Expression of type Lambda ¶

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

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 Conditional, ConditionalSet, ExprRange, IndexedVar, Lambda, U, Variable, m, t
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum import CONTROL, I
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(t, one)
expr = Lambda(sub_expr1, [ExprRange(sub_expr2, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr1, sub_expr2)), Conditional(Gate(operation = I).with_implicit_representation(), NotEquals(sub_expr1, sub_expr2))), one, t).with_case_simplification(), ExprRange(sub_expr2, MultiQubitElem(element = Gate(operation = IndexedVar(U, sub_expr1), part = sub_expr2), targets = Interval(sub_expr3, Add(t, m))), one, m)])

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

{_{-}b} \mapsto \left(\left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } {_{-}b} = 1 \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } {_{-}b} \neq 1\end{array}\right.., \left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } {_{-}b} = 2 \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } {_{-}b} \neq 2\end{array}\right.., \ldots, \left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } {_{-}b} = t \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } {_{-}b} \neq t\end{array}\right..,\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{{_{-}b}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{{_{-}b}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U_{{_{-}b}}~\mbox{part}~m~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} & \qw 
} \end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 41 body: 1
1	ExprTuple	2, 3
2	ExprRange	lambda_map: 4 start_index: 47 end_index: 46
3	ExprRange	lambda_map: 5 start_index: 47 end_index: 42
4	Lambda	parameter: 35 body: 6
5	Lambda	parameter: 35 body: 8
6	Operation	operator: 9 operands: 10
7	ExprTuple	35
8	Operation	operator: 23 operands: 11
9	Literal
10	ExprTuple	12, 13
11	NamedExprs	element: 14 targets: 15
12	Conditional	value: 16 condition: 17
13	Conditional	value: 18 condition: 19
14	Operation	operator: 26 operands: 20
15	Operation	operator: 21 operands: 22
16	Operation	operator: 23 operands: 24
17	Operation	operator: 25 operands: 29
18	Operation	operator: 26 operands: 27
19	Operation	operator: 28 operands: 29
20	NamedExprs	operation: 30 part: 35
21	Literal
22	ExprTuple	43, 31
23	Literal
24	NamedExprs	element: 32 targets: 33
25	Literal
26	Literal
27	NamedExprs	operation: 34
28	Literal
29	ExprTuple	41, 35
30	IndexedVar	variable: 36 index: 41
31	Operation	operator: 44 operands: 38
32	Literal
33	Operation	operator: 39 operand: 43
34	Literal
35	Variable
36	Variable
37	ExprTuple	41
38	ExprTuple	46, 42
39	Literal
40	ExprTuple	43
41	Variable
42	Variable
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Literal

Expression of type Lambda¶

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

Expression of type Lambda ¶

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