U
    L?h                     @   s  d Z ddlmZ ddlmZmZmZ ddlmZ ddl	m
Z
 ddlmZ ddlmZ ddlmZ dd	lmZmZ dd
lmZ ddlmZ ddlmZmZmZmZmZmZmZm Z  ddl!m"Z" ddddgZ#G dd deZ$e$Z%G dd deZ&G dd de&Z'G dd de&Z(dS )at  An implementation of qubits and gates acting on them.

Todo:

* Update docstrings.
* Update tests.
* Implement apply using decompose.
* Implement represent using decompose or something smarter. For this to
  work we first have to implement represent for SWAP.
* Decide if we want upper index to be inclusive in the constructor.
* Fix the printing of Rk gates in plotting.
    )Expr)IIntegerpiSymbol)exp)Matrixsqrt)qapply)QuantumErrorQExpr)eye)matrix_tensor_product)GateHadamardGateSwapGateOneQubitGateCGate	PhaseGateTGateZGate)signQFTIQFTRkGateRkc                   @   sZ   e Zd ZdZdZdZdd Zedd Ze	dd	 Z
e	d
d Ze	dd ZdddZdS )r   z This is the R_k gate of the QTF.r   Rc                 G   s   t |dkrtd| |d }|d }|dkr8t|S |dkrHt|S |dkrXt|S | |}tj| f| }| ||_	|S )N   z)Rk gates only take two arguments, got: %rr         )
lenr   r   r   r   
_eval_argsr   __new__Z_eval_hilbert_spaceZhilbert_space)clsargstargetkinst r*   K/var/www/html/venv/lib/python3.8/site-packages/sympy/physics/quantum/qft.pyr$   1   s     
zRkGate.__new__c                 C   s
   t |S N)r   r#   )r%   r&   r*   r*   r+   r#   F   s    zRkGate._eval_argsc                 C   s
   | j d S Nr    labelselfr*   r*   r+   r(   L   s    zRkGate.kc                 C   s   | j d d S r-   r.   r0   r*   r*   r+   targetsP   s    zRkGate.targetsc                 C   s   d| j t| jf S )Nz$%s_%s$)gate_name_latexstrr(   r0   r*   r*   r+   gate_name_plotT   s    zRkGate.gate_name_plotsympyc                 C   sX   |dkrHt ddgdtt| jtd t t tdt| j  ggS td| d S )Nr6   r    r   r   z#Invalid format for the R_k gate: %r)	r	   r   r   r(   r   r   r   absNotImplementedError)r1   formatr*   r*   r+   get_target_matrixX   s
    @zRkGate.get_target_matrixN)r6   )__name__
__module____qualname____doc__	gate_namer3   r$   classmethodr#   propertyr(   r2   r5   r:   r*   r*   r*   r+   r   ,   s   



c                   @   s\   e Zd ZdZedd Zdd Zdd Zedd	 Z	ed
d Z
edd Zedd ZdS )Fourierz@Superclass of Quantum Fourier and Inverse Quantum Fourier Gates.c                 C   s:   t |dkrtd| |d |d kr0tdt|S )Nr   z*QFT/IQFT only takes two arguments, got: %rr   r    z!Start must be smaller than finish)r"   r   r   r#   )r1   r&   r*   r*   r+   r#   e   s    zFourier._eval_argsc                 K   s   | j d|S )N)N)_represent_ZGate)r1   optionsr*   r*   r+   _represent_default_basiso   s    z Fourier._represent_default_basisc                    s   | dd}|dkrtd|| jk r2td| | j| j  fddtD }t|}| jd dkrtt	d| jd  |}| j|k rt|t	d|| j  }|S )z:
            Represents the (I)QFT In the Z Basis
        nqubitsr   z.The number of qubits must be given as nqubits.z2The number of qubits %r is too small for the gate.c                    s&   g | ]  fd dt D qS )c                    s$   g | ]}|    t  qS r*   r
   ).0i)jomegasizer*   r+   
<listcomp>   s   
z7Fourier._represent_ZGate.<locals>.<listcomp>.<listcomp>)range)rG   rJ   rK   )rI   r+   rL      s   z,Fourier._represent_ZGate.<locals>.<listcomp>r   )
getr   
min_qubitsrK   rJ   rM   r	   r/   r   r   )r1   ZbasisrD   rF   ZarrayFTZmatrixFTr*   rN   r+   rC   r   s.    

