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Expression of type InClass

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 k, m
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import InClass
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult, QmultCodomain
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t
In [2]:
# build up the expression from sub-expressions
expr = InClass(Qmult(NumBra(m, _t), InverseFourierTransform(_t), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)), domain = _m_domain)), QmultCodomain)
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())
\left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Literal
5Literal
6ExprTuple7, 8, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operand: 53
9Operationoperator: 14
operand: 17
10Literal
11ExprTuple16, 53
12Literal
13ExprTuple53
14Literal
15ExprTuple17
16Variable
17Lambdaparameter: 45
body: 19
18ExprTuple45
19Conditionalvalue: 20
condition: 21
20Operationoperator: 22
operands: 23
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple26, 27
24Literal
25ExprTuple45, 28
26Operationoperator: 48
operands: 29
27Operationoperator: 30
operands: 31
28Operationoperator: 32
operands: 33
29ExprTuple34, 35
30Literal
31ExprTuple45, 53
32Literal
33ExprTuple36, 37
34Literal
35Operationoperator: 38
operands: 39
36Literal
37Operationoperator: 40
operands: 41
38Literal
39ExprTuple52, 42, 43, 44, 45
40Literal
41ExprTuple46, 47
42Literal
43Literal
44Literal
45Variable
46Operationoperator: 48
operands: 49
47Operationoperator: 50
operand: 54
48Literal
49ExprTuple52, 53
50Literal
51ExprTuple54
52Literal
53Literal
54Literal