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, m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import NumKet, Z
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _s_wire, _t
from proveit.physics.quantum.circuits import Input, Measure, MultiQubitElem, Output, Qcircuit

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(_Psi_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2)), one, sub_expr2)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(m, _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = Interval(Add(_t, one), sub_expr2)), one, _s)]))

expr:

# 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())

QCIRCUIT\left(VertExprArray\left(\begin{array}{c} \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{\lvert \Psi \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}\right),  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array}, ..\left(t - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \meter 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}, ..\left(s - 3\right) \times.., \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array}\right),  \\ \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert m \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right) \end{array}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
spacing	change the spacing of a circuit using the format '@C=1em @R=.7em' where C is the column spacing and R is the row spacing	@C=1em @R=.7em	@C=1em @R=.7em

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	ExprTuple	6
4	ExprTuple	7, 8
5	ExprTuple	9, 10
6	ExprRange	lambda_map: 11 start_index: 62 end_index: 51
7	ExprRange	lambda_map: 12 start_index: 62 end_index: 63
8	ExprRange	lambda_map: 13 start_index: 62 end_index: 64
9	ExprRange	lambda_map: 14 start_index: 62 end_index: 63
10	ExprRange	lambda_map: 15 start_index: 62 end_index: 64
11	Lambda	parameter: 49 body: 16
12	Lambda	parameter: 49 body: 17
13	Lambda	parameter: 49 body: 18
14	Lambda	parameter: 49 body: 19
15	Lambda	parameter: 49 body: 21
16	Operation	operator: 28 operands: 22
17	Operation	operator: 23 operands: 24
18	Operation	operator: 25 operands: 26
19	Operation	operator: 28 operands: 27
20	ExprTuple	49
21	Operation	operator: 28 operands: 29
22	NamedExprs	element: 30 targets: 31
23	Literal
24	NamedExprs	basis: 32
25	Literal
26	NamedExprs	operation: 33
27	NamedExprs	element: 34 targets: 35
28	Literal
29	NamedExprs	element: 36 targets: 37
30	Operation	operator: 38 operands: 39
31	Operation	operator: 45 operands: 40
32	Literal
33	Literal
34	Operation	operator: 43 operands: 41
35	Operation	operator: 45 operands: 42
36	Operation	operator: 43 operands: 44
37	Operation	operator: 45 operands: 46
38	Literal
39	NamedExprs	state: 47 part: 49
40	ExprTuple	62, 51
41	NamedExprs	state: 48 part: 49
42	ExprTuple	62, 63
43	Literal
44	NamedExprs	state: 60 part: 49
45	Literal
46	ExprTuple	50, 51
47	Operation	operator: 52 operands: 53
48	Operation	operator: 54 operands: 55
49	Variable
50	Operation	operator: 57 operands: 56
51	Operation	operator: 57 operands: 58
52	Literal
53	ExprTuple	59, 60
54	Literal
55	ExprTuple	61, 63
56	ExprTuple	63, 62
57	Literal
58	ExprTuple	63, 64
59	Literal
60	Literal
61	Variable
62	Literal
63	Literal
64	Literal