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 t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, 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 = Interval(one, one))

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}~\{1~\ldotp \ldotp~1\}} 
} \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	Operation	operator: 7 operands: 8
5	Literal
6	NamedExprs	state: 9 part: 49
7	Literal
8	ExprTuple	49, 49
9	Operation	operator: 21 operands: 10
10	ExprTuple	11, 12
11	Operation	operator: 27 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	49, 16
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 40 operands: 19
17	Operation	operator: 30 operand: 24
18	Operation	operator: 21 operands: 22
19	ExprTuple	42, 23
20	ExprTuple	24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Operation	operator: 40 operands: 29
26	Operation	operator: 30 operand: 49
27	Literal
28	ExprTuple	49, 42
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	49
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	42, 36, 37, 38, 39
36	Literal
37	Literal
38	Operation	operator: 40 operands: 41
39	Literal
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 50 operand: 45
44	ExprTuple	45
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Operation	operator: 50 operand: 52
49	Literal
50	Literal
51	ExprTuple	52
52	Variable