 zFourier._represent_ZGatec                 C   s   t | jd | jd S )Nr   r    )rM   r/   r0   r*   r*   r+   r2      s    zFourier.targetsc                 C   s
   | j d S r-   r.   r0   r*   r*   r+   rP      s    zFourier.min_qubitsc                 C   s   d| j d | j d   S )z"Size is the size of the QFT matrixr   r    r   r.   r0   r*   r*   r+   rK      s    zFourier.sizec                 C   s   t dS )NrJ   r   r0   r*   r*   r+   rJ      s    zFourier.omegaN)r;   r<   r=   r>   r@   r#   rE   rC   rA   r2   rP   rK   rJ   r*   r*   r*   r+   rB   b   s   
	


rB   c                   @   s<   e Zd ZdZd Zd Zdd Zdd Zdd Ze	dd	 Z
d
S )r   z&The forward quantum Fourier transform.c                 C   s   | j d }| j d }d}tt||D ]B}t|| }t|| D ]$}t|| d t||d | }qBq&t|| d D ]}t|| || d | }qz|S )z%Decomposes QFT into elementary gates.r   r    r   )r/   reversedrM   r   r   r   r   )r1   startfinishcircuitlevelrH   r*   r*   r+   	decompose   s    

$zQFT.decomposec                 K   s   t |  | S r,   )r   rV   )r1   ZqubitsrD   r*   r*   r+   _apply_operator_Qubit   s    zQFT._apply_operator_Qubitc                 C   s
   t | j S r,   )r   r&   r0   r*   r*   r+   _eval_inverse   s    zQFT._eval_inversec                 C   s   t dt t | j S )Nr   r   r   r   rK   r0   r*   r*   r+   rJ      s    z	QFT.omegaN)r;   r<   r=   r>   r?   r3   rV   rW   rX   rA   rJ   r*   r*   r*   r+   r      s   c                   @   s4   e Zd ZdZd ZdZdd Zdd Zedd Z	d	S )
r   z&The inverse quantum Fourier transform.z
{QFT^{-1}}c                 C   s   | j d }| j d }d}t|| d D ]}t|| || d | }q(t||D ]H}tt|| D ]&}t|| d t|| d | }qft|| }qR|S )z&Decomposes IQFT into elementary gates.r   r    r   )r&   rM   r   rQ   r   r   r   )r1   rR   rS   rT   rH   rU   r*   r*   r+   rV      s    

$zIQFT.decomposec                 C   s
   t | j S r,   )r   r&   r0   r*   r*   r+   rX      s    zIQFT._eval_inversec                 C   s   t dt t | j S )NrY   r0   r*   r*   r+   rJ      s    z
IQFT.omegaN)
r;   r<   r=   r>   r?   r3   rV   rX   rA   rJ   r*   r*   r*   r+   r      s   N))r>   Zsympy.core.exprr   Zsympy.core.numbersr   r   r   Zsympy.core.symbolr   Z&sympy.functions.elementary.exponentialr   Zsympy.matrices.denser	   Zsympy.functionsr   Zsympy.physics.quantum.qapplyr   Zsympy.physics.quantum.qexprr   r   Zsympy.matricesr   Z#sympy.physics.quantum.tensorproductr   Zsympy.physics.quantum.gater   r   r   r   r   r   r   r   Z$sympy.functions.elementary.complexesr   __all__r   r   rB   r   r   r*   r*   r*   r+   <module>   s,   (3?