Expression of type MultiQubitElem

from the theory of proveit.physics.quantum.QPE

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 Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
expr = MultiQubitElem(element = Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1))), part = one), targets = Variable("_a", latex_format = r"{_{-}a}"))

expr:

# 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())

\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)~\mbox{part}~1~\mbox{on}~{_{-}a}} 
} \end{array}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	NamedExprs	element: 3 targets: 4
3	Operation	operator: 5 operands: 6
4	Variable
5	Literal
6	NamedExprs	state: 7 part: 47
7	Operation	operator: 19 operands: 8
8	ExprTuple	9, 10
9	Operation	operator: 25 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	47, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 38 operands: 17
15	Operation	operator: 28 operand: 22
16	Operation	operator: 19 operands: 20
17	ExprTuple	40, 21
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Operation	operator: 38 operands: 27
24	Operation	operator: 28 operand: 47
25	Literal
26	ExprTuple	47, 40
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	47
30	Literal
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	40, 34, 35, 36, 37
34	Literal
35	Literal
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 48 operand: 43
42	ExprTuple	43
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Operation	operator: 48 operand: 50
47	Literal
48	Literal
49	ExprTuple	50
50	Variable