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Expression of type Lambda

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 Conditional, Lambda, k, t
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), InSet(k, Interval(zero, subtract(two_pow_t, one)))))
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())
k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 28
body: 2
1ExprTuple28
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple28, 11
9Operationoperator: 31
operands: 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operands: 16
12ExprTuple17, 18
13Literal
14ExprTuple28, 36
15Literal
16ExprTuple19, 20
17Literal
18Operationoperator: 21
operands: 22
19Literal
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple35, 25, 26, 27, 28
23Literal
24ExprTuple29, 30
25Literal
26Literal
27Literal
28Variable
29Operationoperator: 31
operands: 32
30Operationoperator: 33
operand: 37
31Literal
32ExprTuple35, 36
33Literal
34ExprTuple37
35Literal
36Variable
37Literal