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Expression of type Equals

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.linalg import MatrixProd, ScalarProd
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import U_, phase_, u_
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Ket(u_)
expr = Equals(MatrixProd(U_, sub_expr1), ScalarProd(Exp(e, Mult(two, pi, i, phase_)), sub_expr1))
Out[2]:
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(expr.latex())
\left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \thinspace \lvert u \rangle\right)
In [5]:
expr.style_options()
Out[5]:
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', '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
expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 11
7Literal
8ExprTuple10, 11
9Literal
10Operationoperator: 12
operands: 13
11Operationoperator: 14
operand: 18
12Literal
13ExprTuple16, 17
14Literal
15ExprTuple18
16Literal
17Operationoperator: 19
operands: 20
18Literal
19Literal
20ExprTuple21, 22, 23, 24
21Literal
22Literal
23Literal
24Literal