logo

Expression of type And

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 U
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, IntervalCO, Mult, Real, e, i, one, pi, two, zero
from proveit.physics.quantum import var_ket_u
from proveit.physics.quantum.QPE import phase
In [2]:
# build up the expression from sub-expressions
expr = And(InSet(phase, Real), InSet(phase, IntervalCO(zero, one)), Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u)))
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(\varphi \in \mathbb{R}\right) \land \left(\varphi \in \left[0,1\right)\right) \land \left(\left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\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: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3Operationoperator: 7
operands: 6
4Operationoperator: 7
operands: 8
5Operationoperator: 9
operands: 10
6ExprTuple35, 11
7Literal
8ExprTuple35, 12
9Literal
10ExprTuple13, 14
11Literal
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14Operationoperator: 19
operands: 20
15Literal
16ExprTuple21, 22
17Literal
18ExprTuple23, 25
19Literal
20ExprTuple24, 25
21Literal
22Literal
23Variable
24Operationoperator: 26
operands: 27
25Variable
26Literal
27ExprTuple28, 29
28Literal
29Operationoperator: 30
operands: 31
30Literal
31ExprTuple32, 33, 34, 35
32Literal
33Literal
34Literal
35Variable