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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(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({_{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) \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: 23
operands: 1
1ExprTuple2, 3
2Operationoperator: 4
operands: 5
3Literal
4Literal
5ExprTuple6, 7, 8
6Operationoperator: 9
operands: 10
7Operationoperator: 11
operand: 52
8Operationoperator: 13
operand: 16
9Literal
10ExprTuple15, 52
11Literal
12ExprTuple52
13Literal
14ExprTuple16
15Variable
16Lambdaparameter: 44
body: 18
17ExprTuple44
18Conditionalvalue: 19
condition: 20
19Operationoperator: 21
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple44, 27
25Operationoperator: 47
operands: 28
26Operationoperator: 29
operands: 30
27Operationoperator: 31
operands: 32
28ExprTuple33, 34
29Literal
30ExprTuple44, 52
31Literal
32ExprTuple35, 36
33Literal
34Operationoperator: 37
operands: 38
35Literal
36Operationoperator: 39
operands: 40
37Literal
38ExprTuple51, 41, 42, 43, 44
39Literal
40ExprTuple45, 46
41Literal
42Literal
43Literal
44Variable
45Operationoperator: 47
operands: 48
46Operationoperator: 49
operand: 53
47Literal
48ExprTuple51, 52
49Literal
50ExprTuple53
51Literal
52Literal
53Literal