# 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.
# import Expression classes needed to build the expression
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, two
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _two_pow_t

In [2]:
# build up the expression from sub-expressions
expr = InSet(TensorProd(_Psi_ket, _ket_u), TensorProd(CartExp(Complex, _two_pow_t), CartExp(Complex, Exp(two, _s))))

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(\lvert \Psi \rangle {\otimes} \lvert u \rangle\right) \in \left(\mathbb{C}^{2^{t}} {\otimes} \mathbb{C}^{2^{s}}\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Literal
9Literal
10Operationoperator: 13
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple16, 15
13Literal
14ExprTuple16, 17
15Operationoperator: 19
operands: 18
16Literal
17Operationoperator: 19
operands: 20
18ExprTuple22, 21
19Literal
20ExprTuple22, 23
21Literal
22Literal
23Literal