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Expression of type Qmult

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
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, two
from proveit.physics.quantum import 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 = Qmult(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))
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}}} \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)
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: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3Operationoperator: 19
operands: 6
4Operationoperator: 7
operand: 52
5Operationoperator: 9
operand: 12
6ExprTuple53, 11
7Literal
8ExprTuple52
9Literal
10ExprTuple12
11Operationoperator: 47
operands: 13
12Lambdaparameter: 44
body: 15
13ExprTuple51, 16
14ExprTuple44
15Conditionalvalue: 17
condition: 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Operationoperator: 23
operands: 24
19Literal
20ExprTuple52, 51
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