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, 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 = Lambda([var_ket_psi, b], 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(\lvert \psi \rangle, b\right) \mapsto \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	Lambda	parameters: 1 body: 2
1	ExprTuple	57, 63
2	Conditional	value: 3 condition: 4
3	Operation	operator: 20 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 13 operand: 22
9	Operation	operator: 15 operands: 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 20 operands: 21
13	Literal
14	ExprTuple	22
15	Literal
16	ExprTuple	23, 42
17	ExprTuple	57, 24
18	Literal
19	ExprTuple	63, 25
20	Literal
21	ExprTuple	26, 44
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operand: 40
24	Operation	operator: 31 operands: 32
25	Operation	operator: 33 operands: 34
26	Operation	operator: 35 operand: 57
27	Literal
28	ExprTuple	37, 38, 39
29	Literal
30	ExprTuple	40
31	Literal
32	ExprTuple	41, 42
33	Literal
34	ExprTuple	43, 44
35	Literal
36	ExprTuple	57
37	ExprTuple	45
38	ExprTuple	46
39	ExprTuple	47
40	Operation	operator: 48 operands: 49
41	Literal
42	Literal
43	Literal
44	Literal
45	Operation	operator: 50 operands: 51
46	Operation	operator: 52 operands: 53
47	Operation	operator: 54 operands: 55
48	Literal
49	ExprTuple	56, 57
50	Literal
51	NamedExprs	state: 57
52	Literal
53	NamedExprs	basis: 58
54	Literal
55	NamedExprs	state: 59
56	Operation	operator: 60 operand: 63
57	Variable
58	Literal
59	Operation	operator: 61 operand: 63
60	Literal
61	Literal
62	ExprTuple	63
63	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 ¶