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 = Neg(t)
sub_expr3 = Add(t, one)
sub_expr4 = Add(t, _s)
sub_expr5 = TensorProd(_psi_t_ket, _ket_u)
sub_expr6 = Interval(one, sub_expr4)
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)))), Add(sub_expr2, one), zero).with_decreasing_order(), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(sub_expr3, sub_expr4)), one, _s).with_wrapping_at(2,6)])), Qcircuit(vert_expr_array = VertExprArray([MultiQubitElem(element = Output(state = sub_expr5, part = one), targets = sub_expr6), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = Add(sub_expr1, t)), targets = sub_expr6), Add(sub_expr2, two), zero), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr5, part = sub_expr1), targets = sub_expr6), sub_expr3, sub_expr4).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{2}{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle} \\
& \ghostqout{\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, 14
10	ExprRange	lambda_map: 15 start_index: 16 end_index: 78
11	ExprRange	lambda_map: 17 start_index: 89 end_index: 70
12	Operation	operator: 34 operands: 18
13	ExprRange	lambda_map: 19 start_index: 20 end_index: 78
14	ExprRange	lambda_map: 21 start_index: 52 end_index: 55
15	Lambda	parameter: 102 body: 22
16	Operation	operator: 63 operands: 23
17	Lambda	parameter: 102 body: 24
18	NamedExprs	element: 25 targets: 41
19	Lambda	parameter: 102 body: 26
20	Operation	operator: 63 operands: 27
21	Lambda	parameter: 102 body: 28
22	Operation	operator: 46 operands: 29
23	ExprTuple	33, 89
24	Operation	operator: 34 operands: 30
25	Operation	operator: 46 operands: 31
26	Operation	operator: 34 operands: 32
27	ExprTuple	33, 98
28	Operation	operator: 34 operands: 35
29	NamedExprs	state: 36
30	NamedExprs	element: 37 targets: 38
31	NamedExprs	state: 54 part: 89
32	NamedExprs	element: 39 targets: 41
33	Operation	operator: 100 operand: 81
34	Literal
35	NamedExprs	element: 40 targets: 41
36	Operation	operator: 73 operands: 42
37	Operation	operator: 46 operands: 43
38	Operation	operator: 48 operands: 44
39	Operation	operator: 46 operands: 45
40	Operation	operator: 46 operands: 47
41	Operation	operator: 48 operands: 49
42	ExprTuple	50, 51
43	NamedExprs	state: 69 part: 102
44	ExprTuple	52, 55
45	NamedExprs	state: 54 part: 53
46	Literal
47	NamedExprs	state: 54 part: 102
48	Literal
49	ExprTuple	89, 55
50	Operation	operator: 82 operands: 56
51	Operation	operator: 57 operands: 58
52	Operation	operator: 63 operands: 59
53	Operation	operator: 63 operands: 60
54	Operation	operator: 61 operands: 62
55	Operation	operator: 63 operands: 64
56	ExprTuple	89, 65
57	Literal
58	ExprTuple	66, 67
59	ExprTuple	81, 89
60	ExprTuple	102, 81
61	Literal
62	ExprTuple	68, 69
63	Literal
64	ExprTuple	81, 70
65	Operation	operator: 96 operands: 71
66	Operation	operator: 85 operand: 78
67	Operation	operator: 73 operands: 74
68	Operation	operator: 75 operand: 81
69	Literal
70	Literal
71	ExprTuple	98, 77
72	ExprTuple	78
73	Literal
74	ExprTuple	79, 80
75	Literal
76	ExprTuple	81
77	Operation	operator: 82 operands: 83
78	Literal
79	Operation	operator: 96 operands: 84
80	Operation	operator: 85 operand: 89
81	Variable
82	Literal
83	ExprTuple	89, 98
84	ExprTuple	87, 88
85	Literal
86	ExprTuple	89
87	Literal
88	Operation	operator: 90 operands: 91
89	Literal
90	Literal
91	ExprTuple	98, 92, 93, 94, 95
92	Literal
93	Literal
94	Operation	operator: 96 operands: 97
95	Literal
96	Literal
97	ExprTuple	98, 99
98	Literal
99	Operation	operator: 100 operand: 102
100	Literal
101	ExprTuple	102
102	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 ¶