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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 k
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _m_domain, _phase, _t, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = InSet(VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)), domain = _m_domain), CartExp(Complex, _two_pow_t))
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(\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 \mathbb{C}^{2^{t}}
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: 16
operands: 1
1ExprTuple2, 3
2Operationoperator: 4
operand: 8
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8
6Literal
7ExprTuple9, 38
8Lambdaparameter: 37
body: 11
9Literal
10ExprTuple37
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18, 19
16Literal
17ExprTuple37, 20
18Operationoperator: 40
operands: 21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21ExprTuple26, 27
22Literal
23ExprTuple37, 45
24Literal
25ExprTuple28, 29
26Literal
27Operationoperator: 30
operands: 31
28Literal
29Operationoperator: 32
operands: 33
30Literal
31ExprTuple44, 34, 35, 36, 37
32Literal
33ExprTuple38, 39
34Literal
35Literal
36Literal
37Variable
38Operationoperator: 40
operands: 41
39Operationoperator: 42
operand: 46
40Literal
41ExprTuple44, 45
42Literal
43ExprTuple46
44Literal
45Literal
46Literal