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, Conditional, S, k
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos
from proveit.physics.quantum.circuits import MultiQubitElem, Output

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

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

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple30, 8
7Lambdaparameters: 9
body: 10
8Literal
9ExprTuple28, 29, 24
10Operationoperator: 15
operands: 11
11ExprTuple12, 13
12Operationoperator: 15
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple17, 18
15Literal
16ExprTuple28, 29
17Operationoperator: 20
operands: 19
18Operationoperator: 20
operands: 21
19NamedExprselement: 22
targets: 24
20Literal
21NamedExprselement: 23
targets: 24
22Operationoperator: 26
operands: 25
23Operationoperator: 26
operands: 27
24Variable