logo

Expression of type Mult

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.numbers import Exp, Mult, e, frac, i, one, 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 = Mult(frac(one, Exp(two, frac(_t, two))), 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)))
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())
\frac{1}{2^{\frac{t}{2}}} \cdot \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 [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',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 43
operands: 1
1ExprTuple2, 3
2Operationoperator: 21
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple59, 7
5Literal
6ExprTuple8, 9, 10
7Operationoperator: 53
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 14
operand: 58
10Operationoperator: 16
operand: 20
11ExprTuple57, 18
12Literal
13ExprTuple19, 58
14Literal
15ExprTuple58
16Literal
17ExprTuple20
18Operationoperator: 21
operands: 22
19Variable
20Lambdaparameter: 50
body: 24
21Literal
22ExprTuple58, 57
23ExprTuple50
24Conditionalvalue: 25
condition: 26
25Operationoperator: 27
operands: 28
26Operationoperator: 29
operands: 30
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple50, 33
31Operationoperator: 53
operands: 34
32Operationoperator: 35
operands: 36
33Operationoperator: 37
operands: 38
34ExprTuple39, 40
35Literal
36ExprTuple50, 58
37Literal
38ExprTuple41, 42
39Literal
40Operationoperator: 43
operands: 44
41Literal
42Operationoperator: 45
operands: 46
43Literal
44ExprTuple57, 47, 48, 49, 50
45Literal
46ExprTuple51, 52
47Literal
48Literal
49Literal
50Variable
51Operationoperator: 53
operands: 54
52Operationoperator: 55
operand: 59
53Literal
54ExprTuple57, 58
55Literal
56ExprTuple59
57Literal
58Literal
59Literal