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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, frac, i, one, 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), frac(one, Exp(two, frac(_t, two))), 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 \frac{1}{2^{\frac{t}{2}}} \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: 15
8Literal
9ExprTuple12, 13, 14
10Literal
11ExprTuple15
12Operationoperator: 16
operands: 17
13Operationoperator: 36
operands: 18
14Operationoperator: 19
operand: 62
15Lambdaparameter: 54
body: 22
16Literal
17ExprTuple23, 62
18ExprTuple63, 24
19Literal
20ExprTuple62
21ExprTuple54
22Conditionalvalue: 25
condition: 26
23Variable
24Operationoperator: 57
operands: 27
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operands: 31
27ExprTuple61, 32
28Literal
29ExprTuple33, 34
30Literal
31ExprTuple54, 35
32Operationoperator: 36
operands: 37
33Operationoperator: 57
operands: 38
34Operationoperator: 39
operands: 40
35Operationoperator: 41
operands: 42
36Literal
37ExprTuple62, 61
38ExprTuple43, 44
39Literal
40ExprTuple54, 62
41Literal
42ExprTuple45, 46
43Literal
44Operationoperator: 47
operands: 48
45Literal
46Operationoperator: 49
operands: 50
47Literal
48ExprTuple61, 51, 52, 53, 54
49Literal
50ExprTuple55, 56
51Literal
52Literal
53Literal
54Variable
55Operationoperator: 57
operands: 58
56Operationoperator: 59
operand: 63
57Literal
58ExprTuple61, 62
59Literal
60ExprTuple63
61Literal
62Literal
63Literal