Literal
97	ExprTuple	102
98	Operation	operator: 103 operands: 104
99	Literal
100	Operation	operator: 117 operands: 105
101	Operation	operator: 106 operand: 110
102	Variable
103	Literal
104	ExprTuple	110, 119
105	ExprTuple	108, 109
106	Literal
107	ExprTuple	110
108	Literal
109	Operation	operator: 111 operands: 112
110	Literal
111	Literal
112	ExprTuple	119, 113, 114, 115, 116
113	Literal
114	Literal
115	Operation	operator: 117 operands: 118
116	Literal
117	Literal
118	ExprTuple	119, 120
119	Literal
120	Operation	operator: 121 operand: 123
121	Literal
122	ExprTuple	123
123	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 ¶