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
from proveit.physics.quantum.QPE import _ket_u, _phase, _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 = frac(one, sqrt(two))
expr = Qcircuit(vert_expr_array = VertExprArray([Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1)))), ExprRange(sub_expr1, Output(state = ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1)))), Add(sub_expr2, two), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, _s))), one, _s).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())

\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^{-\left(-t + 1\right)} \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{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 3} \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}

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Qcircuit¶

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

Expression of type Qcircuit ¶

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