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, zero
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(Add(zero, 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}~\{0 + 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: 51
7	Literal
8	ExprTuple	10, 51
9	Operation	operator: 23 operands: 11
10	Operation	operator: 48 operands: 12
11	ExprTuple	13, 14
12	ExprTuple	26, 51
13	Operation	operator: 29 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	51, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 42 operands: 21
19	Operation	operator: 32 operand: 26
20	Operation	operator: 23 operands: 24
21	ExprTuple	44, 25
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 29 operands: 30
26	Literal
27	Operation	operator: 42 operands: 31
28	Operation	operator: 32 operand: 51
29	Literal
30	ExprTuple	51, 44
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	51
34	Literal
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	44, 38, 39, 40, 41
38	Literal
39	Literal
40	Operation	operator: 42 operands: 43
41	Literal
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 52 operand: 47
46	ExprTuple	47
47	Operation	operator: 48 operands: 49
48	Literal
49	ExprTuple	50, 51
50	Operation	operator: 52 operand: 54
51	Literal
52	Literal
53	ExprTuple	54
54	Variable