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}")
expr = Qcircuit(vert_expr_array = VertExprArray([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 = Interval(Add(t, one), Add(t, _s))), one, _s)]))

# 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^{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}

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
4	ExprRange	lambda_map: 6 start_index: 7 end_index: 46
5	ExprRange	lambda_map: 8 start_index: 56 end_index: 40
6	Lambda	parameter: 69 body: 9
7	Operation	operator: 34 operands: 10
8	Lambda	parameter: 69 body: 11
9	Operation	operator: 21 operands: 12
10	ExprTuple	13, 56
11	Operation	operator: 14 operands: 15
12	NamedExprs	state: 16
13	Operation	operator: 67 operand: 39
14	Literal
15	NamedExprs	element: 18 targets: 19
16	Operation	operator: 43 operands: 20
17	ExprTuple	39
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	25, 26
21	Literal
22	NamedExprs	state: 27 part: 69
23	Literal
24	ExprTuple	28, 29
25	Operation	operator: 49 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	ExprTuple	56, 36
31	Literal
32	ExprTuple	37, 38
33	ExprTuple	39, 56
34	Literal
35	ExprTuple	39, 40
36	Operation	operator: 63 operands: 41
37	Operation	operator: 52 operand: 46
38	Operation	operator: 43 operands: 44
39	Variable
40	Literal
41	ExprTuple	65, 45
42	ExprTuple	46
43	Literal
44	ExprTuple	47, 48
45	Operation	operator: 49 operands: 50
46	Literal
47	Operation	operator: 63 operands: 51
48	Operation	operator: 52 operand: 56
49	Literal
50	ExprTuple	56, 65
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56
54	Literal
55	Operation	operator: 57 operands: 58
56	Literal
57	Literal
58	ExprTuple	65, 59, 60, 61, 62
59	Literal
60	Literal
61	Operation	operator: 63 operands: 64
62	Literal
63	Literal
64	ExprTuple	65, 66
65	Literal
66	Operation	operator: 67 operand: 69
67	Literal
68	ExprTuple	69
69	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 ¶