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BraAndKet-0.8.2
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BraAndKet is a library for numeral calculations of discrete quantum systems.
| ویژگی | مقدار |
|---|---|
| سیستم عامل | - |
| نام فایل | BraAndKet-0.8.2 |
| نام | BraAndKet |
| نسخه کتابخانه | 0.8.2 |
| نگهدارنده | [] |
| ایمیل نگهدارنده | [] |
| نویسنده | - |
| ایمیل نویسنده | Zheng Keli <zhengkeli2009@126.com> |
| آدرس صفحه اصلی | - |
| آدرس اینترنتی | https://pypi.org/project/BraAndKet/ |
| مجوز | - |
# BraAndKet
[](https://github.com/ZhengKeli/BraAndKet/blob/master/LICENSE)
BraAndKet is a library for numeral calculations of discrete quantum systems.
# Quickstart
## Before Using
Please notice that this library is still actively developing. The stability and compatibility of APIs are **NOT**
guaranteed. Breaking changes are happening every day! Using this library right now, you may take your own risk.
## Installation
You can install the latest release from [PiPy](https://pypi.org/project/BraAndKet/).
```shell
pip install braandket
```
Then you can import this library with name `bnk`
```python
import braandket as bnk
```
## KetSpace
Any quantum states can exist in some space called _Hilbert space_. You can use `bnk.KetSpace(n)` to define such a space,
where `n` is its dimension. For example, to create a Hilbert space of a q-bit:
```python
qbit = bnk.KetSpace(2)
print(qbit) # output: KetSpace(2)
```
You can define a name for a space using named parameter. The name is to describe this space when debugging. The name can
be a `str`, or any object to be printed out. When printed, the name of space will be shown, which is very helpful when
debugging.
```python
qbit_a = bnk.KetSpace(2, name="a")
print(qbit_a) # output: KetSpace(2, name=a)
qbit_b = bnk.KetSpace(2, name="b")
print(qbit_b) # output: KetSpace(2, name=b)
```
You can call these 4 methods on a `KetSpace` instance to create ket vectors and operators:
* method `.eigenstate(k)` - to get a ket vector, representing the k-th
eigenstate 
* method `.identity()` - to get an identity operator  in this Hilbert space
* method `.operator(k,b)` - to get an operator 
* method `.projector(k)` - to get a projector 
```python
ket_space = bnk.KetSpace(2)
ket_vec = ket_space.eigenstate(0)
identity_op = ket_space.identity()
increase_op = ket_space.operator(1, 0)
zero_proj = ket_space.projector(0)
```
A `KetSpace` is accompanied by a `BraSpace`. You can conveniently get it with `.ct` property. To avoid confusion, is not
allowed to create any vectors or operations with a `BraSpace`. Please do so with its corresponding `KetSpace`.
Calling `.ct` property, you can get back its `KetSpace`.
```python
ket_space = bnk.KetSpace(2)
print(ket_space) # output: KetSpace(2)
bra_space = ket_space.ct
print(bra_space) # output: BraSpace(2)
print(bra_space.ct is ket_space) # output: True
```
## QTensors
`QTensor` is the basic type of computing elements in this library. A `QTensor` instance holds an `np.ndarray` as its
values and a tuple of `Space` instances. Each `Space` corresponds to an axis of the `np.ndarray`.
Any vectors, operators and tensors in quantum world are represented by `QTensor`. All vectors and operators mentioned
above are all `QTensor` instances.
```python
ket_space = bnk.KetSpace(2)
ket_vec = ket_space.eigenstate(0)
print(ket_vec)
# output: QTensor(spaces=(KetSpace(2),), values=[1. 0.])
identity_op = ket_space.identity()
print(identity_op)
# output: QTensor(spaces=(KetSpace(2), BraSpace(2)), values=[[1. 0.] [0. 1.]])
increase_op = ket_space.operator(1, 0)
print(increase_op)
# output: QTensor(spaces=(KetSpace(2), BraSpace(2)), values=[[0. 0.] [1. 0.]])
zero_proj = ket_space.projector(0)
print(zero_proj)
# output: QTensor(spaces=(KetSpace(2), BraSpace(2)), values=[[1. 0.] [0. 0.]])
```
You can easily get a conjugate transposed `QTensor` calling `.ct` property. It should be noted that sometimes, such
operation does not affect the values, but spaces.
```python
ket_space = bnk.KetSpace(2)
ket_vec = ket_space.eigenstate(0)
bra_vec = ket_vec.ct
print(bra_vec)
# output: QTensor(spaces=(BraSpace(2),), values=[1. 0.])
increase_op = ket_space.operator(1, 0)
decrease_op = increase_op.ct
print(decrease_op)
# output: QTensor(spaces=(BraSpace(2), KetSpace(2)), values=[[0. 0.] [1. 0.]])
```
`QTensor` instances can take tensor product using `@` operator. They can automatically inspect which spaces to be
performed the "product-sum" (when the bra on the left meets the matching ket on the right), which to be remained.
### Example1:
```python
qbit = bnk.KetSpace(2)
amp = qbit.eigenstate(0).ct @ qbit.eigenstate(1)
print(amp)
# output: QTensor(spaces=(), values=0.0)
```
### Example2:
```python
qbit_a = bnk.KetSpace(2, name="a")
qbit_b = bnk.KetSpace(2, name="b")
ket_vec_ab = qbit_a.eigenstate(0) @ qbit_b.eigenstate(1)
print(ket_vec_ab)
# output: QTensor(spaces=(KetSpace(2, name=a), KetSpace(2, name=b)), values=[[0. 1.] [0. 0.]])
```
### Example3:
```python
qbit_a = bnk.KetSpace(2, name="a")
qbit_b = bnk.KetSpace(2, name="b")
tensor_ab = qbit_a.eigenstate(0).ct @ qbit_b.eigenstate(1)
print(tensor_ab)
# output: QTensor(spaces=(BraSpace(2, name=a), KetSpace(2, name=b)), values=[[0. 1.] [0. 0.]])
```
### Example4:
```python
qbit = bnk.KetSpace(2)
ket_vec_0 = qbit.eigenstate(0)
ket_vec_1 = qbit.eigenstate(1)
increase_op = qbit.operator(1, 0)
result = increase_op @ ket_vec_0
print(result)
# output: QTensor(spaces=(KetSpace(2),), values=[0. 1.])
print(result == ket_vec_1)
# output: True
```
# Contribution
This library is completely open source. Any contributions are welcomed. You can fork this repository, make some useful
changes and then send a pull request to me on GitHub.
نیازمندی
| مقدار | نام |
|---|---|
| - | numpy |
| - | tensorflow |
زبان مورد نیاز
| مقدار | نام |
|---|---|
| >=3.8 | Python |
نحوه نصب
نصب پکیج whl BraAndKet-0.8.2:
pip install BraAndKet-0.8.2.whl
نصب پکیج tar.gz BraAndKet-0.8.2:
pip install BraAndKet-0.8.2.tar.gz