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
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import I
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _psi__t_ket, _s, _t
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 = Interval(one, _t)
sub_expr3 = Interval(Add(_t, one), Add(_t, _s))
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _psi__t_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr3), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = InverseFourierTransform(_t), part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, _s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _Psi_ket, part = sub_expr1), targets = sub_expr2), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr3), 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{
\qin{\lvert \psi_{t} \rangle} & \gate{{\mathrm {FT}}^{\dag}_{t}} & \qout{\lvert \Psi \rangle} \\
\qin{\lvert u \rangle} & { /^{s} } \qw & \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	ExprRange	lambda_map: 12 start_index: 63 end_index: 64
7	ExprRange	lambda_map: 13 start_index: 63 end_index: 65
8	ExprRange	lambda_map: 14 start_index: 63 end_index: 64
9	ExprRange	lambda_map: 15 start_index: 63 end_index: 65
10	ExprRange	lambda_map: 16 start_index: 63 end_index: 64
11	ExprRange	lambda_map: 17 start_index: 63 end_index: 65
12	Lambda	parameter: 54 body: 18
13	Lambda	parameter: 54 body: 19
14	Lambda	parameter: 54 body: 20
15	Lambda	parameter: 54 body: 21
16	Lambda	parameter: 54 body: 22
17	Lambda	parameter: 54 body: 24
18	Operation	operator: 30 operands: 25
19	Operation	operator: 30 operands: 26
20	Operation	operator: 30 operands: 27
21	Operation	operator: 42 operands: 28
22	Operation	operator: 30 operands: 29
23	ExprTuple	54
24	Operation	operator: 30 operands: 31
25	NamedExprs	element: 32 targets: 37
26	NamedExprs	element: 33 targets: 39
27	NamedExprs	element: 34 targets: 37
28	NamedExprs	operation: 35
29	NamedExprs	element: 36 targets: 37
30	Literal
31	NamedExprs	element: 38 targets: 39
32	Operation	operator: 41 operands: 40
33	Operation	operator: 41 operands: 47
34	Operation	operator: 42 operands: 43
35	Literal
36	Operation	operator: 46 operands: 44
37	Operation	operator: 48 operands: 45
38	Operation	operator: 46 operands: 47
39	Operation	operator: 48 operands: 49
40	NamedExprs	state: 50 part: 54
41	Literal
42	Literal
43	NamedExprs	operation: 51 part: 54
44	NamedExprs	state: 52 part: 54
45	ExprTuple	63, 64
46	Literal
47	NamedExprs	state: 53 part: 54
48	Literal
49	ExprTuple	55, 56
50	Operation	operator: 57 operand: 64
51	Operation	operator: 58 operand: 64
52	Literal
53	Literal
54	Variable
55	Operation	operator: 61 operands: 60
56	Operation	operator: 61 operands: 62
57	Literal
58	Literal
59	ExprTuple	64
60	ExprTuple	64, 63
61	Literal
62	ExprTuple	64, 65
63	Literal
64	Literal
65	Literal

Expression of type Qcircuit¶

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

Expression of type Qcircuit ¶

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