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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, 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 = 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))
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 \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)
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: 4
operands: 1
1ExprTuple2, 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operand: 11
4Literal
5ExprTuple8, 9, 10
6Literal
7ExprTuple11
8Operationoperator: 12
operands: 13
9Operationoperator: 32
operands: 14
10Operationoperator: 15
operand: 58
11Lambdaparameter: 50
body: 18
12Literal
13ExprTuple19, 58
14ExprTuple59, 20
15Literal
16ExprTuple58
17ExprTuple50
18Conditionalvalue: 21
condition: 22
19Variable
20Operationoperator: 53
operands: 23
21Operationoperator: 24
operands: 25
22Operationoperator: 26
operands: 27
23ExprTuple57, 28
24Literal
25ExprTuple29, 30
26Literal
27ExprTuple50, 31
28Operationoperator: 32
operands: 33
29Operationoperator: 53
operands: 34
30Operationoperator: 35
operands: 36
31Operationoperator: 37
operands: 38
32Literal
33ExprTuple58, 57
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