Expression of type QcircuitEquiv ¶

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, TensorProd, 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, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output, Qcircuit, QcircuitEquiv

# 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 = Add(Neg(t), one)
sub_expr5 = TensorProd(_psi_t_ket, _ket_u)
sub_expr6 = Interval(one, sub_expr3)
expr = QcircuitEquiv(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)))), sub_expr4, zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr2, sub_expr3)), one, _s).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = Add(sub_expr1, t)), targets = sub_expr6), sub_expr4, zero), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = sub_expr1), targets = sub_expr6), sub_expr2, sub_expr3).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())

\left(\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}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multiqout{1}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \qout{\vdots} \qwx[1] \\
& \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} \qwx[1] \\
& \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}}
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

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

Expression of type QcircuitEquiv¶

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

Expression of type QcircuitEquiv ¶

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