# from the theory of proveit.physics.quantum.circuits¶

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 import A, B, S, k
from proveit.logic import Forall, NotEquals
from proveit.numbers import NaturalPos
from proveit.physics.quantum.circuits import MultiQubitElem, Output

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [k], instance_expr = Forall(instance_param_or_params = [A, B, S], instance_expr = NotEquals(MultiQubitElem(element = Output(state = A, part = k), targets = S), MultiQubitElem(element = Output(state = B, part = k), targets = S)), condition = NotEquals(A, B)), domain = NaturalPos)

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())

\forall_{k \in \mathbb{N}^+}~\left[\forall_{A, B, S~|~A \neq B}~\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{A~\mbox{part}~k~\mbox{on}~S}
} \end{array} \neq \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{B~\mbox{part}~k~\mbox{on}~S}
} \end{array}\right)\right]

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 33
body: 4
3ExprTuple33
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple33, 12
11Lambdaparameters: 13
body: 14
12Literal
13ExprTuple31, 32, 27
14Conditionalvalue: 15
condition: 16
15Operationoperator: 18
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 21
18Literal
19ExprTuple31, 32
20Operationoperator: 23
operands: 22
21Operationoperator: 23
operands: 24
22NamedExprselement: 25
targets: 27
23Literal
24NamedExprselement: 26
targets: 27
25Operationoperator: 29
operands: 28
26Operationoperator: 29
operands: 30
27Variable