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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 m
from proveit.linear_algebra import LinMap
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, frac, one, two
from proveit.physics.quantum import NumBra, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _t, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = InSet(Qmult(Qmult(NumBra(m, _t), frac(one, Exp(two, frac(_t, two))), InverseFourierTransform(_t))), LinMap(CartExp(Complex, _two_pow_t), 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 \frac{1}{2^{\frac{t}{2}}} \thinspace {\mathrm {FT}}^{\dag}_{t}\right] \in \mathcal{L}\left(\mathbb{C}^{2^{t}}, \mathbb{C}\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',)
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: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 10
operand: 8
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 17
8Operationoperator: 10
operands: 11
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14, 15, 16
12Literal
13ExprTuple17, 18
14Operationoperator: 19
operands: 20
15Operationoperator: 31
operands: 21
16Operationoperator: 22
operand: 33
17Literal
18Operationoperator: 28
operands: 24
19Literal
20ExprTuple25, 33
21ExprTuple26, 27
22Literal
23ExprTuple33
24ExprTuple34, 33
25Variable
26Literal
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple34, 30
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Literal
34Literal