Expression of type Qcircuit

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, 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, _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))
expr = Qcircuit(vert_expr_array = VertExprArray([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)], [ExprRange(sub_expr1, sub_expr5, one, t), ExprRange(sub_expr1, sub_expr5, sub_expr2, sub_expr3)], [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:

# 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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
spacing	change the spacing of a circuit using the format '@C=1em @R=.7em' where C is the column spacing and R is the row spacing	@C=1em @R=.7em	@C=1em @R=.7em

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	ExprTuple	6, 7
4	ExprTuple	8, 9
5	ExprTuple	10, 11
6	ExprRange	lambda_map: 12 start_index: 85 end_index: 68
7	ExprRange	lambda_map: 13 start_index: 85 end_index: 69
8	ExprRange	lambda_map: 14 start_index: 85 end_index: 68
9	ExprRange	lambda_map: 14 start_index: 54 end_index: 55
10	ExprRange	lambda_map: 15 start_index: 16 end_index: 75
11	ExprRange	lambda_map: 17 start_index: 85 end_index: 69
12	Lambda	parameter: 98 body: 18
13	Lambda	parameter: 98 body: 19
14	Lambda	parameter: 98 body: 20
15	Lambda	parameter: 98 body: 21
16	Operation	operator: 62 operands: 22
17	Lambda	parameter: 98 body: 23
18	Operation	operator: 40 operands: 24
19	Operation	operator: 29 operands: 25
20	Operation	operator: 29 operands: 26
21	Operation	operator: 45 operands: 27
22	ExprTuple	28, 85
23	Operation	operator: 29 operands: 30
24	NamedExprs	state: 31
25	NamedExprs	element: 32 targets: 38
26	NamedExprs	element: 33 targets: 34
27	NamedExprs	state: 35
28	Operation	operator: 96 operand: 68
29	Literal
30	NamedExprs	element: 37 targets: 38
31	Operation	operator: 81 operand: 49
32	Operation	operator: 40 operands: 46
33	Operation	operator: 41 operands: 42
34	Operation	operator: 47 operands: 43
35	Operation	operator: 72 operands: 44
36	ExprTuple	68
37	Operation	operator: 45 operands: 46
38	Operation	operator: 47 operands: 48
39	ExprTuple	49
40	Literal
41	Literal
42	NamedExprs	operation: 50 part: 98
43	ExprTuple	85, 55
44	ExprTuple	51, 52
45	Literal
46	NamedExprs	state: 53 part: 98
47	Literal
48	ExprTuple	54, 55
49	Literal
50	Operation	operator: 56 operands: 57
51	Operation	operator: 78 operands: 58
52	Operation	operator: 59 operands: 60
53	Literal
54	Operation	operator: 62 operands: 61
55	Operation	operator: 62 operands: 63
56	Literal
57	ExprTuple	64, 68
58	ExprTuple	85, 65
59	Literal
60	ExprTuple	66, 67
61	ExprTuple	68, 85
62	Literal
63	ExprTuple	68, 69
64	Literal
65	Operation	operator: 92 operands: 70
66	Operation	operator: 81 operand: 75
67	Operation	operator: 72 operands: 73
68	Variable
69	Literal
70	ExprTuple	94, 74
71	ExprTuple	75
72	Literal
73	ExprTuple	76, 77
74	Operation	operator: 78 operands: 79
75	Literal
76	Operation	operator: 92 operands: 80
77	Operation	operator: 81 operand: 85
78	Literal
79	ExprTuple	85, 94
80	ExprTuple	83, 84
81	Literal
82	ExprTuple	85
83	Literal
84	Operation	operator: 86 operands: 87
85	Literal
86	Literal
87	ExprTuple	94, 88, 89, 90, 91
88	Literal
89	Literal
90	Operation	operator: 92 operands: 93
91	Literal
92	Literal
93	ExprTuple	94, 95
94	Literal
95	Operation	operator: 96 operand: 98
96	Literal
97	ExprTuple	98
98	Variable