Expression of type Qcircuit ¶

from the theory of proveit.physics.quantum.circuits ¶

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, U, Variable, VertExprArray, m
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Set
from proveit.numbers import Add, Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import CONTROL, ket0, ket1, ket_plus, var_ket_u, varphi
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(m, one)
sub_expr3 = Interval(two, Add(m, two))
expr = Qcircuit(vert_expr_array = VertExprArray([Input(state = ket_plus), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr3), one, sub_expr2)], [MultiQubitElem(element = CONTROL, targets = Set(two)), ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = U, part = sub_expr1), targets = sub_expr3), one, sub_expr2)], [Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, varphi)), ket1)))), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = sub_expr3), one, sub_expr2)]))

# 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} & \control{} \qw \qwx[1] & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)} \\
\qin{\lvert u \rangle} & \gate{U} & \qout{\lvert u \rangle}
} \end{array}

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Qcircuit¶

from the theory of proveit.physics.quantum.circuits¶

Expression of type Qcircuit ¶

from the theory of proveit.physics.quantum.circuits ¶