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Expression of type Qcircuit

from the theory of proveit.physics.quantum.QPE

In [1]:
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, Literal, Variable, VertExprArray
from proveit.numbers import Add, Exp, Interval, Mod, Mult, Round, one, two
from proveit.physics.quantum import I, NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import QPE
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Literal("t", theory = "proveit.physics.quantum.QPE"), one)
sub_expr3 = Add(Literal("t", theory = "proveit.physics.quantum.QPE"), Literal("s", theory = "proveit.physics.quantum.QPE"))
sub_expr4 = Exp(two, Literal("t", theory = "proveit.physics.quantum.QPE"))
sub_expr5 = Interval(sub_expr2, sub_expr3)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE(Literal("U", theory = "proveit.physics.quantum.QPE"), Literal("t", theory = "proveit.physics.quantum.QPE")), part = sub_expr1), targets = Interval(one, sub_expr3))
expr = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = Literal("|u>", latex_format = r"\lvert u \rangle", theory = "proveit.physics.quantum.QPE"), part = sub_expr1), targets = sub_expr5), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, sub_expr6, one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, sub_expr6, sub_expr2, sub_expr3)], [ExprRange(sub_expr1, Measure(basis = Z), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, Literal("s", theory = "proveit.physics.quantum.QPE"))], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(sub_expr4, Literal("phase", latex_format = r"\varphi", theory = "proveit.physics.quantum.QPE"))), sub_expr4), Literal("t", theory = "proveit.physics.quantum.QPE")), part = sub_expr1), targets = Interval(one, Literal("t", theory = "proveit.physics.quantum.QPE"))), one, Literal("t", theory = "proveit.physics.quantum.QPE")), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = Literal("|u>", latex_format = r"\lvert u \rangle", theory = "proveit.physics.quantum.QPE"), part = sub_expr1), targets = sub_expr5), one, Literal("s", theory = "proveit.physics.quantum.QPE"))]))
expr:
In [3]:
# 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
In [4]:
# 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 + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
spacingchange 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
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5, 6
3ExprTuple7, 8
4ExprTuple9, 10
5ExprTuple11, 12
6ExprTuple13, 14
7ExprRangelambda_map: 15
start_index: 77
end_index: 92
8ExprRangelambda_map: 16
start_index: 77
end_index: 78
9ExprRangelambda_map: 17
start_index: 77
end_index: 92
10ExprRangelambda_map: 17
start_index: 66
end_index: 67
11ExprRangelambda_map: 18
start_index: 77
end_index: 92
12ExprRangelambda_map: 19
start_index: 77
end_index: 78
13ExprRangelambda_map: 20
start_index: 77
end_index: 92
14ExprRangelambda_map: 21
start_index: 77
end_index: 78
15Lambdaparameter: 65
body: 22
16Lambdaparameter: 65
body: 23
17Lambdaparameter: 65
body: 24
18Lambdaparameter: 65
body: 25
19Lambdaparameter: 65
body: 26
20Lambdaparameter: 65
body: 27
21Lambdaparameter: 65
body: 29
22Operationoperator: 51
operands: 30
23Operationoperator: 37
operands: 31
24Operationoperator: 37
operands: 32
25Operationoperator: 33
operands: 34
26Operationoperator: 52
operands: 35
27Operationoperator: 37
operands: 36
28ExprTuple65
29Operationoperator: 37
operands: 38
30NamedExprsstate: 39
31NamedExprselement: 40
targets: 48
32NamedExprselement: 41
targets: 42
33Literal
34NamedExprsbasis: 43
35NamedExprsoperation: 44
36NamedExprselement: 45
targets: 46
37Literal
38NamedExprselement: 47
targets: 48
39Operationoperator: 49
operand: 61
40Operationoperator: 51
operands: 58
41Operationoperator: 52
operands: 53
42Operationoperator: 59
operands: 54
43Literal
44Literal
45Operationoperator: 57
operands: 55
46Operationoperator: 59
operands: 56
47Operationoperator: 57
operands: 58
48Operationoperator: 59
operands: 60
49Literal
50ExprTuple61
51Literal
52Literal
53NamedExprsoperation: 62
part: 65
54ExprTuple77, 67
55NamedExprsstate: 63
part: 65
56ExprTuple77, 92
57Literal
58NamedExprsstate: 64
part: 65
59Literal
60ExprTuple66, 67
61Literal
62Operationoperator: 68
operands: 69
63Operationoperator: 70
operands: 71
64Literal
65Variable
66Operationoperator: 73
operands: 72
67Operationoperator: 73
operands: 74
68Literal
69ExprTuple75, 92
70Literal
71ExprTuple76, 92
72ExprTuple92, 77
73Literal
74ExprTuple92, 78
75Literal
76Operationoperator: 79
operands: 80
77Literal
78Literal
79Literal
80ExprTuple81, 87
81Operationoperator: 82
operand: 84
82Literal
83ExprTuple84
84Operationoperator: 85
operands: 86
85Literal
86ExprTuple87, 88
87Operationoperator: 89
operands: 90
88Literal
89Literal
90ExprTuple91, 92
91Literal
92Literal