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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, 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 = Qmult(NumBra(m, _t), Qmult(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())
{_{t}}\langle m \rvert \thinspace \left({\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: 6
operands: 1
1ExprTuple2, 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 51
6Literal
7ExprTuple9, 10
8Variable
9Operationoperator: 11
operand: 51
10Operationoperator: 13
operand: 15
11Literal
12ExprTuple51
13Literal
14ExprTuple15
15Lambdaparameter: 43
body: 17
16ExprTuple43
17Conditionalvalue: 18
condition: 19
18Operationoperator: 20
operands: 21
19Operationoperator: 22
operands: 23
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple43, 26
24Operationoperator: 46
operands: 27
25Operationoperator: 28
operands: 29
26Operationoperator: 30
operands: 31
27ExprTuple32, 33
28Literal
29ExprTuple43, 51
30Literal
31ExprTuple34, 35
32Literal
33Operationoperator: 36
operands: 37
34Literal
35Operationoperator: 38
operands: 39
36Literal
37ExprTuple50, 40, 41, 42, 43
38Literal
39ExprTuple44, 45
40Literal
41Literal
42Literal
43Variable
44Operationoperator: 46
operands: 47
45Operationoperator: 48
operand: 52
46Literal
47ExprTuple50, 51
48Literal
49ExprTuple52
50Literal
51Literal
52Literal