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Expression of type InSet

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 InSet
from proveit.numbers import Complex, Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
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 = InSet(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)), Complex)
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) \in \mathbb{C}
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: 25
operands: 1
1ExprTuple2, 3
2Operationoperator: 7
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operand: 13
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operand: 54
13Lambdaparameter: 46
body: 19
14Literal
15ExprTuple20, 54
16Literal
17ExprTuple54
18ExprTuple46
19Conditionalvalue: 21
condition: 22
20Variable
21Operationoperator: 23
operands: 24
22Operationoperator: 25
operands: 26
23Literal
24ExprTuple27, 28
25Literal
26ExprTuple46, 29
27Operationoperator: 49
operands: 30
28Operationoperator: 31
operands: 32
29Operationoperator: 33
operands: 34
30ExprTuple35, 36
31Literal
32ExprTuple46, 54
33Literal
34ExprTuple37, 38
35Literal
36Operationoperator: 39
operands: 40
37Literal
38Operationoperator: 41
operands: 42
39Literal
40ExprTuple53, 43, 44, 45, 46
41Literal
42ExprTuple47, 48
43Literal
44Literal
45Literal
46Variable
47Operationoperator: 49
operands: 50
48Operationoperator: 51
operand: 55
49Literal
50ExprTuple53, 54
51Literal
52ExprTuple55
53Literal
54Literal
55Literal