Expression of type Conditional ¶

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, b
from proveit.logic import And, Equals, InSet, Set
from proveit.numbers import Abs, Exp, one, two, zero
from proveit.physics.quantum import Bra, Qmult, QubitSpace, normalized_var_ket_psi, var_ket_psi
from proveit.physics.quantum.circuits import qubit_meas
from proveit.statistics import Prob

# build up the expression from sub-expressions
expr = Conditional(Equals(Prob(qubit_meas), Exp(Abs(Qmult(Bra(b), var_ket_psi)), two)), And(InSet(var_ket_psi, QubitSpace), InSet(b, Set(zero, one)), 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())

\left\{\textrm{Pr}\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert \psi \rangle} & \meter & \qout{\lvert b \rangle}
} \end{array}\right) = \left|\langle b \rvert \thinspace \lvert \psi \rangle\right|^{2} \textrm{ if } \lvert \psi \rangle \in \mathbb{C}^{2} ,  b \in \left\{0, 1\right\} ,  \left \|\lvert \psi \rangle\right \| = 1\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 18 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 11 operand: 20
7	Operation	operator: 13 operands: 14
8	Operation	operator: 16 operands: 15
9	Operation	operator: 16 operands: 17
10	Operation	operator: 18 operands: 19
11	Literal
12	ExprTuple	20
13	Literal
14	ExprTuple	21, 40
15	ExprTuple	55, 22
16	Literal
17	ExprTuple	61, 23
18	Literal
19	ExprTuple	24, 42
20	Operation	operator: 25 operands: 26
21	Operation	operator: 27 operand: 38
22	Operation	operator: 29 operands: 30
23	Operation	operator: 31 operands: 32
24	Operation	operator: 33 operand: 55
25	Literal
26	ExprTuple	35, 36, 37
27	Literal
28	ExprTuple	38
29	Literal
30	ExprTuple	39, 40
31	Literal
32	ExprTuple	41, 42
33	Literal
34	ExprTuple	55
35	ExprTuple	43
36	ExprTuple	44
37	ExprTuple	45
38	Operation	operator: 46 operands: 47
39	Literal
40	Literal
41	Literal
42	Literal
43	Operation	operator: 48 operands: 49
44	Operation	operator: 50 operands: 51
45	Operation	operator: 52 operands: 53
46	Literal
47	ExprTuple	54, 55
48	Literal
49	NamedExprs	state: 55
50	Literal
51	NamedExprs	basis: 56
52	Literal
53	NamedExprs	state: 57
54	Operation	operator: 58 operand: 61
55	Variable
56	Literal
57	Operation	operator: 59 operand: 61
58	Literal
59	Literal
60	ExprTuple	61
61	Variable

Expression of type Conditional¶

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

Expression of type Conditional ¶

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