https://github.com/refraction-ray/qop

manipulation on second quantization operators
https://github.com/refraction-ray/qop

algebra quantum

Last synced: about 2 months ago
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manipulation on second quantization operators

• Host: GitHub
• URL: https://github.com/refraction-ray/qop
• Owner: refraction-ray
• License: mit
• Created: 2020-05-27T03:37:24.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2020-05-31T03:32:43.000Z (over 4 years ago)
• Last Synced: 2024-07-04T22:58:03.375Z (3 months ago)
• Topics: algebra, quantum
• Language: Python
• Size: 89.8 KB
• Stars: 3
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# QOP

*Make quantum operators and algebras native in python*

Behold, the power of qop.

* Boson

```python

from qop.boson import *

assert (b0.D*b0)**3 == b0.D*b0+3*b0.D**2*b0**2+b0.D**3*b0**3

```

* Fermion

```python

from qop.fermion import *

assert (c0.D*c0)**3 == c0.D*c0

```

* Hardcore Boson

```python

from qop.hardcoreboson import *

assert (hb0.D*hb0)**2 ==hb0.D*hb0

assert hb0*hb1 == hb1*hb0

```

* Spin

```python

from qop.spin import *

assert s0.x*s0.y == 1j/2*s0.z

assert s0.z*s1.x == -2j*s1.x*s0.x*s0.y

```

* Grassmann numbers

```python

from qop.grassmann import *

assert (1+g(0)*g(1))**2 == 1+2*g(0)*g(1)

```

* Quaternion numbers

```python

from qop.quaternion import *

assert (1-qi)/(1-qj) == 0.5*(1-qi+qj-qk)

```

* Symbols

```python

from qop.symbol import *

a = Symbol("a")

assert np.conj(2+a).evaluate({"a": 1j}) == 2-1j

```

* Quantum states

```python

from qop.fermion import *

from qop.state import *

assert Sf("1").D | c1.D * c1 | c1.D | Sf() == 1.0

```

And mix all, we have

```python

U = Symbol("U")

assert Sf("12").D | U * (np.array([c1.D, c2.D]) @ np.array([c1, c2])) ** 2 | Sf("12") == 4 * U

```

Or einsum with opt_einsum

```python

from qop.base import *

from qop.symbol import *

from opt_einsum import contract

a,b,c,d = Symbols("abcd")

simplify(contract("ijk,i->jk", d*np.ones([3,3,3]), np.array([a,b,c]), backend="qop"))

```

See more examples in tests.