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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(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(\left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t}\right) \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: 8
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operand: 14
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operand: 55
14Lambdaparameter: 47
body: 20
15Literal
16ExprTuple21, 55
17Literal
18ExprTuple55
19ExprTuple47
20Conditionalvalue: 22
condition: 23
21Variable
22Operationoperator: 24
operands: 25
23Operationoperator: 26
operands: 27
24Literal
25ExprTuple28, 29
26Literal
27ExprTuple47, 30
28Operationoperator: 50
operands: 31
29Operationoperator: 32
operands: 33
30Operationoperator: 34
operands: 35
31ExprTuple36, 37
32Literal
33ExprTuple47, 55
34Literal
35ExprTuple38, 39
36Literal
37Operationoperator: 40
operands: 41
38Literal
39Operationoperator: 42
operands: 43
40Literal
41ExprTuple54, 44, 45, 46, 47
42Literal
43ExprTuple48, 49
44Literal
45Literal
46Literal
47Variable
48Operationoperator: 50
operands: 51
49Operationoperator: 52
operand: 56
50Literal
51ExprTuple54, 55
52Literal
53ExprTuple56
54Literal
55Literal
56Literal