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, Lambda, b
from proveit.logic import And, Bijections, InSet, Set, SetOfAll
from proveit.numbers import one, zero
from proveit.physics.quantum import QubitSpace, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import qubit_meas

# build up the expression from sub-expressions
sub_expr1 = Set(zero, one)
expr = Lambda(var_ket_psi, Conditional(InSet(Lambda(b, qubit_meas), Bijections(sub_expr1, SetOfAll(instance_param_or_params = [b], instance_element = qubit_meas, domain = sub_expr1))).with_wrapping_at(2), And(InSet(var_ket_psi, QubitSpace), normalized_var_ket_psi)))

# 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())

\lvert \psi \rangle \mapsto \left\{\begin{array}{c} \begin{array}{l} \left[b \mapsto \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right)\right] \in  \\ \left[\left\{0, 1\right\} \xrightarrow[\text{onto}]{\text{1-to-1}} \left\{\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right\}_{b \in \left\{0, 1\right\}}\right] \end{array} \end{array} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2} ,  \left \|\lvert \psi \rangle\right \| = 1\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameter: 52 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 33 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Lambda	parameter: 57 body: 29
8	Operation	operator: 11 operands: 12
9	Operation	operator: 33 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	38, 16
13	ExprTuple	52, 17
14	Literal
15	ExprTuple	18, 51
16	Operation	operator: 19 operand: 25
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operand: 52
19	Literal
20	ExprTuple	25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	52
25	Lambda	parameter: 57 body: 28
26	Literal
27	Literal
28	Conditional	value: 29 condition: 30
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operands: 34
31	Literal
32	ExprTuple	35, 36, 37
33	Literal
34	ExprTuple	57, 38
35	ExprTuple	39
36	ExprTuple	40
37	ExprTuple	41
38	Operation	operator: 42 operands: 43
39	Operation	operator: 44 operands: 45
40	Operation	operator: 46 operands: 47
41	Operation	operator: 48 operands: 49
42	Literal
43	ExprTuple	50, 51
44	Literal
45	NamedExprs	state: 52
46	Literal
47	NamedExprs	basis: 53
48	Literal
49	NamedExprs	state: 54
50	Literal
51	Literal
52	Variable
53	Literal
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Variable

Expression of type Lambda¶

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

Expression of type Lambda ¶

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